Patent Publication Number: US-11033848-B2

Title: Honeycomb filter

Description:
The present application is an application based on JP 2017-095954 filed on May 12, 2017 with Japan Patent Office, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a honeycomb filter, and more particularly, it relates to a honeycomb filter which is capable of effectively inhibiting leakage of particulate matter such as soot and inhibiting rise of pressure loss. 
     Description of the Related Art 
     In various industries, internal combustion engines are used as power sources. On the other hand, exhaust gases emitted from the internal combustion engines during combustion of fuel include particulate matter such as soot or ash. For example, regulations on removal of the particulate matter to be emitted from a diesel engine have become stricter worldwide, and as a filter to remove the particulate matter, a honeycomb filter having a honeycomb structure is used. Hereinafter, the particulate matter will occasionally be referred to as “PM”. The PM is an abbreviation for “the particulate matter”. 
     Heretofore, as the honeycomb filter to remove the PM, there has been suggested a honeycomb filter including a honeycomb structure body having porous partition walls which define a plurality of cells, and a plugging portion to plug either one of end portions of each of the cells. 
     Such a honeycomb filter has a structure in which the porous partition walls perform a function of a filter which removes the PM. Specifically, when an exhaust gas containing the PM flows into an inflow end face of the honeycomb filter, the PM is trapped by the porous partition walls to filter the exhaust gas, and then the purified exhaust gas is emitted from an outflow end face of the honeycomb filter. In this way, the PM in the exhaust gas can be removed. 
     In the honeycomb filter, a shape of the cells defined by the partition walls has variously been studied, and there has been suggested, for example, a honeycomb filter in which cells opened on an inflow end face side (hereinafter occasionally referred to as “inflow cells”) are formed in an octagonal shape, or the like. Furthermore, there has been studied a technology of increasing the number of the inflow cells to be larger than the number of cells opened on an outflow end face side (hereinafter occasionally referred to as “outflow cells”), thereby inhibiting rise of pressure loss, or the like. 
     Additionally, as to the honeycomb filter, arrangement of plugging portions to plug open ends of the cells has also variously been studied. For example, a honeycomb filter has been suggested in which eight inflow cells are arranged to surround a periphery of one outflow cell (e.g., see Patent Document 1). 
     In addition, as the honeycomb filter, there has been suggested a technology of forming the outflow cells so that regions corresponding to corner portions in a rectangular shape or a more polygonal shape are circularly formed (e.g., see Patent Document 2). In the honeycomb filter described in Patent Document 2, it is explained that the above constitution is employed, thereby increasing a heat capacity of the honeycomb filter, so that temperature rise during regeneration can be decreased. 
     [Patent Document 1] JP-A-2016-52635 
     [Patent Document 2] JP-A-2010-221159 
     SUMMARY OF THE INVENTION 
     In such a honeycomb filter as described in Patent Document 1, particulate matter such as soot is easily deposited on corner portions of inflow cells, and during actual use, cracks and the like are generated in the corner portions of the inflow cells, thereby causing the problem that the soot and the like leak out from corner portions of outflow cells. 
     Furthermore, in such a honeycomb filter as described in Patent Document 2, regions corresponding to corner portions of outflow cells are only formed in a circular shape, and hence, there is the problem that cracks and the like are easily generated among inflow cells. 
     Additionally, in the honeycomb filter to trap and remove PM included in an exhaust gas, the PM is trapped by porous partition walls, thereby increasing its pressure loss. In recent years, it has been an important problem to inhibit rise of the pressure loss of the honeycomb filter, and there has been an increasing demand for development of a honeycomb filter which is capable of effectively inhibiting leakage of particulate matter such as soot and inhibiting rise of pressure loss. 
     The present invention has been developed in view of such problems of conventional technologies. According to the present invention, there is provided a honeycomb filter which is capable of effectively inhibiting leakage of particulate matter such as soot and inhibiting rise of pressure loss. In particular, there is provided a honeycomb filter which is capable of effectively inhibiting rise of pressure loss when particulate matter such as ash is deposited on the surfaces of partition walls. 
     According to the present invention, there is provided a honeycomb filter as follows. 
     According to a first aspect of the present invention, a honeycomb filter is provided including: 
     a honeycomb structure body having porous partition walls arranged to surround a plurality of cells extending from an inflow end face to an outflow end face to form through channels for a fluid, and 
     a plugging portion disposed to plug either one of end portions of each of the cells on the side of the inflow end face or the side of the outflow end face, 
     wherein among the plurality of cells, the cells in which the plugging portions are arranged in end portions on the outflow end face side and which are opened on the inflow end face side are defined as inflow cells, and the cells in which the plugging portions are arranged in end portions on the inflow end face side and which are opened on the outflow end face side are defined as outflow cells, 
     the honeycomb structure body has a plurality of cell rows in which two or more cells are arranged along one direction, in a cross section of the honeycomb structure body which is perpendicular to an extending direction of the cells, 
     the plurality of cell rows include a first cell row and a second cell row, 
     the first cell row is a cell row having a constitution in which the cells arranged along the one direction include at least the inflow cells and in which in the cross section perpendicular to the extending direction of the cells, a through channel area SA occupied by the inflow cells is larger than a through channel area SB occupied by the outflow cells, 
     the second cell row is a cell row in which the cells arranged along the one direction include at least the outflow cells, 
     in the cross section perpendicular to the extending direction of the cells, each of the cells has a polygonal shape of which corner portions are formed in a curved shape of a curvature radius R, and 
     a width P 1  (mm) of the first cell row, a width P 2  (mm) of the second cell row and the curvature radius R (μm) satisfy a relation of Equation (1) mentioned below:
 
0.4≤( R/ 1000)/(( P 1+ P 2)/2)×100≤20.  Equation (1):
 
     According to a second aspect of the present invention, the honeycomb filter according to the above first aspect is provided, wherein the width P 1  (mm) of the first cell row and the width P 2  (mm) of the second cell row satisfy a relation of Equation (2) mentioned below:
 
2≤100−( P 2/ P 1×100)≤50.  Equation (2):
 
     According to a third aspect of the present invention, the honeycomb filter according to the above first or second aspects is provided, wherein an average value of the width P 1  of the first cell row and the width P 2  of the second cell row is from 0.7 to 3.5 mm. 
     According to a fourth aspect of the present invention, the honeycomb filter according to any one of the above first to third aspects is provided, wherein the width P 1  of the first cell row is from 0.7 to 4.0 mm. 
     According to a fifth aspect of the present invention, the honeycomb filter according to any one of the above first to fourth aspects is provided, wherein the width P 2  of the second cell row is from 0.7 to 2.7 mm. 
     According to a sixth aspect of the present invention, the honeycomb filter according to any one of the above first to fifth aspects is provided, wherein in the first cell row, the through channel area SA occupied by the inflow cells is 1.1 times or more as large as the through channel area SB occupied by the outflow cells in the cross section perpendicular to the extending direction of the cells. 
     According to a seventh aspect of the present invention, the honeycomb filter according to any one of the above first to fifth aspects is provided, wherein the first cell row is a cell row constituted of the inflow cells. 
     According to an eighth aspect of the present invention, the honeycomb filter according to any one of the above first to seventh aspects is provided, wherein in the cross section perpendicular to the extending direction of the cells, a ratio N2/N1 of the number N2 of the second cell rows to the number N1 of the first cell rows is from 1/4 to 4.0. 
     According to a ninth aspect of the present invention, the honeycomb filter according to any one of the above first to eighth aspects is provided, wherein the second cell row is a cell row in which the inflow cells and the outflow cells are mixed. 
     According to a tenth aspect of the present invention, the honeycomb filter according to any one of the above first to eighth aspects is provided, wherein the second cell row is a cell row constituted of the outflow cells. 
     According to an eleventh aspect of the present invention, the honeycomb filter according to any one of the above first to tenth aspects is provided, wherein in the cross section perpendicular to the extending direction of the cells, the first cell rows are arranged on both sides of the second cell row, respectively. 
     According to a twelfth aspect of the present invention, the honeycomb filter according to the above eleventh aspect is provided, wherein in the cross section perpendicular to the extending direction of the cells, the first cell rows and the second cell rows are alternately arranged in a direction perpendicular to the respective rows. 
     According to a thirteenth aspect of the present invention, the honeycomb filter according to any one of the above first to twelfth aspects is provided, which has two or more regions having different constitutions of the cell row in the cross section perpendicular to the extending direction of the cells, wherein the honeycomb structure body is present in at least a part of the region. 
     According to a fourteenth aspect of the present invention, the honeycomb filter according to any one of the above first to twelfth aspects is provided, which includes a plurality of honeycomb structure bodies, wherein each of the honeycomb structure bodies is constituted of a pillar-shaped honeycomb segment, and side surfaces of a plurality of honeycomb segments are bonded to one another by a bonding layer. 
     A honeycomb filter of the present invention has a constitution in which a width P 1  (mm) of a first cell row, a width P 2  (mm) of a second cell row and a curvature radius R (μm) satisfy Equation (1) mentioned above. Consequently, it is possible to effectively inhibit leakage of particulate matter such as soot from the honeycomb filter and also to inhibit rise of pressure loss. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view schematically showing a first embodiment of a honeycomb filter of the present invention and seen from the side of an inflow end face; 
         FIG. 2  is a plan view schematically showing the inflow end face of the honeycomb filter shown in  FIG. 1 ; 
         FIG. 3  is a plan view schematically showing an outflow end face of the honeycomb filter shown in  FIG. 1 ; 
         FIG. 4  is an enlarged plan view of an enlarged part of the inflow end face of the honeycomb filter shown in  FIG. 2 ; 
         FIG. 5  is an enlarged plan view of an enlarged part of the outflow end face of the honeycomb filter shown in  FIG. 3 ; 
         FIG. 6  is a cross-sectional view schematically showing a cross section taken along the A-A′ line of  FIG. 4 ; 
         FIG. 7  is a cross-sectional view schematically showing a cross section taken along the B-B′ line of  FIG. 4 ; 
         FIG. 8  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a second embodiment of the honeycomb filter of the present invention; 
         FIG. 9  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the second embodiment of the honeycomb filter of the present invention; 
         FIG. 10  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a third embodiment of the honeycomb filter of the present invention; 
         FIG. 11  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the third embodiment of the honeycomb filter of the present invention; 
         FIG. 12  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a fourth embodiment of the honeycomb filter of the present invention; 
         FIG. 13  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the fourth embodiment of the honeycomb filter of the present invention; 
         FIG. 14  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a fifth embodiment of the honeycomb filter of the present invention; 
         FIG. 15  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the fifth embodiment of the honeycomb filter of the present invention; 
         FIG. 16  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a sixth embodiment of the honeycomb filter of the present invention; 
         FIG. 17  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the sixth embodiment of the honeycomb filter of the present invention; 
         FIG. 18  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a seventh embodiment of the honeycomb filter of the present invention; 
         FIG. 19  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the seventh embodiment of the honeycomb filter of the present invention; 
         FIG. 20  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing an eighth embodiment of the honeycomb filter of the present invention; 
         FIG. 21  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the eighth embodiment of the honeycomb filter of the present invention; 
         FIG. 22  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a ninth embodiment of the honeycomb filter of the present invention; 
         FIG. 23  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the ninth embodiment of the honeycomb filter of the present invention; 
         FIG. 24  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a tenth embodiment of the honeycomb filter of the present invention; 
         FIG. 25  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the tenth embodiment of the honeycomb filter of the present invention; 
         FIG. 26  is a plan view of an inflow end face, schematically showing another embodiment of the honeycomb filter of the present invention; 
         FIG. 27  is a plan view of an inflow end face, schematically showing still another embodiment of the honeycomb filter of the present invention; 
         FIG. 28  is a plan view of an inflow end face, schematically showing a further embodiment of the honeycomb filter of the present invention; 
         FIG. 29  is a perspective view schematically showing a still further embodiment of the honeycomb filter of the present invention and seen from the side of an inflow end face; 
         FIG. 30  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing honeycomb filters of Example 22 and Example 23; 
         FIG. 31  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the honeycomb filters of Example 22 and Example 23; 
         FIG. 32  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing an eleventh embodiment of the honeycomb filter of the present invention; 
         FIG. 33  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the eleventh embodiment of the honeycomb filter of the present invention; 
         FIG. 34  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing a twelfth embodiment of the honeycomb filter of the present invention; and 
         FIG. 35  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the twelfth embodiment of the honeycomb filter of the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, description will be made as to embodiments of the present invention. However, the present invention is not limited to the following embodiments. Therefore, it should be understood that changes, improvements and the like are suitably addable to the following embodiments on the basis of ordinary knowledge of a person skilled in the art without departing from the gist of the present invention. 
     (1) Honeycomb Filter (First Embodiment) 
     As shown in  FIG. 1  to  FIG. 7 , a first embodiment of a honeycomb filter of the present invention is a honeycomb filter  100  including a honeycomb structure body  4  having porous partition walls  1 , and a plugging portion  5  disposed in either one of end portions of each of cells  2  formed in the honeycomb structure body  4 . Here,  FIG. 1  is a perspective view schematically showing a first embodiment of the honeycomb filter of the present invention and seen from the side of an inflow end face.  FIG. 2  is a plan view schematically showing the inflow end face of the honeycomb filter shown in  FIG. 1 .  FIG. 3  is a plan view schematically showing an outflow end face of the honeycomb filter shown in  FIG. 1 .  FIG. 4  is an enlarged plan view of an enlarged part of the inflow end face of the honeycomb filter shown in  FIG. 2 .  FIG. 5  is an enlarged plan view of an enlarged part of the outflow end face of the honeycomb filter shown in  FIG. 3 .  FIG. 6  is a cross-sectional view schematically showing a cross section taken along the A-A′ line of  FIG. 4 .  FIG. 7  is a cross-sectional view schematically showing a cross section taken along the B-B′ line of  FIG. 4 . 
     The partition walls  1  of the honeycomb structure body  4  are arranged to surround a plurality of cells  2  extending from an inflow end face  11  to an outflow end face  12  to form through channels for a fluid. That is, the plurality of cells  2  are defined by the porous partition walls  1 . The plugging portion  5  is disposed to plug either one of the end portions of each of the cells  2  formed in the honeycomb structure body  4 . Consequently, either one of the end portions of each of the plurality of cells  2  is plugged with the plugging portion  5  disposed at an open end of the cell on the side of the inflow end face  11  or the outflow end face  12 . In the honeycomb filter  100  of the present embodiment, the porous partition walls  1  function as a filtering material to trap PM in an exhaust gas. Here, among the plurality of cells  2 , the cells  2  in which the plugging portions  5  are arranged at the open ends on the side of the outflow end face  12  and which are opened on the side of the inflow end face  11  are defined as inflow cells  2   a . Furthermore, among the plurality of cells  2 , the cells  2  in which the plugging portions  5  are arranged at the open ends on the side of the inflow end face  11  and which are opened on the side of the outflow end face  12  are defined as outflow cells  2   b.    
     The honeycomb structure body  4  has a plurality of cell rows in which two or more cells  2  are arranged along one direction, in a cross section of the honeycomb structure body  4  which is perpendicular to an extending direction of the cells  2 . Furthermore, the plurality of cell rows include a first cell row  15  and a second cell row  16  as described hereinafter. 
     The first cell row  15  is a cell row in which the cells  2  arranged along the one direction include at least the inflow cells  2   a . Furthermore, in the first cell row  15  is a cell row having a constitution in which in the cross section perpendicular to the extending direction of the cells  2 , a through channel area SA occupied by the inflow cells  2   a  is larger than a through channel area SB occupied by the outflow cells  2   b . Here, “the through channel area SA occupied by the inflow cells  2   a ” means a total through channel area obtained by adding through channel areas of the inflow cells  2   a  among the plurality of cells  2  constituting the first cell row  15  in the above cross section. Furthermore, “the through channel area SB occupied by the outflow cells  2   b ” means a total through channel area obtained by adding through channel areas of the outflow cells  2   b  among the plurality of cells  2  constituting the first cell row  15  in the above cross section. It is to be noted that the first cell row  15  may be a cell row constituted only of the inflow cells  2   a  or a cell row in which the inflow cells  2   a  and the outflow cells  2   b  are mixed. When the first cell row  15  is constituted only of the inflow cells  2   a , “the through channel area SB occupied by the outflow cells  2   b ” in the first cell row  15  is zero (0). The honeycomb filter  100  shown in  FIG. 1  to  FIG. 7  is an example where the first cell row  15  is constituted only of the inflow cells  2   a.    
     The second cell row  16  is a cell row in which the cells  2  arranged along the one direction include at least the outflow cells  2   b . The second cell row  16  may be a cell row constituted only of the outflow cells  2   b  or a cell row in which the outflow cells  2   b  and the inflow cells  2   a  are mixed. Additionally, it is preferable that the second cell row  16  is a cell row in which when the second cell row is compared with the first cell row  15 , a ratio of “the through channel area SA occupied by the inflow cells  2   a ” in the second cell row  16  is relatively small. For example, it is preferable that the second cell row  16  is a cell row having a constitution in which the number of the inflow cells  2   a  is the same as the number of the outflow cells  2   b  or smaller than the number of the outflow cells  2   b . Furthermore, the second cell row  16  may be a cell row having a constitution in which in the cross section perpendicular to the extending direction of the cells  2 , the through channel area SA occupied by the inflow cells  2   a  is the same as the through channel area SB occupied by the outflow cells  2   b  or smaller than the through channel area SB occupied by the outflow cells  2   b.    
     The honeycomb filter  100  of the present embodiment has characteristics in a shape of each of the cells  2  in the cross section perpendicular to the extending direction of the cells  2 . That is, in the cross section perpendicular to the extending direction of the cells  2 , each of the cells  2  has a polygonal shape of which corner portions are formed in a curved shape of a curvature radius R (μm). In  FIG. 4  and  FIG. 5 , reference numeral  6  indicates the corner portions  6  formed in the curved shape in the shape of the cells  2  in the cross section perpendicular to the extending direction of the cells  2 . Then, in the honeycomb filter  100  of the present embodiment, a width P 1  (mm) of the first cell row  15 , a width P 2  (mm) of the second cell row  16  and the curvature radius R (mm) satisfy a relation of Equation (1) mentioned below. In Equation (1) mentioned below, R indicates the curvature radius R (unit: μm) of a curved region in each of the corner portions  6  of the cells  2 . Furthermore, P 1  indicates the width P 1  (unit: mm) of the first cell row  15  and P 2  indicates the width P 2  (unit: mm) of the second cell row  16 .
 
0.4≤( R/ 1000)/(( P 1+ P 2)/2)×100≤20  Equation (1):
 
     According to such a constitution, the honeycomb filter  100  of the present embodiment is capable of effectively inhibiting leakage of particulate matter such as soot. That is, in the honeycomb filter  100  of the present embodiment, each of the cells  2  has the polygonal shape of which the corner portions are formed in the curved shape of the curvature radius R. Then, the honeycomb filter has a constitution in which respective sizes of the above-mentioned R, P 1  and P 2  satisfy the relation of Equation (1) mentioned above, and hence, it is possible to effectively inhibit the leakage of particulate matter such as the soot from the honeycomb filter  100 . Furthermore, it is possible to effectively inhibit rise of pressure loss. Additionally, the honeycomb filter  100  of the present embodiment has the first cell row  15  having the constitution in which the through channel area SA occupied by the inflow cells  2   a  is relatively large, and hence, it is possible to acquire a large capacity for ash to be deposited. 
     In Equation (1), when a value of “(R/1000)/((P 1 +P 2 )/2)×100” is less than 0.4, the soot or the like easily leaks out from the honeycomb filter  100 . In Equation (1), when the value of “(R/1000)/((P 1 +P 2 )/2)×100” is in excess of 20, the pressure loss noticeably increases. In Equation (1), the value of “(R/1000)/((P 1 +P 2 )/2)×100” is especially preferably 1 or more. Furthermore, the value of “(R/1000)/((P 1 +P 2 )/2)×100” is especially preferably 15 or less. 
     In each of the cells  2 , the curvature radius R of each of the corner portions  6  formed in the curved shape can be measured as follows. Initially, the inflow end face  11  and the outflow end face  12  of the honeycomb filter  100  are imaged with an image measuring instrument. Then, images of the imaged inflow end face  11  and outflow end face  12  are analyzed, thereby obtaining the curvature radius R of each of the corner portions  6  of the cells  2 . In a method of the image analysis, for example, “VM-2520 (tradename)” manufactured by Nikon Corporation is usable. The curvature radius R of the corner portion  6  of the cell  2  is obtainable by obtaining a radius (or a diameter) of an inscribed circle of the corner portions  6  in curve fitting to the corner portions  6  of the cell  2  by the above image analysis. 
     In the honeycomb filter  100  of the present embodiment, a cell row directing direction, i.e., the above-mentioned one direction may be an optional direction in the cross section of the honeycomb structure body  4  which is perpendicular to the extending direction of the cells  2 , as long as two or more cells  2  are linearly arranged in the direction. However, when the width P 1  of the first cell row  15  is compared with the width P 2  of the second cell row  16 , the respective cell rows are parallel cell rows extending in the same direction. 
     In the cross section of the honeycomb structure body  4  which is perpendicular to the extending direction of the cells  2 , at least one row may be present as the first cell row  15 . Furthermore, in the cross section of the honeycomb structure body  4  which is perpendicular to the extending direction of the cells  2 , at least one row may be present as the second cell row  16 . 
     In the honeycomb filter  100  of the present embodiment, it is preferable that the width P 1  of the first cell row  15  and the width P 2  of the second cell row  16  satisfy a relation of Equation (2) mentioned below. In Equation (2) mentioned below, P 1  indicates the width P 1  (unit: mm) of the first cell row  15 , and P 2  indicates the width P 2  (unit: mm) of the second cell row  16 . In the honeycomb structure body  4  shown in  FIG. 4  and  FIG. 5 , a side edge in measuring the width of each cell row is an intermediate position of a thickness of the partition wall  1  disposed at the side edge of each cell row. In this way, the side edges on both sides of each cell row are obtained, and a distance between two side edges is measured. The measured distance between the two side edges is considered as the width of each of the cell rows.
 
2≤100−( P 2/ P 1×100)≤50  Equation (2):
 
     The honeycomb filter is constituted to satisfy Equation (2), so that it is possible to acquire the large capacity for the ash to be deposited, and it is possible to remarkably effectively inhibit the rise of the pressure loss when particulate matter such as the ash is deposited on the surfaces of the partition walls  1 . In Equation (2), when a value of “100−(P 2 /P 1 ×100)” is less than 2, it is hard to acquire a sufficient capacity for the ash to be deposited in the cells  2 , and hence, pressure loss when the ash is deposited might deteriorate. Furthermore, in Equation (2), when the value of “100−(P 2 /P 1 ×100)” is in excess of 50, a ratio of the number of the outflow cells  2   b  to the number of the inflow cells  2   a  decreases. Consequently, when a small amount of soot is deposited from a state where any soot is not deposited on the partition walls  1 , the rise of the pressure loss of the honeycomb filter  100  might increase. In Equation (2), the value of “100−(P 2 /P 1 ×100)” is especially preferably 5 or more. Furthermore, the value of “100−(P 2 /P 1 ×100)” is especially preferably 45 or less. 
     An average value of the width P 1  of the first cell row  15  and the width P 2  of the second cell row  16  is preferably from 0.7 to 3.5 mm and further preferably from 1.0 to 2.5 mm. When the above average value is less than 0.7 mm, clogging of the cells  2  due to the depositing of the soot unfavorably easily occurs. Furthermore, when the above average value is in excess of 3.5 mm, the number of the cells  2  substantially decreases, thereby increasing an amount of the soot to be deposited per cell  2 , and the rise of the pressure loss is unfavorably caused. 
     The width P 1  of the first cell row  15  is preferably from 0.7 to 4.0 mm and further preferably from 1.0 to 3.0 mm. When the width P 1  of the first cell row  15  is less than 0.7 mm, the clogging of the cells  2  due to the depositing of the soot unfavorably easily occurs. Furthermore, when the width P 1  of the first cell row  15  is in excess of 4.0 mm, the number of the cells  2  substantially decreases, thereby increasing the amount of the soot to be deposited per cell  2 , and the rise of the pressure loss is unfavorably caused. 
     The width P 2  of the second cell row  16  is preferably from 0.7 to 2.7 mm and further preferably from 1.0 to 2.0 mm. When the width P 2  of the second cell row  16  is less than 0.7 mm, the clogging of the cells  2  due to the depositing of the soot unfavorably easily occurs. Furthermore, when the width P 2  of the second cell row  16  is in excess of 2.7 mm, the number of the cells  2  substantially decreases, thereby increasing the amount of the soot to be deposited per cell  2 , and the rise of the pressure loss is unfavorably caused. 
     In each of the first cell row  15  and the second cell row  16 , there are not any special restrictions on the number of the cells  2  to be linearly arranged. However, in each of the cell rows, it is preferable that five or more cells  2  are linearly arranged, and it is further preferable that ten or more cells  2  are linearly arranged. It is to be noted that an upper limit of the number of the cells  2  to be linearly arranged is the number of all the cells  2  that are linearly present from one peripheral edge to the other peripheral edge of the honeycomb structure body  4 . 
     In the cross section perpendicular to the extending direction of the cells  2 , each of a number N1 of the first cell rows  15  and a number N2 of the second cell rows  16  may be at least one. In the honeycomb filter  100  of the present embodiment, a ratio N2/N1 of the number N2 of the second cell rows  16  to the number N1 of the first cell rows  15  is preferably from ¼ to 4.0 and further preferably from ⅓ to 3.0. According to such a constitution, it is possible to effectively inhibit the rise of the pressure loss while acquiring a large capacity for ash to be deposited. It is to be noted that when the above ratio N2/N1 is less than ¼, the ratio of the number of the outflow cells  2   b  to the number of the inflow cells  2   a  decreases. Consequently, when a small amount of soot is deposited from the state where any soot is not deposited on the partition walls  1 , the rise of the pressure loss of the honeycomb filter  100  might increase. Furthermore, when the above ratio N2/N  1  is in excess of 4.0, the capacity for the ash to be deposited might decrease due to the decrease of the inflow cells  2   a.    
     In the cross section perpendicular to the extending direction of the cells  2 , the first cell row  15  is disposed adjacent to the second cell row  16  via the partition wall  1 . For example, as in the honeycomb filter  100  shown in  FIG. 1  to  FIG. 7 , the first cell rows  15  may be arranged on both sides of the second cell row  16 , respectively, in the cross section perpendicular to the extending direction of the cells  2 . In the honeycomb filter  100 , the first cell rows  15  and the second cell rows  16  are alternately arranged in a direction perpendicular to the respective rows in the cross section perpendicular to the extending direction of the cells  2 . In the honeycomb filter  100  having such a constitution, it is possible to comparatively uniformly acquire the capacity for the ash to be deposited in respective places of the above cross section. 
     There are not any special restrictions on an overall shape of the honeycomb filter  100 . An example of the overall shape of the honeycomb filter  100  shown in  FIG. 1  is a round pillar shape in which the inflow end face  11  and the outflow end face  12  are round. Although not shown in the drawing, another example of the overall shape of the honeycomb filter may be a pillar shape in which an inflow end face and an outflow end face have a substantially round shape such as an elliptic shape, a racetrack shape, or an oblong shape. Alternatively, the overall shape of the honeycomb filter may be a prismatic columnar shape in which an inflow end face and an outflow end face have a polygonal shape such as a quadrangular shape or a hexagonal shape. 
     A thickness of the partition walls  1  is preferably from 50 to 600 pun, further preferably from 100 to 500 m, and especially preferably from 150 to 450 μm. When the thickness of the partition walls  1  is less than 50 μm, an isostatic strength of the honeycomb filter  100  might deteriorate. When the thickness of the partition walls  1  is in excess of 600 μm, the pressure loss might increase, and drop of an engine output or deterioration of a fuel efficiency might be caused. The thickness of the partition walls  1  is a value measured by a method of observing a cross section of the honeycomb filter  100  which is perpendicular to an axial direction with an optical microscope. 
     A porosity of the partition walls  1  is, for example, preferably from 20 to 90%, further preferably from 25 to 80%, and especially preferably from 30 to 75%. When the porosity of the partition walls  1  is less than 20%, the pressure loss of the honeycomb filter  100  might increase, and the drop of the engine output or the deterioration of the fuel efficiency might be caused. When the porosity of the partition walls  1  is 30% or more, the above problem is harder to occur. On the other hand, when the porosity of the partition walls  1  is in excess of 90%, the isostatic strength of the honeycomb filter  100  might deteriorate. When the porosity of the partition walls  1  is 75% or less, the above problem is harder to occur. It is to be noted that the porosity of the partition walls  1  is a value measured with a mercury porosimeter. An example of the mercury porosimeter is AutoPore 9500 (tradename) manufactured by Micromeritics Instrument Corp. 
     There are not any special restrictions on the original polygonal shape of the cells  2  as long as the corner portions of the polygonal shape are formed in the curved shape of the curvature radius R. As described later, examples of the shape of the cells  2  include a quadrangular shape, a hexagonal shape and an octagonal shape. 
     There are not any special restrictions on a material constituting the partition walls  1 , but from the viewpoints of strength, heat resistance, durability and the like, it is preferable that a main component is any type of ceramics of an oxide or a non-oxide, a metal, or the like. Specifically, it is considered that examples of ceramics include cordierite, mullite, alumina, spinel, silicon carbide, silicon nitride, and aluminum titanate. It is considered that examples of the metal include a Fe—Cr—Al based metal and metal silicon. It is preferable to use at least one selected from the group consisting of these materials as the main component. From the viewpoints of a high strength, a high heat resistance and the like, it is especially preferable to use at least one selected from the group consisting of alumina, mullite, aluminum titanate, cordierite, silicon carbide and silicon nitride, as the main component. Furthermore, from the viewpoints of a high thermal conductivity, a high heat resistance and the like, silicon carbide or a silicon-silicon carbide composite material is especially suitable. Here, “the main component” means a component constituting 50 mass % or more, preferably 70 mass % or more and further preferably 80 mass % or more of the partition walls  1 . 
     It is preferable that a material of the plugging portions  5  is a material which is considered to be the preferable material of the partition walls  1 . The material of the plugging portions  5  and the material of the partition walls  1  may be the same material or different materials. 
     In the honeycomb filter  100  of the present embodiment, an exhaust gas purifying catalyst may be loaded onto at least one of each of the surfaces of the partition walls  1  of the honeycomb structure body  4  and each of pores of the partition walls  1 . According to this constitution, CO, NO x , HC and the like in the exhaust gas can be changed to harmless substances by a catalytic reaction. Furthermore, oxidation of the soot trapped in the partition walls  1  can be promoted. 
     When the catalyst is loaded onto the honeycomb filter  100  of the present embodiment, it is preferable that the catalyst includes at least one selected from the group consisting of an SCR catalyst, a NO x  absorber catalyst and an oxidation catalyst. The SCR catalyst is a catalyst to selectively reduce components to be purified. In particular, it is preferable that the SCR catalyst is a NO x  selectively reducing SCR catalyst to selectively reduce NO 1  in the exhaust gas. Furthermore, an example of the SCR catalyst is a metal-substituted zeolite. Examples of a metal in the metal-substituted zeolite include iron (Fe) and copper (Cu). A suitable example of zeolite is a beta zeolite. Furthermore, the SCR catalyst may be a catalyst containing at least one selected from the group consisting of vanadium and titania, as a main component. Examples of the NO x  absorber catalyst include an alkali metal and an alkali earth metal. Examples of the alkali metal include potassium, sodium, and lithium. An example of the alkali earth metal is calcium. An example of the oxidation catalyst is a catalyst containing a noble metal. Specifically, it is preferable that the oxidation catalyst contains at least one selected from the group consisting of platinum, vanadium and rhodium. 
     (2) Honeycomb Filters (Second Embodiment to Tenth Embodiment) 
     Next, description will be made as to a second embodiment to a tenth embodiment of the honeycomb filter of the present invention with reference to  FIG. 8  to  FIG. 25 . Here, each of  FIG. 8  to  FIG. 25  is an enlarged plan view of an enlarged part of an inflow end face or an outflow end face, schematically showing the second embodiment to the tenth embodiment of the honeycomb filter of the present invention. 
     Honeycomb filters  200 ,  300  and  400  of the second embodiment to the fourth embodiment shown in  FIG. 8  to  FIG. 13  are constituted to satisfy Equation (1) mentioned above in the same manner as in the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like). That is, in the honeycomb filters  200 ,  300  and  400  of the second embodiment to the fourth embodiment, respective cells  2  have a constitution in which corner portions of a polygonal shape are formed in a curved shape of a curvature radius R (μm). The honeycomb filters  200 ,  300  and  400  of the second embodiment to the fourth embodiment is different from the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like) in arrangement of a first cell row  15  and a second cell row  16 . Furthermore, it is preferable that the honeycomb filters have a constitution similar to the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like) except for the arrangement of the first cell row  15  and the second cell row  16 . 
     As shown in  FIG. 8  and  FIG. 9 , in the honeycomb filter  200  of the second embodiment, positions at which plugging portions  5  are to be arranged in the second cell row  16  are different from those in the second cell row of the honeycomb filter of the first embodiment. Specifically, in the honeycomb filter  200  of the second embodiment, a cell row in which inflow cells  2   a  and outflow cells  2   b  are alternately arranged is present also in a direction perpendicular to an extending direction of the first cell row  15  and the second cell row  16 . On the other hand, in the honeycomb filter  100  of the first embodiment shown in  FIG. 4  and  FIG. 5 , in two second cell rows  16  arranged via the first cell row  15 , the arrangement positions of the plugging portions  5  are shifted as much as a half pitch. In the honeycomb filter  200  of the second embodiment, a row of the cells  2  in which the plugging portions are not linearly arranged is present also in a longitudinal direction of a paper surface of each of  FIG. 8  and  FIG. 9 , in the same manner as in the first cell row  15 . Consequently, in the honeycomb filter  200 , the first cell rows  15  can be arranged along both of longitudinal and lateral axes of the paper surface when necessary. On the other hand, for example, when the cell row in the longitudinal direction of the paper surface of each of  FIG. 8  and  FIG. 9  does not have to be adjusted in the width P 1  similar to that of the first cell row  15 , the cells  2  may be arranged as in the honeycomb filter  100  shown in  FIG. 4  and  FIG. 5  or the honeycomb filter  200  shown in  FIG. 8  and  FIG. 9 . 
     As shown in  FIG. 10  and  FIG. 11 , in the honeycomb filter  300  of the third embodiment, the first cell row  15  has a constitution in which inflow cells  2   a  are linearly arranged, and two first cell rows are continuously arranged in a direction perpendicular to the first cell row  15 . In this way, the first cell rows  15  and the second cell rows  16  do not have to be alternately arranged in a direction perpendicular to the respective rows. The honeycomb filter  300  having this constitution has a cell row in which plugging portions are linearly arranged in all the cells, and hence, strength during canning of the honeycomb filter  300  is easily acquired. Here, the canning means storage of the honeycomb filter in a case such as a metal case. 
     As shown in  FIG. 12  and  FIG. 13 , the honeycomb filter  400  of the fourth embodiment is the honeycomb filter  400  having the first cell row  15  and the second cell row  16  extending in a right-left direction (e.g., a lateral direction) of a paper surface of  FIG. 12 , and the first cell row  15  and the second cell row  16  extending in an upward-downward direction (e.g., a longitudinal direction) of the paper surface of  FIG. 12 . The first cell row  15  and the second cell row  16  extending in the right-left direction of the paper surface have a constitution in which a width P 1  of the first cell row  15  is larger than a width P 2  of the second cell row  16 . Furthermore, the first cell row  15  and the second cell row  16  extending in the upward-downward direction of the paper surface have a constitution in which a width P 1 ′ of the first cell row  15  is larger than a width P 2 ′ of the second cell row  16 . Then, the honeycomb filter  400  of the fourth embodiment is constituted to satisfy Equation (1) mentioned above in respective longitudinal and lateral cell rows of the paper surface. In the honeycomb filter  400  having this constitution, an arrangement in the longitudinal direction can be the same as an arrangement in the lateral direction, and a permissible range as to directionality in arrangement of the honeycomb filter  400  preferably enlarges. 
     In honeycomb filters  500 ,  600 ,  700  and  800  of a fifth embodiment to an eighth embodiment shown in  FIG. 14  to  FIG. 21 , cells  22  defined by partition walls  21  have a substantially quadrangular shape and a substantially octagonal shape. The substantially quadrangular shape is a shape in which corner portions of a quadrangular shape are formed in a curved shape, and the substantially octagonal shape is a shape in which corner portions of an octagonal shape are formed in a curved shape. Hereinafter, the substantially quadrangular shape in which the corner portions of the quadrangular shape are formed in the curved shape will occasionally be referred to simply as “the quadrangular shape”. Furthermore, the substantially octagonal shape in which the corner portions of the octagonal shape are formed in the curved shape will occasionally be referred to simply as “the octagonal shape”. Each of the honeycomb filters  500 ,  600 ,  700  and  800  of the fifth embodiment to the eighth embodiment is constituted to satisfy Equation (1) mentioned above, when a curved region in each of the corner portions of the cells  22  has a curvature radius R. 
     In the honeycomb filters  500 ,  600 ,  700  and  800  of the fifth embodiment to the eighth embodiment, quadrangular cells  22  and octagonal cells  22  are alternately formed in a cross section of a honeycomb structure body  24  which is perpendicular to an extending direction of the cells  22 . It is preferable that the honeycomb filters of the fifth embodiment to the eighth embodiment have a constitution similar to the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like), except for the shape of the cells  22  and arrangement of a first cell row  35  and a second cell row  36 . Additionally, it is preferable that the honeycomb filters  500 ,  600 ,  700  and  800  of the fifth embodiment to the eighth embodiment have a constitution in which a width P 1  of the first cell row  35  is larger than a width P 2  of the second cell row  36 . 
     Here, description is made as to a method of measuring the width P 1  of the first cell row  35  and the width P 2  of the second cell row  36  in the honeycomb filters  500 ,  600 ,  700  and  800  of the fifth embodiment to the eighth embodiment shown in  FIG. 14  to  FIG. 21 , with reference to  FIG. 14  and  FIG. 15 . Initially, in the honeycomb filter  500  shown in  FIG. 14  and  FIG. 15 , a cell row constituted of inflow cells  22   a  in which plugging portions  25  are arranged in end portions on the side of an outflow end face  32  and which are opened on the side of an inflow end face  31  is defined as the first cell row  35 . Furthermore, in cell rows in which the cells  22  are arranged along one direction, a cell row including outflow cells  22   b  is defined as the second cell row  36 . To measure the width of each cell row, initially, when the first cell row  35  denoted with reference numeral  35  is defined as “a measurement target cell row”, a cell  22   x  disposed on an innermost side of the cell row is found from the cells  22  constituting the measurement target cell row. Next, as to the cell row disposed adjacent to this measurement target cell row, a cell  22   y  disposed on an innermost side of the cell row is found from the cells  22  constituting the adjacent cell row. Then, an intermediate position between the cell  22   x  and the cell  22   y  in a direction perpendicular to the extending direction of the cell rows is defined as a side edge of “the measurement target cell row” on one side. By the above-mentioned method, side edges on both sides of “the measurement target cell row” are obtained and a distance between the two side edges is measured. The measured distance between the two side edges is considered as a width of “the measurement target cell row”. 
     The honeycomb filters  500 ,  600 ,  700  and  800  of the fifth embodiment to the eighth embodiment shown in  FIG. 14  to  FIG. 21  are honeycomb filters which are effective when an amount of soot in an exhaust gas is large and an amount of the soot to be deposited increases. In other words, these embodiments are suitable when it is more necessary to inhibit rise of pressure loss in a state where the soot is deposited than to inhibit rise of pressure loss when any soot is not deposited. 
     It is to be noted that the honeycomb filter  800  of the eighth embodiment shown in  FIG. 20  and  FIG. 21  is a honeycomb filter of a segmented structure which will be described later. Consequently, a structure of the cells  22  shown in  FIG. 20  and  FIG. 21  shows a part of an end face of one honeycomb segment constituting the honeycomb filter of the segmented structure. 
     In honeycomb filters  900  and  1000  of a ninth embodiment and a tenth embodiment shown in  FIG. 22  to  FIG. 25 , a shape of cells  42  defined by partition walls  41  is substantially hexagonal. The substantially hexagonal shape is a shape in which corner portions of a hexagonal shape are formed in a curved shape. Hereinafter, the substantially hexagonal shape in which the corner portions of the hexagonal shape are formed in the curved shape will occasionally be referred to simply as “the hexagonal shape”. Each of the honeycomb filters  900  and  1000  of the ninth embodiment and the tenth embodiment is constituted to satisfy Equation (1) mentioned above, when a curved region in each of the corner portions of the cells  42  has a curvature radius R. It is to be noted that  FIG. 22  to  FIG. 25  are schematic views to explain arrangements of the hexagonal cells  42  in the honeycomb filters  900  and  1000  of the ninth embodiment and the tenth embodiment, and hence, the curved regions in the corner portions of the hexagonal cells  42  are omitted from the drawing. 
       FIG. 22  to  FIG. 25  schematically show only the shape of the cells  42  defined by the partition walls  41 . Specifically,  FIG. 22  to  FIG. 25  show the partition walls  41  by straight lines, and show a thickness of the partition walls  41  in an abstracted state. It is preferable that the honeycomb filters  900  and  1000  of the ninth embodiment and the tenth embodiment have a constitution in which a width P 1  of a first cell row  55  is larger than a width P 2  of a second cell row  56  in a cross section of a honeycomb structure body  44  which is perpendicular to an extending direction of the cells  42 . 
     In the honeycomb filters  900  and  1000  of the ninth embodiment and the tenth embodiment shown in  FIG. 22  to  FIG. 25 , during canning, uniformity of strength is achievable not only in longitudinal and lateral directions of each paper surface but also in a circumferential direction. 
     Description will be made as to a method of measuring the width P 1  of the first cell row  55  and the width P 2  of the second cell row  56  in the honeycomb filters  900  and  1000  of the ninth embodiment and the tenth embodiment shown in  FIG. 22  to  FIG. 25 , with reference to  FIG. 22  and  FIG. 23 . Initially, in the honeycomb filter  900  shown in  FIG. 22  and  FIG. 23 , a cell row constituted of inflow cells  42   a  in which plugging portions  45  are arranged in end portions on the side of an outflow end face  52  and which are opened on the side of an inflow end face  51  is defined as the first cell row  55 . Furthermore, in cell rows in which the cells  42  are arranged along one direction, a cell row including outflow cells  42   b  is defined as the second cell row  56 . A side edge in measuring the width of each cell row is an intermediate position between an inwardly dented region and an outwardly projecting region in each of side edges of the respective cell rows. In this way, the side edges of each cell row on both sides are obtained and a distance between the two side edges is measured. The measured distance between the two side edges is considered as the width of the cell row. 
     (3) Honeycomb Filters (Eleventh Embodiment and Twelfth Embodiment) 
     Next, description will be made as to an eleventh embodiment and a twelfth embodiment of the honeycomb filter of the present invention with reference to  FIG. 32  to  FIG. 35 . Here, each of  FIG. 32  to  FIG. 35  is an enlarged plan view of an enlarged part of an inflow end face or an outflow end face, schematically showing the eleventh embodiment and the twelfth embodiment of the honeycomb filter of the present invention. It is to be noted that in  FIG. 32  and  FIG. 33 , constituent elements similar to those of the honeycomb filter  100  of the first embodiment shown in  FIG. 1  to  FIG. 7  are denoted with the same reference numerals and the description is occasionally omitted. Furthermore, in  FIG. 34  and  FIG. 35 , constituent elements similar to those of the honeycomb filter  500  of the fifth embodiment shown in  FIG. 14  and  FIG. 15  are denoted with the same reference numerals and the description is occasionally omitted. 
     A honeycomb filter  1200  of the eleventh embodiment shown in  FIG. 32  and  FIG. 33  is constituted to satisfy Equation (1) mentioned above in the same manner as in the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like). That is, the honeycomb filter  1200  of the eleventh embodiment has a constitution where each of cells  2  has a polygonal shape of which corner portions are formed in a curved shape of a curvature radius R (m). An arrangement of a first cell row  15  and a second cell row  16  in the honeycomb filter  1200  of the eleventh embodiment is different from that in the honeycomb filter  100  of the first embodiment (see  FIG. 4  and the like). 
     In the honeycomb filter  1200  of the eleventh embodiment, the first cell row  15  is a cell row constituted of inflow cells  2   a  and outflow cells  2   b . Then, in the first cell row  15 , the number of the inflow cells  2   a  is relatively larger than the number of the outflow cells  2   b , and eventually, the honeycomb filter has a constitution in which a through channel area SA occupied by the inflow cells  2   a  is larger than a through channel area SB occupied by the outflow cells  2   b . Furthermore, in the honeycomb filter  1200  of the eleventh embodiment, a width P 1  of the first cell row  15  and a width P 2  of the second cell row  16  have the same value. Also in the honeycomb filter  1200  having this constitution, it is possible to effectively inhibit leakage of particulate matter such as soot and also to inhibit rise of pressure loss. 
     In the first cell row  15 , the through channel area SA occupied by the inflow cells  2   a  is preferably 1.1 times or more and more preferably 1.2 times or more as large as the through channel area SB occupied by the outflow cells  2   b  in a cross section perpendicular to an extending direction of the cells  2 . It is to be noted that the first cell row  15  may be a cell row constituted only of the inflow cells  2   a , and hence, there are not any special restrictions on an upper limit of the above magnification. That is, when the upper limit is daringly prescribed, the upper limit corresponds to a case where any outflow cells  2   b  are not present in the first cell row  15  and the through channel area SB occupied by the outflow cells  2   b  is zero (0). 
     In a honeycomb filter  1300  of the twelfth embodiment shown in  FIG. 34  and  FIG. 35 , cells  22  defined by partition walls  21  have a substantially quadrangular shape and a substantially octagonal shape. The honeycomb filter  1300  of the twelfth embodiment is constituted to satisfy Equation (1) mentioned above, when a curved region in each of corner portions of the cells  22  has a curvature radius R. 
     In the honeycomb filter  1300  of the twelfth embodiment, a first cell row  35  is a cell row constituted of inflow cells  22   a  and outflow cells  22   b . Then, in the honeycomb filter  1300  of the twelfth embodiment, a through channel area of one inflow cells  22   a  is larger than a through channel area of one outflow cells  22   b . As a result, the honeycomb filter has a constitution in which in the first cell row  35 , a through channel area SA occupied by the inflow cells  22   a  is larger than a through channel area SB occupied by the outflow cells  22   b . Furthermore, in the honeycomb filter  1300  of the twelfth embodiment, a width P 1  of the first cell row  35  and a width P 2  of the second cell row  36  have the same value. Also in the honeycomb filter  1300  having this constitution, it is possible to effectively inhibit leakage of particulate matter such as soot and also to inhibit rise of pressure loss. 
     (4) Honeycomb Filters (Other Embodiments) 
     Next, description will be made as to the other embodiments of the honeycomb filter of the present invention with reference to  FIG. 26  to  FIG. 29 . Here,  FIG. 26  is a plan view of an inflow end face, schematically showing another embodiment of the honeycomb filter of the present invention.  FIG. 27  is a plan view of an inflow end face, schematically showing still another embodiment of the honeycomb filter of the present invention.  FIG. 28  is a plan view of an inflow end face, schematically showing a further embodiment of the honeycomb filter of the present invention.  FIG. 29  is a perspective view schematically showing a still further embodiment of the honeycomb filter of the present invention and seen from the side of an inflow end face. 
     In a honeycomb filter  2000  shown in  FIG. 26 , a range of a central portion of an inflow end face  11  of the honeycomb filter  2000  which is shown by a broken line corresponds to a honeycomb structure body  4  which satisfies characteristics of the present invention. That is, in  FIG. 26 , the honeycomb structure body  4  of the range surrounded with the broken line and denoted with reference numeral  4  is constituted to satisfy Equation (1) mentioned above. The honeycomb filter  2000  shown in  FIG. 26  is effective for, for example, a case where an exhaust gas flows, in a concentrated manner, through the central portion of the honeycomb filter  2000  which is surrounded with the broken line. It is to be noted that in the honeycomb filter  2000  shown in  FIG. 26 , a range other than the range surrounded with the broken line and denoted with the reference numeral  4  does not have to satisfy Equation (1) mentioned above. 
     In a honeycomb filter  2100  shown in  FIG. 27 , a ¼ fan-shaped range of the upper left of a paper surface corresponds to a honeycomb structure body  4  which satisfies the characteristics of the present invention, in an inflow end face  11  of the honeycomb filter  2100 . That is, in  FIG. 27 , the honeycomb structure body  4  of the fan-shaped range surrounded with a broken line and denoted with reference numeral  4  is constituted to satisfy Equation (1) mentioned above. Thus, in the honeycomb filter, unevenness might occur in a situation where particulate matter such as ash is deposited, in accordance with a layout in using the honeycomb filter, uneven flow of an exhaust gas, and the like. Consequently, as in the honeycomb filter  2100  shown in  FIG. 27 , the whole region of the end face of the honeycomb filter  2100  does not have to satisfy Equation (1) mentioned above. For example, in the honeycomb filter  2100 , it is possible to effectively inhibit rise of pressure loss while acquiring a large capacity for the ash to be deposited, in accordance with the layout in using the honeycomb filter, the uneven flow of the exhaust gas, and the like. The present embodiment is effective for, for example, a case where the exhaust gas flows, in a concentrated manner, through a portion of the honeycomb filter  2100  which is surrounded with the broken line. 
     In a honeycomb filter  2200  shown in  FIG. 28 , a range of a central portion of an inflow end face  11  of the honeycomb filter  2200  which is shown by a broken line corresponds to a honeycomb structure body  4  which satisfies the characteristics of the present invention. The honeycomb filter  2200  shown in  FIG. 28  is effective for, for example, a case where an exhaust gas flows less in the vicinity of a circumferential portion. 
     A honeycomb filter  3000  shown in  FIG. 29  is the honeycomb filter  3000  including honeycomb structure bodies  4 , and a plugging portion  5  disposed in either one of end portions of each of cells  2  formed in the honeycomb structure bodies  4 . Especially in the honeycomb filter  3000 , each of the honeycomb structure bodies  4  is constituted of a pillar-shaped honeycomb segment  64 , and side surfaces of a plurality of honeycomb segments  64  are bonded to one another by a bonding layer  65 . That is, in the honeycomb filter  3000  of the present embodiment, each of the individual honeycomb segments  64  constituting the honeycomb filter  3000  of a segmented structure corresponds to the honeycomb structure body  4  in the honeycomb filter  3000 . Here, “the honeycomb filter of the segmented structure” is a honeycomb filter having a constitution in which a plurality of individually prepared honeycomb segments  64  are bonded. It is to be noted that the honeycomb filter  100  in which the partition walls  1  of the honeycomb structure body  4  are all monolithically formed as shown in  FIG. 1  to  FIG. 7  will occasionally be referred to as “a monolithic honeycomb filter”. The honeycomb filter of the present invention may be “the honeycomb filter of the segmented structure” or “the monolithic honeycomb filter”. 
     In the honeycomb filter  3000 , it is preferable that at least one of the honeycomb segments  64  has a constitution similar to the honeycomb structure body of the honeycomb filter of the hitherto described first embodiment. Specifically, at least one of the honeycomb segments  64  has a plurality of cell rows in which two or more cells  2  are linearly arranged along one direction. Then, the plurality of cell rows include a first cell row constituted of inflow cells  2   a , and a second cell row including outflow cells  2   b . Furthermore, at least one of the honeycomb segments  64  is constituted to satisfy Equation (1) mentioned above. Also in the honeycomb filter  3000 , technological effects similar to those of the honeycomb filter of the hitherto described first embodiment are obtainable. The plurality of honeycomb segments  64  may have the same cell structure, or may have different cell structures. 
     It is preferable that a circumferential wall  3  in the honeycomb filter  3000  is a circumference coating layer made of a circumference coating material. The circumference coating material is a coating material which is coated on a circumference of a bonded body in which the plurality of honeycomb segments  64  are bonded, to form the circumference coating layer. Furthermore, in the bonded body in which the plurality of honeycomb segments  64  are bonded, it is preferable that a circumferential portion of the bonded body is ground and the above-mentioned circumference coating layer is disposed. 
     In the honeycomb filter  3000  shown in  FIG. 29 , a shape of the cells  2  is quadrangular. However, the shape of the cells  2  in the respective honeycomb segments  64  is not limited to the quadrangular shape, and the shapes of the cells in the hitherto described honeycomb filters of the first embodiment to the tenth embodiment are employable. 
     (4) Manufacturing Method of Honeycomb Filter 
     Next, description will be made as to a method of manufacturing the honeycomb filter of the present invention. An example of the manufacturing method of the honeycomb filter of the present invention is a method including a step of preparing a honeycomb formed body, a step of forming plugging portions in open ends of cells, and a step of drying and firing the honeycomb formed body. 
     (4-1) Forming Step: 
     A forming step is a step of extruding a kneaded material obtained by kneading a forming raw material into a honeycomb shape to obtain the honeycomb formed body. The honeycomb formed body has partition walls which define cells extending from a first end face to a second end face, and a circumferential wall formed to surround an outermost circumference of the partition walls. A part of a honeycomb structure constituted of the partition walls corresponds to a honeycomb structure body. In the forming step, the forming raw material is initially kneaded to obtain the kneaded material. Next, the obtained kneaded material is extruded, thereby obtaining the honeycomb formed body in which the partition walls and the circumferential wall are monolithically formed. 
     It is preferable that the forming raw material is a ceramic raw material to which a dispersing medium and an additive are added. Examples of the additive include an organic binder, a pore former, and a surfactant. An example of the dispersing medium is water. As the forming raw material, there is usable a material similar to a forming raw material used in a heretofore known honeycomb filter manufacturing method. 
     An example of a method of kneading the forming raw material to form the kneaded material is a method in which a kneader, a vacuum pugmill or the like is used. The extrusion can be performed by using an extruding die in which slits corresponding to a sectional shape of the honeycomb formed body are formed. For example, as the extruding die, it is preferable to use a die in which there are formed slits corresponding to the shapes of the cells in each of the hitherto described honeycomb filters of the first embodiment to the tenth embodiment. 
     (4-2) Plugging Step: 
     A plugging step is a step of plugging open ends of the cells to form the plugging portions. For example, in the plugging step, the open ends of the cells are plugged with a material similar to the material used in manufacturing the honeycomb formed body, to form the plugging portions. The method of forming the plugging portions can be performed in conformity with the heretofore known honeycomb filter manufacturing method. 
     (4-3) Firing Step: 
     A firing step is a step of firing the honeycomb formed body in which the plugging portions are formed, to obtain the honeycomb filter. The obtained honeycomb formed body may be dried with, for example, microwaves and hot air, before the honeycomb formed body in which the plugging portions are formed is fired. Alternatively, for example, the firing step of firing the honeycomb formed body is initially performed before the plugging portions are formed, and then, the above-mentioned plugging step may be performed to a honeycomb fired body obtained in the firing step. 
     A firing temperature in firing the honeycomb formed body can suitably be determined in accordance with a material of the honeycomb formed body. For example, when the material of the honeycomb formed body is cordierite, the firing temperature is preferably from 1380 to 1450° C. and further preferably from 1400 to 1440° C. Furthermore, it is preferable that a firing time is from about 4 to 6 hours as a time to keep the highest temperature. 
     EXAMPLES 
     Hereinafter, the present invention will further specifically be described in accordance with examples, but the present invention is not limited to these examples. 
     Example 1 
     To 100 parts by mass of cordierite forming raw material, 0.5 parts by mass of pore former, 33 parts by mass of dispersing medium and 5.6 parts by mass of organic binder were added, mixed and kneaded to prepare a kneaded material. As the cordierite forming raw material, alumina, aluminum hydroxide, kaolin, talc and silica were used. Water was used as the dispersing medium, a water absorbable polymer having an average particle diameter of 10 to 50 μm was used as the pore former, methylcellulose was used as the organic binder, and dextrin was used as a dispersing agent. 
     Next, the kneaded material was extruded by using a predetermined die, to obtain a honeycomb formed body in which a cell shape was substantially quadrangular and an overall shape was a round pillar shape. 
     Then, the honeycomb formed body was dried in a hot air drier. As drying conditions, the drying was performed at 95 to 145° C. 
     Next, plugging portions were formed in the dried honeycomb formed body. Specifically, a mask was initially applied to an inflow end face of the honeycomb formed body to cover inflow cells. Afterward, an end portion of the masked honeycomb formed body was immersed into a plugging slurry, to charge the plugging slurry into open ends of outflow cells which were not masked. Afterward, also as to an outflow end face of the honeycomb formed body, the plugging slurry was charged into open ends of the inflow cells by a method similar to the above method. Then, the honeycomb formed body in which the plugging portions were formed was further dried with the hot air drier. 
     Next, the dried honeycomb formed body was fired. As firing conditions, the honeycomb formed body was fired at 1350 to 1440° C. for 10 hours, thereby preparing a honeycomb filter of Example 1. 
     In the honeycomb filter of Example 1, a thickness of partition walls was 300 μm. Each of cells had a polygonal shape of which corner portions were formed in a curved shape of a curvature radius of 20 μm. Table 1 shows the thickness of the partition walls and the cell shape, in a column of “cell structure”. It is to be noted that Table 1 simply shows a polygonal shape as a shape in which corner portions of the polygonal shape are formed in a curved shape in a column of “cell shape”. Additionally, the curvature radius was measured by the following method. Initially, an inflow end face and an outflow end face of the honeycomb filter were imaged by using an image measuring instrument, for example, “VM-2520 (tradename)” manufactured by Nikon Corporation. Next, images of the imaged inflow end face and outflow end face were analyzed, thereby obtaining a curvature radius of each of the corner portions of the cells. In Example 1, curvature radiuses of 20 regions of the inflow end face and 20 regions of the outflow end face were measured, and an average value of the radiuses was considered as the curvature radius of the corner portions of the cells. In Example 1, the curvature radius of the corner portions of the cells was 20 nm. 
     In the honeycomb filter of Example 1, a shape of a cross section perpendicular to an axial direction was round, and a honeycomb structure body had a first cell row  15  and a second cell row  16  as shown in  FIG. 4 . A diameter of the inflow end face of the honeycomb filter was 266.7 mm, and a length (a total length) from the inflow end face to the outflow end face was 304.8 mm. Table 1 shows a shape of the honeycomb filter of Example 1 in columns of “a sectional shape”, “a shape of a circumference” and “a total length”. 
     Table 2 shows a width P 1  (mm) of the first cell row and a width P 2  (mm) of the second cell row in the honeycomb filter of Example 1. Furthermore, Table 2 shows a value of “100−(P 2 /P 1 ×100)” in a column of “P 1 , P 2  ratio (%)”. Table 2 shows a value of “(P 1 +P 2 )/2” in a column of “average (mm) of P 1  and P 2 ”. Table 2 shows a value of a curvature radius R of the corner portions of the cells in a column of “curvature radius (μm)”. Table 2 shows a value of “(R/1000)/((P 1 +P 2 )/2)×100” in a column of “X (%)”. The “X (%)” in Table 2 is a value represented by Equation (1) in the present description. Furthermore, Table 2 shows a cell structure in the honeycomb filter of each of the examples and comparative examples in a column of “cell structure”. For example, when the table shows  FIG. 4  in the column of “cell structure”, it is indicated that the manufactured honeycomb filter has the cell structure shown in  FIG. 4 . 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
             
            
               
                   
                   
               
               
                   
                 Cell structure 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                 Thickness of 
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                   
                 partition walls 
                   
                 Sectional 
                 Dia. 
                 Long dia. 
                 Short dia. 
                 Total length 
                 Porosity 
               
               
                   
                 Material 
                 (μm) 
                 Cell shape 
                 shape 
                 (mm) 
                 (mm) 
                 (mm) 
                 (mm) 
                 (%) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Example 1 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 2 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 3 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 4 
                 Cordierite 
                 254 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 48 
               
               
                 Example 5 
                 Cordierite 
                 254 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 48 
               
               
                 Example 6 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 254.0 
                 58 
               
               
                 Example 7 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 254.0 
                 58 
               
               
                 Example 8 
                 Cordierite 
                 406 
                 Quadrangular 
                 Round 
                 190.5 
                 — 
                 — 
                 254.0 
                 65 
               
               
                 Example 9 
                 Cordierite 
                 406 
                 Quadrangular 
                 Round 
                 190.5 
                 — 
                 — 
                 254.0 
                 65 
               
               
                 Example 10 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 11 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 12 
                 Cordierite 
                 203 
                 Quadrangular, 
                 Elliptic 
                 — 
                 228.6 
                 137.2 
                 203.2 
                 58 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 13 
                 Cordierite 
                 203 
                 Quadrangular, 
                 Elliptic 
                 — 
                 228.6 
                 137.2 
                 203.2 
                 58 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 14 
                 Cordierite 
                 356 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 254.0 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 15 
                 Cordierite 
                 356 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 254.0 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 16 
                 SiC 
                 254 
                 Quadrangular, 
                 Round 
                 143.8 
                 — 
                 — 
                 177.8 
                 41 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 17 
                 SiC 
                 254 
                 Quadrangular, 
                 Round 
                 143.8 
                 — 
                 — 
                 177.8 
                 41 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 18 
                 Cordierite 
                 254 
                 Hexagonal 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 19 
                 Cordierite 
                 254 
                 Hexagonal 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 20 
                 Cordierite 
                 300 
                 Hexagonal 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 21 
                 Cordierite 
                 300 
                 Hexagonal 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 22 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 23 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 24 
                 Cordierite 
                 254 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 25 
                 Cordierite 
                 254 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 26 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 60 
               
               
                 Example 27 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 60 
               
               
                 Example 28 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172.0 
                 — 
                 — 
                 177.8 
                 52 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Example 29 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172.0 
                 — 
                 — 
                 177.8 
                 52 
               
               
                   
                   
                   
                 octagonal 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 P1 
                 P2 
                 P1, P2 ratio 
                 Average of P1 and P2 
                 Curvature radius 
                 X 
                   
               
               
                   
                 (mm) 
                 (mm) 
                 (%) 
                 (mm) 
                 (μm) 
                 (%) 
                 Cell structure 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Example 1 
                 1.54 
                 1.47 
                 4.5 
                 1.505 
                 20 
                 1.3 
                 FIG. 4 
               
               
                 Example 2 
                 1.90 
                 1.47 
                 22.6 
                 1.685 
                 20 
                 1.2 
                 FIG. 4 
               
               
                 Example 3 
                 2.80 
                 1.47 
                 47.5 
                 2.135 
                 20 
                 0.9 
                 FIG. 4 
               
               
                 Example 4 
                 1.52 
                 1.47 
                 3.3 
                 1.495 
                 50 
                 3.3 
                 FIG. 8 
               
               
                 Example 5 
                 2.00 
                 1.47 
                 26.5 
                 1.735 
                 50 
                 2.9 
                 FIG. 8 
               
               
                 Example 6 
                 1.53 
                 1.47 
                 3.9 
                 1.5 
                 50 
                 3.3 
                 FIG. 10 
               
               
                 Example 7 
                 2.35 
                 1.47 
                 37.4 
                 1.91 
                 50 
                 2.6 
                 FIG. 10 
               
               
                 Example 8 
                 1.85 
                 1.80 
                 2.7 
                 1.825 
                 100 
                 5.5 
                 FIG. 12 
               
               
                 Example 9 
                 3.30 
                 1.80 
                 45.5 
                 2.55 
                 100 
                 3.9 
                 FIG. 12 
               
               
                 Example 10 
                 1.51 
                 1.47 
                 2.6 
                 1.49 
                 80 
                 5.4 
                 FIG. 14 
               
               
                 Example 11 
                 2.60 
                 1.47 
                 43.5 
                 2.035 
                 80 
                 3.9 
                 FIG. 14 
               
               
                 Example 12 
                 1.54 
                 1.47 
                 4.5 
                 1.505 
                 50 
                 3.3 
                 FIG. 16 
               
               
                 Example 13 
                 2.10 
                 1.47 
                 30.0 
                 1.785 
                 50 
                 2.8 
                 FIG. 16 
               
               
                 Example 14 
                 1.54 
                 1.47 
                 4.5 
                 1.505 
                 100 
                 6.6 
                 FIG. 18 
               
               
                 Example 15 
                 2.10 
                 1.47 
                 30.0 
                 1.785 
                 100 
                 5.6 
                 FIG. 18 
               
               
                 Example 16 
                 1.53 
                 1.47 
                 3.9 
                 1.5 
                 70 
                 4.7 
                 FIG. 20 
               
               
                 Example 17 
                 1.88 
                 1.47 
                 21.8 
                 1.675 
                 70 
                 4.2 
                 FIG. 20 
               
               
                 Example 18 
                 1.51 
                 1.47 
                 2.6 
                 1.49 
                 50 
                 3.4 
                 FIG. 22 
               
               
                 Example 19 
                 2.30 
                 1.47 
                 36.1 
                 1.885 
                 50 
                 2.7 
                 FIG. 22 
               
               
                 Example 20 
                 1.41 
                 1.37 
                 2.8 
                 1.39 
                 100 
                 7.2 
                 FIG. 24 
               
               
                 Example 21 
                 1.71 
                 1.37 
                 19.9 
                 1.54 
                 100 
                 6.5 
                 FIG. 24 
               
               
                 Example 22 
                 1.54 
                 1.47 
                 4.5 
                 1.505 
                 100 
                 6.6 
                 FIG. 4, FIG. 26 
               
               
                 Example 23 
                 2.15 
                 1.47 
                 31.6 
                 1.81 
                 100 
                 5.5 
                 FIG. 4, FIG. 26 
               
               
                 Example 24 
                 1.53 
                 1.47 
                 3.9 
                 1.5 
                 100 
                 6.7 
                 FIG. 14, FIG. 27 
               
               
                 Example 25 
                 1.80 
                 1.47 
                 18.3 
                 1.635 
                 100 
                 6.1 
                 FIG. 14, FIG. 27 
               
               
                 Example 26 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 50 
                 3.4 
                 FIG. 32, FIG. 33 
               
               
                 Example 27 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 100 
                 6.8 
                 FIG. 32, FIG. 33 
               
               
                 Example 28 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 20 
                 1.4 
                 FIG. 34, FIG. 35 
               
               
                 Example 29 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 80 
                 5.4 
                 FIG. 34, FIG. 35 
               
               
                   
               
            
           
         
       
     
     Examples 2 to 29 
     The procedure of Example 1 was repeated except that a cell structure, a sectional shape, a shape of a circumference and the like were changed as shown in Table 1 and Table 2, to prepare honeycomb filters of Examples 2 to 29. Here,  FIG. 30  is an enlarged plan view of an enlarged part of an inflow end face, schematically showing the honeycomb filters of Examples 22 and Example 23.  FIG. 31  is an enlarged plan view of an enlarged part of an outflow end face, schematically showing the honeycomb filters of Examples 22 and 23. In a honeycomb filter  1100  shown in  FIG. 30  and  FIG. 31 , constituent elements similar to those of the honeycomb filter shown in  FIG. 4  are denoted with the same reference numerals, and the description is omitted. 
     In Examples 16 and 17, as a material to prepare the honeycomb filter, silicon carbide (SiC) was used. The honeycomb filters of Examples 16 and 17 are honeycomb filters of segmented structures. Furthermore, in Examples 26 to 29, a first cell row was a cell row in which inflow cells and outflow cells were mixed, and the honeycomb filters had a constitution in which in this first cell row, a through channel area SA occupied by the inflow cells was larger than a through channel area SB occupied by the outflow cells. Additionally, in Examples 26 to 29, a width P 1  (mm) of the first cell row and a width P 2  (mm) of a second cell row had the same value. 
     Examples 30 to 43 
     The procedure of Example 1 was repeated except that a cell structure, a sectional shape, a shape of a circumference and the like were changed as shown in Table 4 and Table 5, to prepare honeycomb filters of Examples 30 to 43. In Example 39, as a material to prepare the honeycomb filter, silicon carbide (SiC) was used. The honeycomb filter of Example 39 is a honeycomb filter of a segmented structure. 
     Comparative Examples 1 to 19 
     The procedure of Example 1 was repeated except that a cell structure, a sectional shape, a shape of a circumference and the like were changed as shown in Table 4 and Table 5, to prepare honeycomb filters of Comparative Examples 1 to 19. 
     As to the honeycomb filters of Examples 1 to 43 and Comparative Examples 1 to 19, evaluations were performed as to “soot leakage” and “pressure loss-1” by the following methods. Table 3 and Table 6 show the results. Furthermore, as to the honeycomb filters of Examples 1 to 25 and 30 to 43 and Comparative Examples 1 to 15, evaluations were performed as to “pressure loss-2” by the following method. Table 3 and Table 6 show the results. 
     (Soot Leakage) 
     Initially, as to the honeycomb filter of each example, a hot vibration test was carried out by the following method. A ceramic mat which was not thermally expandable was first wound around a circumferential surface of the honeycomb filter. Next, the honeycomb filter around which the ceramic mat was wound was stored in two divided stainless steel (SUS430) can bodies, and then, the can bodies were welded, to store the honeycomb filter in the can body. Hereinafter, the can body in which the honeycomb filter is stored will be referred to as “the can body for the test”. Next, the can body for the test was attached to a hot vibration test device, and a burning gas of propane was supplied from the hot vibration test device into the can body for the test. The burning gas was supplied at a gas temperature of 900° C. at maximum in the inflow end face of the honeycomb filter, and a gas flow rate was set to 2.5 Nm 3 /min. Furthermore, heating and cooling were repeated at an interval of 20 minutes to provide a heat cycle. Next, in a state where the above burning gas was continuously supplied into the can body for the test, vibration was applied to this can body in a direction perpendicular to an extending direction of the cells of the honeycomb filter. As conditions of the vibration applied to the can body, vibration of 40 G was applied at 150 Hz for 10 hours. Afterward, the can body for the test was rotated as much as 90° around a central axis of the honeycomb filter. The above operation was repeated four times in total. Therefore, a test time was 10 hours×4 times, i.e., 40 hours in total. 
     In the evaluation of soot leakage, the above-mentioned hot vibration test was carried out, and then, soot was deposited in an amount of 4 g/L in the honeycomb filter by use of a PM generator used in the evaluation of the pressure loss, to confirm leakage of the soot from the honeycomb filter. When the soot leakage from the honeycomb filter was not confirmed, the evaluation was “A”. When soot leakage from one region was confirmed in the honeycomb filter, the evaluation was “C”. When soot leakage from two or more regions was confirmed in the honeycomb filter, the evaluation was “D”. In the evaluation of the soot leakage, the evaluation “A” was a pass. 
     (Pressure Loss-1) 
     Initially, a PM containing gas was generated by using a PM generator described in JP-A-2007-155708. Additionally, light oil was used as fuel of the PM generator. The PM containing gas generated from this PM generator was introduced from an inflow end face side of the honeycomb filter. Then, when the gas kept at a constant temperature of 200° C. flowed at a flow rate of 10 Nm 3 /min, a pressure difference between the inflow end face and the outflow end face in the honeycomb filter was obtained. The pressure difference obtained when soot was deposited in an amount of 4 g/L in the honeycomb filter was “a pressure loss value of the honeycomb filter” in “pressure loss-1”. Then, when the measured pressure loss value was compared with a pressure loss value of an evaluation standard mentioned below, a honeycomb filter in which a pressure loss value was equal to or less than that of the evaluation standard was evaluated “A”, a honeycomb filter in which a pressure loss rise remained within 5% was evaluated as “B”, and a honeycomb filter in which a pressure loss rise in excess of 5% was seen was evaluated as “C”. In the evaluation of the pressure loss, the evaluation “A” or the evaluation “B” was a pass. In the evaluation of “pressure loss-1”, the honeycomb filter of the evaluation standard was evaluated as “A”. 
     (Pressure Loss-2) 
     Initially, the PM containing gas was generated by using the PM generator described in JP-A-2007-155708. Additionally, the light oil was used as the fuel of the PM generator. The PM containing gas generated from this PM generator was introduced from the inflow end face side of the honeycomb filter. In this way, ash in the PM containing gas was deposited in a range of ⅓ of a total length of the honeycomb filter on the surfaces of the partition walls of the honeycomb filter. Then, when the gas kept at the constant temperature of 200° C. flowed at a flow rate of 10 Nm 3 /min, a pressure difference between the inflow end face and the outflow end face in the honeycomb filter was obtained. The pressure difference obtained in this manner was considered as “a pressure loss value of the honeycomb filter” in “pressure loss-2”. Then, when the measured pressure loss value was compared with the pressure loss value of the evaluation standard mentioned below, a honeycomb filter in which a pressure loss decrease of 5% or more and less than 10% was seen was evaluated “B”, and a honeycomb filter in which a pressure loss decrease of 10% or more was seen was evaluated as “A”. Furthermore, a honeycomb filter in which a pressure loss decrease was less than 5% or the pressure loss increased was evaluated as “C”. In the evaluation of the pressure loss, the evaluation “A” or the evaluation “B” was considered to be excellent. In the evaluation of “pressure loss-2”, the honeycomb filter of the evaluation standard was evaluated as “C”. 
     In the evaluations of “pressure loss-1” and “pressure loss-2”, respective evaluation standards are as follows. 
     In Examples 1 to 3 and 30 to 32 and Comparative Examples 1 to 4, Comparative Example 1 is the evaluation standard. 
     In Examples 4, 5 and 33 and Comparative Example 5, Comparative Example 5 is the evaluation standard. 
     In Examples 6, 7 and 34 and Comparative Example 6, Comparative Example 6 is the evaluation standard. 
     In Examples 8, 9 and 35 and Comparative Example 7, Comparative Example 7 is the evaluation standard. 
     In Examples 10, 11 and 36 and Comparative Example 8, Comparative Example 8 is the evaluation standard. 
     In Examples 12, 13 and 37 and Comparative Example 9, Comparative Example 9 is the evaluation standard. 
     In Examples 14, 15 and 38 and Comparative Example 10, Comparative Example 10 is the evaluation standard. 
     In Examples 16, 17 and 39 and Comparative Example 11, Comparative Example 11 is the evaluation standard. 
     In Examples 18, 19 and 40 and Comparative Example 12, Comparative Example 12 is the evaluation standard. 
     In Examples 20, 21 and 41 and Comparative Example 13, Comparative Example 13 is the evaluation standard. 
     In Examples 22, 23 and 42 and Comparative Example 14, Comparative Example 14 is the evaluation standard. 
     In Examples 24, 25 and 43 and Comparative Example 15, Comparative Example 15 is the evaluation standard. 
     In Examples 26 and 27 and Comparative Examples 16 and 17, Comparative Example 16 is the evaluation standard. 
     In Examples 28 and 29 and Comparative Examples 18 and 19, Comparative Example 18 is the evaluation standard. 
     (General Judgment) 
     When the honeycomb filter passed both of two evaluations of “soot leakage” and “pressure loss-1”, the result was “OK”. When the honeycomb filter failed even in one of the two evaluations of “soot leakage” and “pressure loss-1”, the result was “NG”. It is to be noted that the evaluation of “pressure loss-2” is regarded as a complementary evaluation, and is not included in the results of this general judgment. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 Soot 
                 Pressure 
                 General 
                 Pressure 
               
               
                   
                 leakage 
                 loss-1 
                 judgment 
                 loss-2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Example 1 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 2 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 3 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 4 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 5 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 6 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 7 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 8 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 9 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 10 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 11 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 12 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 13 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 14 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 15 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 16 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 17 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 18 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 19 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 20 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 21 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 22 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 23 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 24 
                 A 
                 A 
                 OK 
                 B 
               
               
                   
                 Example 25 
                 A 
                 A 
                 OK 
                 A 
               
               
                   
                 Example 26 
                 A 
                 A 
                 OK 
                 Not 
               
               
                   
                   
                   
                   
                   
                 performed 
               
               
                   
                 Example 27 
                 A 
                 A 
                 OK 
                 Not 
               
               
                   
                   
                   
                   
                   
                 performed 
               
               
                   
                 Example 28 
                 A 
                 A 
                 OK 
                 Not 
               
               
                   
                   
                   
                   
                   
                 performed 
               
               
                   
                 Example 29 
                 A 
                 A 
                 OK 
                 Not 
               
               
                   
                   
                   
                   
                   
                 performed 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
             
               
                   
                 TABLE 4 
               
             
            
               
                   
                   
               
               
                   
                 Cell structure 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                   
                 Thickness of 
                   
                   
                   
                   
                   
                   
                   
               
               
                   
                   
                 partition walls 
                   
                 Sectional 
                 Dia. 
                 Long dia. 
                 Short dia. 
                 Total length 
                 Porosity 
               
               
                   
                 Material 
                 (μm) 
                 Cell shape 
                 shape 
                 (mm) 
                 (mm) 
                 (mm) 
                 (mm) 
                 (%) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 1 
               
               
                 Example 30 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 2 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 3 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 4 
               
               
                 Example 31 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 32 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 52 
               
               
                 Example 33 
                 Cordierite 
                 254 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 48 
               
               
                 Comparative 
                 Cordierite 
                 254 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 48 
               
               
                 Example 5 
               
               
                 Example 34 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 254.0 
                 58 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 254.0 
                 58 
               
               
                 Example 6 
               
               
                 Example 35 
                 Cordierite 
                 406 
                 Quadrangular 
                 Round 
                 190.5 
                 — 
                 — 
                 254.0 
                 65 
               
               
                 Comparative 
                 Cordierite 
                 406 
                 Quadrangular 
                 Round 
                 190.5 
                 — 
                 — 
                 254.0 
                 65 
               
               
                 Example 7 
               
               
                 Example 36 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 8 
                   
                   
                 octagonal 
               
               
                 Example 37 
                 Cordierite 
                 203 
                 Quadrangular, 
                 Elliptic 
                 — 
                 228.6 
                 137.2 
                 203.2 
                 58 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 203 
                 Quadrangular, 
                 Elliptic 
                 — 
                 228.6 
                 137.2 
                 203.2 
                 58 
               
               
                 Example 9 
                   
                   
                 octagonal 
               
               
                 Example 38 
                 Cordierite 
                 356 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 254.0 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 356 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 254.0 
                 65 
               
               
                 Example 10 
                   
                   
                 octagonal 
               
               
                 Example 39 
                 SiC 
                 254 
                 Quadrangular, 
                 Round 
                 143.8 
                 — 
                 — 
                 177.8 
                 41 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Comparative 
                 SiC 
                 254 
                 Quadrangular, 
                 Round 
                 143.8 
                 — 
                 — 
                 177.8 
                 41 
               
               
                 Example 11 
                   
                   
                 octagonal 
               
               
                 Example 40 
                 Cordierite 
                 254 
                 Hexagonal 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Comparative 
                 Cordierite 
                 254 
                 Hexagonal 
                 Round 
                 172 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 12 
               
               
                 Example 41 
                 Cordierite 
                 300 
                 Hexagonal 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Hexagonal 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 13 
               
               
                 Example 42 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 143.8 
                 — 
                 — 
                 203.2 
                 65 
               
               
                 Example 14 
               
               
                 Example 43 
                 Cordierite 
                 254 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 65 
               
               
                   
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 254 
                 Quadrangular, 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 65 
               
               
                 Example 15 
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 60 
               
               
                 Example 16 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular 
                 Round 
                 266.7 
                 — 
                 — 
                 304.8 
                 60 
               
               
                 Example 17 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172.0 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 18 
                   
                   
                 octagonal 
               
               
                 Comparative 
                 Cordierite 
                 300 
                 Quadrangular, 
                 Round 
                 172.0 
                 — 
                 — 
                 177.8 
                 52 
               
               
                 Example 19 
                   
                   
                 octagonal 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 P1 
                 P2 
                 P1, P2 ratio 
                 Average of P1 and P2 
                 Curvature radius 
                 X 
                   
               
               
                   
                 (mm) 
                 (mm) 
                 (%) 
                 (mm) 
                 (μm) 
                 (%) 
                 Cell structure 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Comparative Example 1 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 0 
                 0.0 
                 FIG. 4 
               
               
                 Example 30 
                 1.49 
                 1.47 
                 1.3 
                 1.48 
                 20 
                 1.4 
                 FIG. 4 
               
               
                 Comparative Example 2 
                 1.55 
                 1.47 
                 5.2 
                 1.51 
                 0 
                 0.0 
                 FIG. 4 
               
               
                 Comparative Example 3 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 5 
                 0.3 
                 FIG. 4 
               
               
                 Comparative Example 4 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 310 
                 21.1 
                 FIG. 4 
               
               
                 Example 31 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 6 
                 0.4 
                 FIG. 4 
               
               
                 Example 32 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 280 
                 19.0 
                 FIG. 4 
               
               
                 Example 33 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 50 
                 3.4 
                 FIG. 8 
               
               
                 Comparative Example 5 
                 1.47 
                 1.47 
                 0.0 
                 1.49 
                 0 
                 0.0 
                 FIG. 8 
               
               
                 Example 34 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 50 
                 3.4 
                 FIG. 10 
               
               
                 Comparative Example 6 
                 1.47 
                 1.47 
                 0.0 
                 1.515 
                 0 
                 0.0 
                 FIG. 10 
               
               
                 Example 35 
                 1.62 
                 1.80 
                 −11.1 
                 1.71 
                 100 
                 5.8 
                 FIG. 12 
               
               
                 Comparative Example 7 
                 1.82 
                 1.80 
                 1.1 
                 1.81 
                 5 
                 0.3 
                 FIG. 12 
               
               
                 Example 36 
                 1.46 
                 1.47 
                 −0.7 
                 1.465 
                 80 
                 5.5 
                 FIG. 14 
               
               
                 Comparative Example 8 
                 1.47 
                 1.47 
                 0.0 
                 1.535 
                 0 
                 0.0 
                 FIG. 14 
               
               
                 Example 37 
                 1.48 
                 1.47 
                 0.7 
                 1.475 
                 50 
                 3.4 
                 FIG. 16 
               
               
                 Comparative Example 9 
                 1.49 
                 1.47 
                 1.3 
                 1.48 
                 0 
                 0.0 
                 FIG. 16 
               
               
                 Example 38 
                 1.45 
                 1.47 
                 −1.4 
                 1.46 
                 100 
                 6.8 
                 FIG. 18 
               
               
                 Comparative Example 10 
                 1.47 
                 1.47 
                 0.0 
                 1.635 
                 0 
                 0.0 
                 FIG. 18 
               
               
                 Example 39 
                 1.48 
                 1.47 
                 0.7 
                 1.475 
                 70 
                 4.7 
                 FIG. 20 
               
               
                 Comparative Example 11 
                 1.47 
                 1.47 
                 0.0 
                 1.57 
                 2 
                 0.1 
                 FIG. 20 
               
               
                 Example 40 
                 1.46 
                 1.47 
                 −0.7 
                 1.465 
                 50 
                 3.4 
                 FIG. 22 
               
               
                 Comparative Example 12 
                 1.47 
                 1.47 
                 0.0 
                 1.535 
                 0 
                 0.0 
                 FIG. 22 
               
               
                 Example 41 
                 1.37 
                 1.37 
                 0.0 
                 1.37 
                 100 
                 7.3 
                 FIG. 24 
               
               
                 Comparative Example 13 
                 1.37 
                 1.37 
                 0.0 
                 1.62 
                 2 
                 0.1 
                 FIG. 24 
               
               
                 Example 42 
                 1.47 
                 1.47 
                 0.0 
                 1.47 
                 70 
                 4.8 
                 FIG. 4, FIG. 26 
               
               
                 Comparative Example 14 
                 1.47 
                 1.47 
                 0.0 
                 1.48 
                 0 
                 0.0 
                 FIG. 4, FIG. 26 
               
               
                 Example 43 
                 1.46 
                 1.47 
                 −0.7 
                 1.465 
                 50 
                 3.4 
                 FIG. 14, FIG. 27 
               
               
                 Comparative Example 15 
                 1.47 
                 1.47 
                 0.0 
                 1.66 
                 0 
                 0.0 
                 FIG. 14, FIG. 27 
               
               
                 Comparative Example 16 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 0 
                 0.0 
                 FIG. 32, FIG. 33 
               
               
                 Comparative Example 17 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 350 
                 23.8 
                 FIG. 32, FIG. 33 
               
               
                 Comparative Example 18 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 0 
                 0.0 
                 FIG. 34, FIG. 35 
               
               
                 Comparative Example 19 
                 1.47 
                 1.47 
                 — 
                 1.47 
                 320 
                 21.8 
                 FIG. 34, FIG. 35 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 Soot 
                 Pressure 
                 General 
                 Pressure 
               
               
                   
                 leakage 
                 loss-1 
                 judgment 
                 loss-2 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 Comparative Example 1 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 30 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 2 
                 D 
                 A 
                 NG 
                 A 
               
               
                 Comparative Example 3 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Comparative Example 4 
                 A 
                 C 
                 NG 
                 C 
               
               
                 Example 31 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Example 32 
                 A 
                 B 
                 OK 
                 C 
               
               
                 Example 33 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 5 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Example 34 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 6 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Example 35 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 7 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Example 36 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 8 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Example 37 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 9 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 38 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 10 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 39 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 11 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Example 40 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 12 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 41 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 13 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 42 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 14 
                 D 
                 A 
                 NG 
                 C 
               
               
                 Example 43 
                 A 
                 A 
                 OK 
                 C 
               
               
                 Comparative Example 15 
                 C 
                 A 
                 NG 
                 C 
               
               
                 Comparative Example 16 
                 D 
                 A 
                 NG 
                 Not 
               
               
                   
                   
                   
                   
                 performed 
               
               
                 Comparative Example 17 
                 A 
                 C 
                 NG 
                 Not 
               
               
                   
                   
                   
                   
                 performed 
               
               
                 Comparative Example 18 
                 D 
                 A 
                 NG 
                 Not 
               
               
                   
                   
                   
                   
                 performed 
               
               
                 Comparative Example 19 
                 A 
                 C 
                 NG 
                 Not 
               
               
                   
                   
                   
                   
                 performed 
               
               
                   
               
            
           
         
       
     
     (Result) 
     As to the honeycomb filters of Examples 1 to 43, in the evaluation of “soot leakage”, the soot leakage from each honeycomb filter was not confirmed, and the result was evaluation “A”. Furthermore, the honeycomb filters of Examples 1 to 43 satisfied passing criteria also in the evaluation of “pressure loss-1”, and a result of “OK” was obtainable in the general judgment. On the other hand, the honeycomb filters of Comparative Examples 1 to 19 did not satisfy the passing criteria in at least one of the evaluations of “soot leakage” and “pressure loss-1”, and a result of “NG” was obtained in the general judgment. Especially, in the honeycomb filters of Comparative Examples 1 to 16 and 18, in the evaluation of “soot leakage”, soot leakage from at least one region was confirmed, and the result of the evaluation of the soot leakage was “C” or “D”. In the honeycomb filters of Comparative Examples 17 and 19, the result of the evaluation of “pressure loss-1” was a failure. Furthermore, the honeycomb filters of Examples 1 o 25 had a constitution in which a value of “P 1 , P 2  ratio (%)” of Table 2 satisfied the relation of Equation (2) mentioned above, and an excellent result was obtainable also in the evaluation of “pressure loss-2”. 
     A honeycomb filter of the present invention is utilizable as a filter to trap particulate matter in an exhaust gas. 
     DESCRIPTION OF REFERENCE NUMERALS 
       1 ,  21  and  41 : partition wall,  2 ,  22  and  42 : cell,  2   a ,  22   a  and  42   a : inflow cell,  2   b ,  22   b  and  42   b : outflow cell,  3 : circumferential wall,  4 ,  24  and  44 : honeycomb structure body,  5 ,  25  and  45 : plugging portion,  6 : corner portion,  11 ,  31  and  51 : inflow end face,  12  and  32 : outflow end face,  15 ,  35  and  55 : first cell row,  16 ,  36  and  56 : second cell row,  64 : honeycomb segment,  65 : bonding layer,  100 ,  200 ,  300 ,  400 ,  500 ,  600 ,  700 ,  800 ,  900 ,  1000 ,  1200 ,  1300 ,  2000 ,  2100 ,  2200  and  3000 : honeycomb filter, P 1 : width (the width of the first cell row), and P 2 : width (the width of the second cell row).