Patent Publication Number: US-7712679-B2

Title: Mist ejection head, image forming apparatus comprising mist ejection head, and liquid ejection apparatus comprising mist ejection head

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a mist ejection head, an image forming apparatus comprising a mist ejection head, and a liquid ejection apparatus comprising a mist ejection head, and more particularly, to a mist ejection head which uses a high-focus low-attenuation type of reflector for a mist ejection head, and an image forming apparatus and a liquid ejection apparatus comprising such a mist ejection head. 
     2. Description of the Related Art 
     Conventionally, image forming apparatuses are known which form desired images by atomizing liquid ink to form a cloud of ink, known as an ink mist, and selectively depositing this ink mist onto a recording medium. 
     For example, each of Japanese Patent Application Publication No. 62-85948 and Japanese Patent Application Publication No. 62-111757 discloses an ink mist image recording apparatus which generates a charged ink mist locally from the front tip of a fine ultrasonic vibrating needle which vibrates ultrasonically in accordance with an image signal, and performs recording by depositing the ink mist selectively on a recording medium by applying an electric field to the charged ink mist. 
     Furthermore, for example, each of Japanese Patent Application Publication No. 2002-59540 and Japanese Patent Application Publication No. 2002-166541 discloses a liquid ejection apparatus in which an ultrasonic wave is supplied to the ink inside a cavity for storing ink provided inside an ink tank, by means of a piezoelectric transducer (oscillator) provided on the bottom surface of cavity, the ultrasonic wave is reflected by the inner walls of the cavity, which are formed with a parabolic cross-section, the reflected wave concentrates at the focal point of the parabola, thereby raising the acoustic energy density in the ink, and ink is sprayed in the form of a mist from an ejection port formed in the vicinity of the focal point. 
     An ultrasonic wave of the MHz order is generally used to create a mist of liquid ink. More specifically, the method of creating a mist of a liquid ink uses cavitation atomization based on a cavitation phenomenon, or capillary atomization based on a capillary wave. Using the latter method enables the generation of a mist having more uniform particle size, and it also has good energy efficiency. 
     In the case of capillary atomization, a capillary wave is generated by applying a planar wave from below in the direction of the free liquid surface, and if the planar wave has a frequency and amplitude at or above a certain level, then a capillary wave starts to oscillate. Consequently, as the capillary wave grows, minute liquid droplets break away from the peaks of the wave, thereby creating a mist. 
     In this case, as shown in Japanese Patent Application Publication No. 2002-59540 and Japanese Patent Application Publication No. 2002-166541, for example, the inner walls of a cavity of the ink tank which reflect an ultrasonic wave are designed to form a reflector having a parabolic surface shape, which increases the energy efficiency by focusing the ultrasonic wave in the region of the wavelength level. 
       FIG. 8  shows a cross-sectional view of a conventional mist ejection head which uses a parabolic surface-shaped reflector of this kind. 
     The conventional mist ejection head  100  shown in  FIG. 8  comprises an ink tank  110 , a cavity section  112  for storing ink which is provided inside the ink tank  110 , and an ultrasonic wave generating device  114  provided in the bottom surface of the cavity section  112 . The ultrasonic wave generating device  114  comprises a diaphragm  116  and a piezoelectric element  118 . 
     The inner wall of the cavity section  112  forms a reflector (reflective wall)  120  which reflects an ultrasonic wave generated by the ultrasonic wave generating device  114 . The reflector  120  has a parabolic form, with a cross-sectional shape such as that shown on the right-hand side of the drawing. Furthermore, the upper end side of the cavity section  112  forms a straight cylinder section  122  having a straight shape, and the focal point  124  of the parabola formed by the cross-sectional shape of the reflector  120  is positioned in the center of the upper part of this straight cylinder section  122 . 
     Moreover, a nozzle plate  126  is formed on the upper side of the cavity section  112 , and a nozzle  128 , which is an opening for ejecting ink, is formed at a position corresponding to the focal point  124 . Furthermore, an ink supply channel  130  for supplying ink to the cavity section  112  from the sides, is provided at the bottom surface of the cavity section  112 . 
     When ejecting an ink mist, an ultrasonic wave  132  is applied (in an approximately planar shape) in parallel with the axial direction of the parabola formed by the cross-sectional shape of the reflector  120 , from the ultrasonic wave generating device  114 , to the ink inside the cavity section  112 . The ultrasonic wave  132  is reflected by the reflector  120 . Since the reflector  120  has the cross-section of a parabolic shape, the reflected ultrasonic wave  132  is concentrated at the focal point  124  of the parabola. 
     Moreover, since the nozzle  128  is formed at the position of the focal point  124 , then the ultrasonic wave  132  is concentrated at the nozzle  128 , the acoustic energy of the ink is raised at the nozzle  128 , and an ink droplet is ejected in the form of an ink mist, from the nozzle  128 . 
     In this way, in the mist ejection head  100  according to the related art, the cross-sectional shape of the reflector (reflective wall)  120  is formed to have a parabolic shape, and furthermore, as shown on the right-hand side of  FIG. 8 , the portion P 1  which is situated on the farther side than the focal point F of the parabola with respect to the apex C (in the case of  FIG. 8 , the portion of the parabola below the focal point F) is used as the reflective surface. 
     Next, the effective amplitude focusing factor (magnification) in a mist ejection head using the conventional parabolic surface-shaped reflector shown in  FIG. 8  is described below. 
     Here, a case is considered in which the vibrational energy of an acoustic source (the ultrasonic wave generating device  114 ) is focused at the inlet of the nozzle (the side of the nozzle  128  adjacent to the cavity section  112 ), by means of the parabolic surface-shaped reflector (reflective wall  120 ) shown in  FIG. 8 . 
     Firstly, the geometrical focusing factor “m” of the energy when using a parabolic surface-shaped reflector is given by the following equation, (1).
 
 m= ( D   2   −d   2 )/λ 2   (1)
 
     As shown in  FIG. 8 , D (m) is the diameter (inlet diameter) of the inlet side I t  of the reflector (namely, the diameter of the bottom surface side of the cavity section  112 ), and d (m) is the diameter (outlet diameter) of the outlet side O t  of the reflector (namely, the diameter of the upper end side of the cavity section  112 ). Furthermore, λ is the wavelength of the longitudinal wave in a fluid, which is expressed by the ratio between the speed of sound in a fluid (speed of propagation of longitudinal wave) v (m/s) and the frequency f (Hz) of the sound source, as indicated by the following equation, (2).
 
λ= v/f   (2)
 
     Moreover, the vibrational energy of a continuous body is directly proportional to the square of the amplitude, and the amplitude amplification rate is the square root of m, or √(m). 
     Therefore, the effective amplitude focusing factor Γ is defined by the following equation, (3), as the product of the geometric focusing factor of the amplitude due to the reflector, √(m), and the transmissibility T based on the viscous damping.
 
Γ= T×√ ( m )  (3)
 
     Here, the transmissibility T is given by the following equation, (4).
 
 T= exp(−α L )  (4)
 
     Here, the coefficient α is α=0.8361×μf 2 ×10 −13  (neper·m −1 ), L(m) is the propagation distance, and μ(cP) is the coefficient of viscosity. 
     By consolidating the aforementioned equations, the effective amplitude focusing factor Γ is given by the following equation, (5).
 
Γ= f√ ( D   2   −d   2 )/ v× exp(0.8361×μ f   2 ×10 −13   ×L )  (5)
 
     Next, the shape of the reflector (reflective wall  120 ) is described below. As shown in  FIG. 9 , the reflector (reflective wall  120 ) has a parabolic surface shape, having a cross-sectional shape which comprises a portion of a parabola having axial symmetrical (as shown on the left-hand side of  FIG. 9 ) on the far side of the focal point F of the parabola from the apex C of same (in the case of the parabola shown in  FIG. 9 , the portion below the focal point F). 
     Here, in order to describe the reflector (reflective wall)  120  in terms of an equation, the parabolic surface shape of the reflector is expressed by the following equation, (6), using the coordinate axes r and z, as shown on the right-hand side in  FIG. 9 .
 
 z ( r )=( g+p+u+q )−( a   1   /R   B1 ) r   2   (6)
 
     The meaning of the respective symbols used in the equation (6) is as described below. 
     Firstly, as shown in  FIG. 9 , the radius (inlet radius) of the inlet side I t  of the reflector (the bottom surface side of the cavity section  112 ) is taken to be R B1 , the radius (outlet radius) of the outlet side O t  of the reflector (the upper side of the cavity section  112 ) is taken to be R A1 , the height of the parabola is taken to be h as illustrated on the left-hand side of  FIG. 9 , and the distance between the focal point F and the apex C is taken to be p. 
     In this case, a 1  is defined by the following equation, (7).
 
h=a 1 R B1   (7)
 
     If a 1  is defined in this way, then by means of a simple calculation, the coefficient of the quadratic term of this parabola (the coefficient of r 2 ), A, is a 1 /R B1 . 
     Moreover, since the distance p between the focal point F of the parabola and the apex C of same is generally expressed by 1/(4A), using the coefficient A of the quadratic term (r 2 ), then this distance p can be expressed as shown below in the equation (8), using the above results.
 
 p=R   B1 /(4 a   1 )  (8)
 
     Furthermore, the length q of the reflector in the axial direction shown on the right-hand side of  FIG. 9  is expressed by the following equation, (9).
 
 q= ( a   1   /R   B1 )×( R   B1   2   −R   A1   2 )  (9)
 
     Moreover, from the drawing, the length g of the straight cylinder portion  122  of the cavity section  112  in the axial direction is expressed by the following equation, (10).
 
 g=h− ( p+q )  (10)
 
     Furthermore, as shown in  FIG. 9 , it is known that if the reflector has the shape of a parabolic surface, then the propagation distance L 1  of the ultrasonic wave until reaching the focal point F, after the ultrasonic wave has entered in parallel to the axis of the parabolic surface from the inlet side I t  of the cavity section  112  and has been reflected by the parabolic surface, is generally a characteristic property of the parabolic surface and is a uniform distance regardless of the position of reflection. Consequently, looking in particular at a case where the ultrasonic wave is reflected at the point of radius R A1  on the outlet side O t  of the cavity section  112 , from the drawing, it can be seen that the distance L 1  can be expressed by the following equation, (11).
 
 L   1   =q+√ ( R   A1   2   +g   2 )  (11)
 
     Here, if calculation is made by formulas (7) to (10), then the following equation, (12), is obtained.
 
 L   1 ={(4 a   1   2 +1)/4 a   1   }×R   B1   (12)
 
     Furthermore, it can be seen that this expression can be further developed to give L 1 =a 1 R B1 +R B1 /4a 1 =h+p. 
     Moreover, the focal point F of the parabolic surface must be situated to the upper side of the outlet of the cavity section  112 , in other words, at least inside the straight cylinder section  122  as shown in  FIG. 9 , and therefore the condition stated in the formula (13) below is necessary.
 
g≧0  (13)
 
     As described above, taking the diameter (inlet diameter) on the inlet side I t  of the reflector (the bottom surface side of the cavity section  112 ) to be D, and taking the diameter (outlet diameter) on the outlet side O t  of the reflector (the upper end side of the cavity section  112 ) to be d, then “D=2R B1 ” and “d=2R A1 ” are satisfied. Therefore, by using formulas (7) to (10) to rewrite formula (13), the following relationship, (14), is obtained. In other words, in order that the focal point F is positioned inside the straight cylinder section  122 , it is necessary to satisfy the following relationship, (14).
 
 d≧D/ 2 a   1   (14)
 
     Here, considering a case where g=0 as an ideal state, the diameter (outlet diameter) d at the outlet side O t  of the reflector (the upper end side of the cavity section  112 ) is redefined by the following equation, (15).
 
 d= min( d )= D/ 2 a   1   (15)
 
     Here, min(d) is a symbol which expresses the minimum value of d. 
     In this way, the effective focusing factor Γ is expressed by the following equation, (16), as a function of the speed v of sound in the fluid, the frequency f of the acoustic source, the coefficient μ of viscosity, the diameter u of the ink supply channel (see  FIG. 9 ), the diameter (inlet diameter) D on the inlet side I t  of the reflector, and the value a 1  defined in formula (7) above. 
     
       
         
           
             
               
                 
                   
                     Γ 
                     ⁡ 
                     
                       ( 
                       
                         v 
                         , 
                         f 
                         , 
                         μ 
                         , 
                         u 
                         , 
                         D 
                         , 
                         
                           a 
                           1 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       fD 
                       ⁢ 
                       
                         
                           
                             4 
                             ⁢ 
                             
                               a 
                               1 
                               2 
                             
                           
                           - 
                           1 
                         
                       
                     
                     
                       2 
                       ⁢ 
                       
                         a 
                         1 
                       
                       ⁢ 
                       v 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           
                             0.8361 
                             × 
                             μ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               f 
                               2 
                             
                             × 
                             
                               10 
                               
                                 - 
                                 13 
                               
                             
                             ⁢ 
                             u 
                           
                           + 
                           
                             
                               
                                 
                                   4 
                                   ⁢ 
                                   
                                     a 
                                     1 
                                     2 
                                   
                                 
                                 + 
                                 1 
                               
                               
                                 8 
                                 ⁢ 
                                 
                                   a 
                                   1 
                                 
                               
                             
                             ⁢ 
                             D 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Moreover, this equation, (16), is written as shown below in (17), taking γ to be γ=0.8361×10 −13 . 
     
       
         
           
             
               
                 
                   
                     
                       Γ 
                       ⁡ 
                       
                         ( 
                         
                           v 
                           , 
                           f 
                           , 
                           μ 
                           , 
                           u 
                           , 
                           D 
                           , 
                           
                             a 
                             1 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         fD 
                         ⁢ 
                         
                           
                             
                               4 
                               ⁢ 
                               
                                 a 
                                 1 
                                 2 
                               
                             
                             - 
                             1 
                           
                         
                       
                       
                         2 
                         ⁢ 
                         
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                           1 
                         
                         ⁢ 
                         v 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ⅇ 
                           
                             
                               γ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               μ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 f 
                                 2 
                               
                               ⁢ 
                               u 
                             
                             + 
                             
                               
                                 
                                   
                                     4 
                                     ⁢ 
                                     
                                       a 
                                       1 
                                       2 
                                     
                                   
                                   + 
                                   1 
                                 
                                 
                                   8 
                                   ⁢ 
                                   
                                     a 
                                     1 
                                   
                                 
                               
                               ⁢ 
                               D 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     γ 
                     = 
                     
                       0.8361 
                       × 
                       
                         10 
                         
                           - 
                           13 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     In this way, it can be seen that if the effective focusing factor Γ is considered to be a function of D and a 1  only, then the turning values in the D direction and the a 1  direction are situated on a curve in the plane D-a 1 , as given by the following equations, (18) and (19). 
     
       
         
           
             
               
                 
                   
                     D 
                     ⁢ 
                     
                       | 
                       
                         
                           
                             ∂ 
                             Γ 
                           
                           / 
                           
                             ∂ 
                             D 
                           
                         
                         = 
                         0 
                       
                     
                   
                   = 
                   
                     
                       8 
                       ⁢ 
                       
                         a 
                         1 
                       
                     
                     
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       μ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             4 
                             ⁢ 
                             
                               a 
                               1 
                               2 
                             
                           
                           + 
                           1 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
             
               
                 
                   
                     D 
                     ⁢ 
                     
                       | 
                       
                         
                           
                             ∂ 
                             Γ 
                           
                           / 
                           
                             ∂ 
                             a 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                   
                   = 
                   
                     
                       8 
                       ⁢ 
                       
                         a 
                         1 
                       
                     
                     
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       μ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               4 
                               ⁢ 
                               
                                 a 
                                 1 
                                 2 
                               
                             
                             - 
                             1 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     For example,  FIG. 10  shows the effective focusing factor Γ(D, a 1 ) for various values of D and a 1 , when v=1500 (m/s), f=10 (MHz), μ=20 (cP) and u=0 (m). These contour-shaped curves indicating the values of the effective focusing factor Γ(D, a 1 ) are known as “contour lines”. 
     In  FIG. 10 , two curves C 1  and C 2  which intersect these contour lines are depicted, and the curve C 1  is a curve which gives the maximum value of Γ when the value of a 1  given by equation (18) is uniform, and the curve C 2  is a curve which gives the maximum value of Γ when the value of the D given by equation (19) is uniform. 
     The maximum value of the effective focusing factor Γ obtained for all of the values of (D, a 1 ) is located at an intersection of these two curves C 1  and C 2 . This is obtained by solving the following equation, (20).
 
∂Γ/∂ D=∂Γ/∂a   1 =0  (20)
 
     By solving this equation, (20), then the values of D and a 1  which give the maximum value of the effective focusing factor Γ, namely, D′ and a 1 ′, are obtained as shown in the following equation, (21). 
     
       
         
           
             
               
                 
                   
                     
                       D 
                       ′ 
                     
                     = 
                     
                       
                         3 
                       
                       
                         γ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         μ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           2 
                         
                       
                     
                   
                   , 
                   
                     
                       a 
                       1 
                       ′ 
                     
                     = 
                     
                       
                         3 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
     
     Moreover, here, the maximum value of the effective focusing factor Γ, namely, max (Γ), is given by the following equation, (22). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           max 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             Γ 
                             ) 
                           
                         
                         = 
                         
                           Γ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 D 
                                 ′ 
                               
                               , 
                               
                                 a 
                                 1 
                                 ′ 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             3 
                           
                           
                             v 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             γ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             uf 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 1 
                                 + 
                                 
                                   γ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   μ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     f 
                                     2 
                                   
                                   ⁢ 
                                   u 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     In the case of  FIG. 10 , when these values are actually calculated, the results shown in the following equation, (23), are obtained. In other words, the maximum effective focusing factor Γ in this case is approximately 20.74.
 
D′≈10.36 [mm], a′ 1 ≈0.866, max(Γ)≈20.74  (23)
 
     However, in a mist ejection head which uses a conventional parabolic surface-shaped reflector such as that described above, since a portion of the parabola having axial symmetry (such as that shown on the right-hand side of  FIG. 8 ) which is a far from the apex C with respect to the focal point F of same, (namely, the portion of the parabola below the focal point F in the case of  FIG. 8 ) P 1 , is used as a reflector, then the area of the direct wave region which does not contribute to focusing is wasted and hence the spatial usage efficiency of the cavity section is poor. 
     Furthermore, if, on the other hand, the outlet diameter of the cavity section is reduced in order to reduce the direct wave region, then the propagation distance of the ultrasonic wave until the focal point of the parabola formed by the cross-sectional shape of the reflector becomes long, and therefore the effective focusing factor declines due to viscous damping. 
     SUMMARY OF THE INVENTION 
     The present invention has been contrived in view of these circumstances, an object thereof being to provide a mist ejection head, and an image forming apparatus and a liquid ejection head comprising a mist ejection head, in which the spatial usage efficiency of a cavity section of a parabolic surface-shaped reflector can be improved, while also improving the effective focusing factor without causing the propagation distance of an ultrasonic wave until the focal point to become long even if the outlet diameter of the cavity section is restricted. 
     In order to attain the aforementioned object, the present invention is directed to a mist ejection head, comprising: a nozzle plate in which a nozzle hole for ejecting liquid is formed; a liquid chamber connected to the nozzle hole; an ultrasonic wave generating device which applies an ultrasonic wave to the liquid in the liquid chamber; and a reflective wall which reflects the ultrasonic wave applied to the liquid, wherein: the reflective wall is disposed so as to oppose the nozzle plate and has an axially symmetrical shape comprising a portion of a parabolic surface, the portion including an apex of the parabolic surface and being on an apex side with respect to a focal point of the parabolic surface; an axis of the parabolic surface passes through the nozzle hole; and the focal point of the parabolic surface is positioned in a vicinity of the nozzle hole. 
     In this aspect of the present invention, since the portion of a parabola on the side of the apex from the focal point of the parabola is used as the reflector (reflective wall) of the mist ejection head, then the diameter (outlet diameter) of the outlet side of the reflector can be restricted to the nozzle diameter, at minimum, and furthermore, since there is no consequent lengthening of the propagation distance of the ultrasonic wave, then it is possible to improve the effective focusing factor in comparison with the related art. 
     Preferably, the ultrasonic wave generating device is disposed in a vicinity of the nozzle hole on an opposite side of the nozzle plate from the liquid chamber, in such a manner that the ultrasonic wave generated by the ultrasonic wave generating device is applied to the liquid in the liquid chamber via the nozzle plate, travels in parallel to the axis toward the reflective wall, is reflected by the reflective wall and focuses at the focal point. 
     In this aspect of the present invention, by disposing an ultrasonic wave generating device in the vicinity of the nozzle, the heat generated by the ultrasonic wave generating device is applied to the meniscus of the liquid, and hence the viscosity can be reduced. Moreover, since a pressure is applied directly to the nozzle plate from the ultrasonic wave generating device, an elastic wave is generated efficiently in the nozzle plate, in comparison with the case of indirect application of pressure via the fluid, and by transmitting this wave to the nozzle edge, it is possible to assist the generation of a capillary wave. Furthermore, rather than forming a nozzle in a slit shape by means of an opening of the ultrasonic wave generating device itself, a nozzle hole is formed in the nozzle plate and the ultrasonic wave generating device is disposed in the vicinity of the nozzle hole in the nozzle plate, and therefore the dimensional accuracy of the ultrasonic wave generating device does not affect the dimensional accuracy of the nozzle hole. Moreover, since the ultrasonic wave generating device is disposed on the opposite side of the nozzle plate from the liquid chamber, it is possible readily to form wires to the electrode of the ultrasonic wave generating device. 
     Preferably, a supply channel which supplies the liquid to the liquid chamber is formed between a liquid chamber plate in which the liquid chamber is formed, and the nozzle plate, on a side adjacent to the nozzle plate. 
     In this aspect of the present invention, since the supply channel does not impair the shape of the reflective surface of the reflective wall, then it has little detrimental effect on the reflection and focusing of the ultrasonic wave, and furthermore, the occurrence of air bubbles inside the liquid chamber can be suppressed. 
     In order to attain the aforementioned object, the present invention is also directed to an image forming apparatus comprising any one of the above-mentioned mist ejection heads. 
     In this aspect of the present invention, it is possible to eject a liquid mist efficiently, and therefore images can be formed efficiently. 
     In order to attain the aforementioned object, the present invention is also directed to a liquid ejection apparatus comprising any one of the above-mentioned mist ejection heads. 
     In this aspect of the present invention, it is possible to eject a liquid mist efficiently. 
     As described above, according to the present invention, since the portion of a parabola on the apex side with respect to the focal point of the parabola is used as the reflector (reflective wall) of the mist ejection head, then the diameter (outlet diameter) of the outlet side of the reflector can be restricted to the nozzle diameter, at minimum, and furthermore, since there is no consequent lengthening of the propagation distance of the ultrasonic wave, then it is possible to improve the effective focusing factor in comparison with the related art. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The nature of this invention, as well as other objects and advantages thereof, will be explained in the following with reference to the accompanying drawings, in which like reference characters designate the same or similar parts throughout the figures and wherein: 
         FIG. 1  is a cross-sectional diagram showing the approximate composition of a mist ejection head according to one embodiment of the present invention; 
         FIG. 2  is a graph of the effective focusing factor for comparing the differences in the focusing factor between the one embodiment and the related art; 
         FIG. 3  is a graph of a contour line showing the focusing factor of a reflector according to the one embodiment; 
         FIG. 4  is a general schematic drawing showing the general composition of an image forming apparatus comprising a mist ejection head according to the one embodiment; 
         FIG. 5  is an enlarged diagram of the periphery of a mist ejection unit of the image forming apparatus shown in  FIG. 4 ; 
         FIG. 6  is a plan view perspective diagram showing one example of a mist ejection head; 
         FIG. 7  is a partial block diagram showing the system composition of an image forming apparatus according to one embodiment; 
         FIG. 8  is a cross-sectional diagram showing a related art mist ejection head which uses a parabolic surface-shaped reflector; 
         FIG. 9  is a cross-sectional diagram of one quarter part of the mist ejection head shown in  FIG. 8 ; and 
         FIG. 10  is a graph of contour lines showing the focusing factor in the mist ejection head according to the related art. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       FIG. 1  is a cross-sectional diagram showing the approximate composition of a mist ejection head according to one embodiment of the present invention. 
     As shown in  FIG. 1 , the mist ejection head  10  according to the present embodiment is formed by putting a nozzle plate  12  on a liquid chamber plate  14 , a nozzle hole  16  (hereinafter, simply called “nozzle  16 ”) for ejecting ink is formed in the nozzle plate  12 , and an ink chamber  18  forming a cavity section for storing ink is formed in the liquid chamber plate  14 . 
     The inner wall of the ink liquid chamber  18  that faces the nozzle  16  forms a reflector (reflective wall)  20  which serves to reflect an ultrasonic wave. The nozzle plate  12  also serves as a diaphragm, and a piezoelectric element  22  forming an ultrasonic wave generating device is disposed about the perimeter of the nozzle  16 . Moreover, an ink supply channel  24  for supplying ink to the ink chamber  18  is formed on the side of the ink chamber  18  adjacent to the nozzle plate  12 . 
     The reflector  20  is a parabolic surface-shaped reflector (reflective wall), having a cross-sectional shape constituted by a portion of a parabola, as indicated on the right-hand side of  FIG. 1 , namely, the portion on the apex C side of the parabola from the focal point F of the parabola (in other words, the portion including the apex C above the focal point F in the case of the parabola in  FIG. 1 ) P 2 . Moreover, the reflector  20  is formed in such a manner that the axis of the parabola passes through the center of the nozzle  16 , and the focal point F of the paraboloid is located in a position corresponding to the center of the nozzle  16 , on the side of the nozzle plate  12  adjacent to the ink chamber  18 . 
     An ultrasonic wave  26  generated by the piezoelectric element  22  forming the ultrasonic wave generating device is transmitted to the ink inside the ink chamber  18  by means of the nozzle plate  12 , which also serves as a diaphragm, and it advances towards the reflector  20  in the form of a planar wave, following the axis of the parabolic surface of the reflector  20 . The ultrasonic wave  26  is then reflected by the reflector  20 . 
     In this case, when the ultrasonic wave  26  which was advancing in parallel to the axis of the parabolic surface has been reflected by the parabola-shaped reflector  20 , it converges at the focal point F. Moreover, since the focal point F is formed at a position in the center of the nozzle  16 , then the ultrasonic wave  26  reflected by the reflector  20  is focused at the position of the nozzle  16 . Consequently, the acoustic energy of the ink in the nozzle  16  is raised, and an ink droplet is ejected from the nozzle  16  in the form of an ink mist. 
     By disposing the piezoelectric element  22  forming the ultrasonic wave generating device in the vicinity of the nozzle in this way, the heat generated by the piezoelectric element  22  is applied to the meniscus of the ink, and therefore it is possible to reduce the viscosity of the ink. Moreover, since a pressure is applied directly to the nozzle plate  12  from the ultrasonic wave generating device, an elastic wave is generated more efficiently in the nozzle plate  12  in comparison with the case of indirect application of pressure via the fluid, and by transmitting this wave to the nozzle edge, it is possible to assist the generation of a surface acoustic wave. 
     Furthermore, as shown in  FIG. 1 , the inlet side I t  of the reflector  20  according to the present embodiment is the portion where the parabolic surface forming the reflector  20  is opened to the greatest width about the axis of the parabola, and the radius (inlet radius) at the inlet side I t  of the reflector is taken to be R B2 . Moreover, the outlet side O t  of the reflector  20  is the section where the piezoelectric element  22  acting as an ultrasonic wave generating device is formed, in the vicinity of the nozzle  16  where the ultrasonic wave  26  reflected by the reflector  20  converges. The radius (outlet radius) of the outlet side O t  of the reflector  20  is taken to be R A2 . 
     In the present embodiment, as shown in  FIG. 1 , the focal point F is situated more closely to the sound source (piezoelectric element  22 ) than the inlet side I t  of the reflector. In a conventional reflector (reflective wall  120 ), as shown in  FIG. 8 , the focal point F is situated further away from the sound source (piezoelectric element  118 ) than the inlet side I t  of the reflector. The propagation distance L until reaching the focal point F, after the ultrasonic wave  26  generated by the ultrasonic wave generating device (piezoelectric element  22 ) has been input from the inlet side I t  of the reflector and reflected by the reflector  20 , is expressed by the above equation (12), as in the related art. 
     In this case, in the related art, the diameter (outlet diameter) on the outlet side O t  of the reflector, and the diameter (inlet diameter) on the inlet side I t  of the reflector must satisfy equation (14) stated above; however, in the present embodiment, there is no restriction of this kind, and therefore, it is possible to reduce the diameter 2R A2  of the outlet side O t  of the reflector, which corresponds to the value d in equation (5), to the order of the nozzle diameter at the minimum, without causing a wasteful increase in the depth of the reflector from the inlet side I t  of the reflector to the outlet side O t  of the reflector. 
     As equation (9) reveals, in a related art reflector  120  which uses a reflecting surface constituted by the portion of the paraboloid on the far side of the focal point with respect to the apex (the portion P 1  in  FIG. 8 ), if the inlet diameter RBI is reduced with respect to a fixed outlet diameter R A1 , then the length of the reflector  120  in the axial direction (the inlet-outlet distance), q, inevitably becomes longer. Consequently, the propagation distance L of the ultrasonic wave becomes longer. However, in the reflector  20  according to the present embodiment, it is possible to increase the effective focusing factor without lengthening the propagation distance L of the ultrasonic wave. 
     Since the ultrasonic wave generating device (piezoelectric element  22 ) is located in the vicinity of the nozzle in this way, then the phase of the ultrasonic wave focused at the nozzle  16  and the phase of oscillation of the piezoelectric element  22  do not necessarily coincide and it can be expected that they will interfere with each other and cause mutual attenuation. However, since there is a several hundred-fold difference between the energy density in the acoustic field generated at the nozzle surface, and the energy density at the focal point, then the aforementioned interference effect is relatively negligible and it does not present a problem. 
     Here, in the parabola on the right-hand side in  FIG. 1 , similarly to  FIG. 8  or  FIG. 9  relating to the related art, if the ratio a 2  of the height h of the parabola with respect to the length R B2  of the lateral axis at the inlet side I t  of the reflector is taken to be h=a 2 R B2 , then the coefficient A of the quadratic term r 2  of this parabola is A=a 2 /R B2 , and hence the distance p between the focal point F and the apex C of the parabola in  FIG. 1 , and the length R of the lateral axis at the focal point F, are given respectively by the following equations. More specifically, R is expressed by equation (24) below and p is expressed by equation (25) below.
 
 R=R   B2 /2 a   2   (24)
 
 p=R   B2 /4 a   2   (25)
 
     Moreover, from  FIG. 1 , the diameter u of the ink supply channel  24  is expressed by the following equation, (26).
 
 u=p−h=p−a   2   R   B2   (26)
 
     Furthermore, as described previously, the propagation distance L 2  until reaching the focal point F, as traveled by the ultrasonic wave  26  generated by the ultrasonic wave generating device forming the sound source and reflected by the reflector  20 , is generally uniform, regardless of the reflection position at the reflector  20 ; therefore, considering a case where the ultrasonic wave is reflected at the inlet side I t  of the reflector, the propagation distance L 2  is calculated as shown in equation (27) below, by using the value u and the inlet radius R B2  of the reflector.
 
 L   2   =u+√ ( u   2   +R   B2   2 )= R   B2 /2 a   2   =R   (b 27)
 
     Here, if the surface area of the sound source which contributes to the focusing of the ultrasonic wave  26  is calculated in respect of a related art reflector  120  (see  FIG. 8 ) and a reflector  20  according to the present embodiment, then the surface area A 1  of the sound source with respect to the reflector  120  of the related art shown in  FIG. 8  is expressed by the following equation (28).
 
 A   1 =π( R   B1   2   −R   A1   2 )  (28)
 
     Moreover, the surface area A 2  of the sound source with respect to the reflector  20  according to the present embodiment shown in  FIG. 1  is expressed by the following equation, (29).
 
 A   2 =π( R   B2   2   −R   A2   2 )  (29)
 
     If the frequency f is constant, then the focusing factor is dependent on the surface area of the sound source, and supposing that the focusing factor is the same in both the related art and the present embodiment, then the surface areas of the sound sources A 1  and A 2  are equal. Therefore, supposing that “A 1 =A 2 ” is satisfied, then “R B1   2 −R A1   2 =R B2   2 −R A2   2 ” is obtained from equations (28) and (29), and by developing it to a certain degree on the basis of equations (25) and (26), the following equation, (30), is obtained.
 
 R   B2 =2 a   2   {u+√ ( u   2   −R   A1   2   +R   B1   2   +R   A2   2 )}  (30)
 
     Consequently, from this, the propagation distance L 2  of the ultrasonic wave in the case of the reflector  20  according to the present embodiment is expressed by the following equation, (31).
 
 L   2   =u+√ ( u   2   −R   A1   2   +R   B1   2   +R   A2   2 )  (31)
 
     Moreover, here, the ideal state shown in equation (15), namely, d=D/2a 1 , is assumed, in such a manner that the straight cylinder section (straight section)  122  of the related art reflector  120  is eliminated. More specifically, if “R A1 =R B1 /2a 1 ”, which is obtained from “2R A1 =2R B1 /2a 1 ”, is introduced into equation (31), then the following equation (32) is obtained.
 
 L   2 ={(2 a   1   u+ 1)/2 a   1 }×√(4 a   1   2   u   2 +(4 a   1   2 −1) R   B1   2 +4 a   1   2   R   A2   2 )  (32)
 
     Here, if the following equation (33) is satisfied, then the propagation distance L 2  of the ultrasonic wave reflected by the reflector  20  according to the present embodiment, at the same focusing factor, is less than the propagation distance L 1  of the ultrasonic wave reflected by the reflector  120  according to the related art. Therefore, the effective focusing factor according to the present embodiment, based on viscous damping, is substantially improved with respect to the reflector of the related art.
 
L 2 &lt;L 1   (33)
 
     Next, the following simultaneous relationships (34) are considered.
 
L 2 ≦L 1 , ½≦a 1 , 0&lt;R B1 , 0&lt;R A2 , u=0  (34)
 
     The second relationship in (34) means that in the related art composition, the outlet diameter is always smaller than the inlet diameter. Moreover, in the fifth relationship in (34), similarly to the investigation of the related art composition described above, the distance from the sound source to the inlet side I t  of the reflector is assumed to take an ideal state, namely, u=0. By solving the relationships in (34), the following relationship, (35), is obtained.
 
0 &lt;R   A2   ≦R   B1 √(16 a   1   4 −8 a   1   2 +5)/4 a   1   (35)
 
     Provided that this relationship is satisfied, then at the same geometrical focusing factor, the reflector according to the present embodiment has a shorter propagation distance of the ultrasonic wave compared to the related art reflector, and consequently, it can be seen that the effective focusing factor is improved in comparison with the related art composition. Moreover, the relationship in (35) can be satisfied readily. 
     Here, for the purpose of comparison, equations (36) and (37) show the propagation distances of the ultrasonic wave in the case of the related art, L 1 , and in the case of the present embodiment, L 2 , supposing that the present embodiment has the same geometrical factor as the related art (namely, assuming that the outlet surface of the related art composition coincides with the focal point). Here, the distance from the sound source to the inlet side I t  of the reflector is u 1  in the related art, and u 2  in the present embodiment.
 
 L   1   =u   1 +{(4 a   1   2 +1)/4 a   1   }R   B1   (36)
 
 L   2 ={(2 a   1   u   2 +1)/2 a   1 }×√(4 a   1   2   u   2   2 +(4 a   1   2 −1) R   B1   2 +4 a   1   2   R   A2   2 )  (37)
 
     For example, if a 1 =1.5, u 1 =u 2 =0.5 (mm), R A1 =0.5 (mm), R B1 =1.0 (mm), and R A2 =10 (μm), then the relationship (35) becomes approximately equal to the relationship (39) below, and this relationship is satisfied.
 
0&lt;10×10 −6 &lt;1.374×10 −3   (39)
 
     In practice, the following relationship, (40), is obtained.
 
L 1 =2.166 [mm], L 2 ≈1.567 [mm], R B2 ≈0.866 [mm]  (40)
 
     In this way, the propagation distance in the case of the present embodiment, L 2 =1.567, is some 27.6% smaller than the propagation distance according to the related art, L 1 =2.166, since (2.166−1.567)/2.166≈0.276. Moreover, the diameter of the piezoelectric element is substantially equal to the diameter (inlet diameter) on the inlet side I t  of the reflector, but whereas the inlet radius according to the present embodiment is R B2 =0.866, the inlet radius according to the related art is R B1 =1.0. Therefore, comparing the diameters, since (2R B1 −2R B2 )/2R B1 =(2.0−1.732)/2.0=0.134, then the piezoelectric element according to the present embodiment is 13.4% smaller than the diameter of the piezoelectric element according to the related art. As a result, in the present embodiment, at the same focusing factor, the propagation distance is some 27.6% shorter, and the diameter of the piezoelectric element forming the ultrasonic wave generating device is some 13.4% smaller, than in the reflector according to the related art. 
     In this way, by means of the reflector according to the present embodiment, the effective focusing factor accounting for viscous damping is improved, and the suitability for high-density arrangement is improved, at the same value for the geometrical focusing factor. 
     Next, the upper limit of the effective focusing factor in the reflector according to the present embodiment is described below. 
     In the reflector according to the present embodiment, on the basis of equation (27) above, the propagation distance L 2  traveled by the ultrasonic wave from the inlet side I t  of the reflector until reaching the focal point after reflection is expressed by the following equation (41).
 
 L   2   =u+ √( u   2   +R   B2   2 )  (41)
 
     The effective focusing factor in this case is as shown in equation (42) below. 
     
       
         
           
             
               
                 
                   
                     
                       Γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           v 
                           , 
                           f 
                           , 
                           μ 
                           , 
                           
                             D 
                             N 
                           
                           , 
                           u 
                           , 
                           D 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         f 
                         ⁢ 
                         
                           
                             
                               D 
                               2 
                             
                             - 
                             
                               D 
                               N 
                               2 
                             
                           
                         
                       
                       
                         
                           v 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               
                                 γ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 μ 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   f 
                                   2 
                                 
                                 ⁢ 
                                 u 
                               
                               + 
                               
                                 
                                   
                                     u 
                                     2 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         D 
                                         / 
                                         2 
                                       
                                       ) 
                                     
                                     2 
                                   
                                 
                               
                             
                           
                         
                         , 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     γ 
                     = 
                     
                       0.8361 
                       × 
                       
                         10 
                         
                           - 
                           13 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     Here, D=2R B2  and D N =2R A2 . Moreover, as shown in this equation (42), the effective focusing factor Γ does not depend on the value of a 2  given by equation (24) or equation (25). This point is a major difference with respect to the case of the related art indicated by equation (16), where the effective focusing factor Γ depends on the value of a 1  defined in equation (7). 
     Furthermore, the point at which the effective focusing factor Γ(D) takes a maximum value in the R B2  direction (D direction) is given by the solution of the following quintic equation, (43).
 
∂Γ( D )/∂ D= 0  (43)
 
     However, the physically significant part of the solution of this equation is that shown in the following equation, (44). 
     
       
         
           
             
               
                 
                   
                     D 
                     ⁢ 
                     
                       | 
                       
                         
                           
                             ∂ 
                             Γ 
                           
                           / 
                           
                             ∂ 
                             D 
                           
                         
                         = 
                         0 
                       
                     
                   
                   = 
                   
                     
                       
                         2 
                         + 
                         
                           
                             γ 
                             2 
                           
                           ⁢ 
                           
                             μ 
                             2 
                           
                           ⁢ 
                           
                             f 
                             2 
                           
                           ⁢ 
                           
                             D 
                             N 
                             2 
                           
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             
                               1 
                               + 
                               
                                 
                                   γ 
                                   2 
                                 
                                 ⁢ 
                                 
                                   μ 
                                   2 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   
                                     f 
                                     4 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         4 
                                         U 
                                         2 
                                       
                                       + 
                                       
                                         D 
                                         N 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                     
                       γ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       μ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         f 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
     Moreover, in the reflector according to the related art, the maximum effective focusing factor with respect to a certain value of D is given by the following equation, (45).
 
Γ( D,a   1 | ∂Γ/∂a1=0 )  (45)
 
     Here, the value of a 1  which gives the maximum value of the effective focusing factor is the value of a 1  where ∂Γ/∂a 1 =0, and this is obtained by solving the following quartic equation (46). 
     
       
         
           
             
               
                 
                   
                     
                       a 
                       1 
                       4 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                       ⁢ 
                       
                         a 
                         1 
                         4 
                       
                     
                     - 
                     
                       
                         1 
                         
                           2 
                           ⁢ 
                           γ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           μ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             f 
                             2 
                           
                           ⁢ 
                           D 
                         
                       
                       ⁢ 
                       
                         a 
                         1 
                       
                     
                     + 
                     
                       1 
                       16 
                     
                   
                   = 
                   0 
                 
               
               
                 
                   ( 
                   46 
                   ) 
                 
               
             
           
         
       
     
     In  FIG. 2 , the maximum effective focusing factor in a related art type reflector, as obtained by determining the values of a 1  mathematically for the respective values of D by using the Hitchcock-Bairstow method and applying them to equation (45) above, and the effective focusing factor of the reflector according to the present embodiment as expressed by equation (42) above, are plotted according to the same conditions. In other words,  FIG. 2  shows the difference in the focusing factor according to the related art and the present embodiment, when v=1500 (m/s), f=10 (MHz), μ=20 (cP), u=0 (m), and D N =20 (μm), plotting D on the horizontal axis and Γ on the vertical axis. 
     In  FIG. 2 , “New” is a graph indicating the focusing factor Γ New (D) in the reflector according to the present embodiment, and “Conv” is a graph indicating the focusing factor Γ Conv (D) in the reflector according to the related art. 
     The point N 1  on the graph “New” of the focusing factor according to the present embodiment is the point where the focusing factor Γ New (D) becomes a maximum, and this value is given by the equation below, (48). Furthermore, the point C 1  on the graph “Conv” of the focusing factor according to the related art is the point where the focusing factor Γ Conv (D) becomes a maximum, and this value is given by the equation below, (47).
 
Γ conv. ( D′   conv. )≡max(Γ conv (≈20.74  (47)
 
Γ New ( D′   New )≡max(Γ New )≡29.33  (48)
 
     Furthermore, the point N 2  on the graph “New” and the point C 2  on the graph “Conv” are points where the values of D expressing the opening diameters of the reflectors are replaced with each other. These values are expressed in the following equations, where equation (49) indicates the value relating to the related art and the equation (50) indicates the value relating to the present embodiment.
 
Γ conv. ( D′   New )≈20.54  (49)
 
Γ New ( D′   conv. )≈29.04  (50)
 
     Moreover, the value of D at the point N 1  on the graph “New” where the focusing factor Γ New (D) in the present embodiment is a maximum value is given by the following equation, (52), and similarly, the value of D at the point C 1  on the graph “Conv” where the focusing factor Γ Conv (D) according to the related art is a maximum value is given by the following equation, (51).
 
D′ conv. ≈10.36[mm]  (51)
 
D′ New ≈11.96[mm]  (52)
 
     The graph “Conv” relating to the related art in  FIG. 2  is a graph which indicates the values of Γ observed by following the value of a 1  that gives the maximum value of Γ, with respect to particular values of D in  FIG. 10  relating to the related art. 
     Moreover, the value of a 1  in the equation (47) above is given by the following equation (53).
 
a1≡a′ conv. ≈0.866  (53)
 
     Furthermore, the value of a 1  in the equation (49) above is given by the following equation (54).
 
a 1 ≈0.842  (54)
 
     In this way, as revealed by  FIG. 2 , the effective focusing factor Γ Conv (D) of the reflector according to the related art never exceeds the effective focusing factor Γ New (D) of the reflector according to the present embodiment, at all values of D. 
     Furthermore, in the present embodiment, from equation (48) above, the upper limit of the effective focusing factor is Γ New (D)=29.33, which is an improvement of more than 41% with respect to the upper limit of the effective focusing factor according to the related art, Γ Conv (D)=20.74. 
     From equation (52) above, the value of D in this case is D New =11.96 in the case of the present embodiment, and this value is more than 15% greater than the value of D according to the related art, D Conv =10.36, given by equation (51) above. 
     Moreover,  FIG. 3  shows contour lines according to the present embodiment, which correspond to the contour lines according to the related art shown in  FIG. 10 . As stated previously, in the present embodiment, there is no dependence on the value of a 1  (a 2  in the present embodiment), unlike the related art, and therefore the graph does not form contour-shaped lines. In other words, in the present embodiment, as stated previously, Γ New  assumes a maximum value at D=11.96, but since this value is not dependent on a 2 , then in the graph in  FIG. 3 , the straight line parallel to the a 2  axis at D=11.96 indicates the maximum value of the effective focusing factor Γ New . 
     Below, an image forming apparatus and a liquid ejection apparatus which comprise the mist ejection head described above will be explained. 
       FIG. 4  shows the general composition of the image forming apparatus comprising a mist ejection head of this kind. 
     As shown in  FIG. 4 , the image forming apparatus  30  shown in  FIG. 4  comprises: a mist ejection unit  32  having a plurality of mist ejection heads  32 K,  32 C,  32 M and  32 Y provided for ink colors of black (K), cyan (C), magenta (M) and yellow (Y), respectively; an ink storing and loading unit  34  for storing inks to be supplied to the mist ejection heads  32 K,  32 C,  32 M and  32 Y; a paper supply unit  38  for supplying recording paper  36  forming a recording medium; a decurling unit  40  for removing curl in the recording paper  36 ; a conveyance unit  42 , disposed facing the nozzle face (ink ejection face) of the mist ejection unit  32 , for conveying the recording paper  36  while keeping the recording paper  36  flat; an ejection determination unit  44  for reading in the ejection result produced by the mist ejection unit  32 ; and a paper output unit  46  for outputting recorded recording paper (printed matter) to the exterior. 
     The ink storing and loading unit  34  has ink tanks for storing the inks of the colors corresponding to the mist ejection heads  32 K,  32 C,  32 M and  32 Y, and the tanks are connected to the heads  32 K,  32 C,  32 M and  32 Y by means of prescribed channels. 
     In  FIG. 4 , a magazine for rolled paper (continuous paper) is shown as an example of the paper supply unit  38 ; however, a plurality of magazines with papers of different paper width and quality may be jointly provided. Moreover, papers may be supplied in cassettes which contain cut papers loaded in layers and which are used jointly or in lieu of magazines for rolled papers. 
     The recording paper  36  delivered from the paper supply unit  38  retains curl due to having been loaded in the magazine. In order to remove the curl, heat is applied to the recording paper  36  in the decurling unit  40  by a heating drum  48  in the direction opposite to the curl direction in the magazine. 
     In the case of the configuration in which roll paper is used, a cutter (a first cutter)  50  is provided as shown in  FIG. 4 , and the roll paper is cut into a desired size by the cutter  50 . When cut paper is used, the cutter  50  is not required. 
     After decurling, the cut recording paper  36  is nipped and conveyed by the pair of conveyance rollers  52 , and is supplied onto the platen  54 . A pair of conveyance rollers  56  is also disposed on the downstream side of the platen  54  (the downstream side of the mist ejection unit  32 ), and the recording paper  36  is conveyed at a prescribed speed by the joint action of the front side pair of conveyance rollers  52  and the rear side pair of conveyance rollers  56 . 
     The platen  54  functions as a member (recording medium supporting device) which holds the recording paper  36  (supporting same from below), while keeping the recording paper  36  flat, as well as functioning as a rear surface electrode for attracting the ink mist ejected from the mist ejection unit  32  and causing same to be deposited on the recording paper  36 . The platen  54  in  FIG. 4  has a width dimension which is greater than the width of the recording paper  36 , and at least the portion of the platen  54  opposing the nozzle surface of the mist ejection unit  32  and the sensor surface of the ejection determination unit  44  is a horizontal surface (flat surface). 
     A heating fan  58  is provided in the conveyance path of the recording paper  36 , on the upstream side of the mist ejection unit  32 . This heating fan  58  blows heated air onto the recording paper  36  before ink is ejected onto the paper and thereby heats up the recording paper  36 . Heating the recording paper  36  immediately before ink ejection has the effect of making the ink dry more readily after landing on the paper. 
       FIG. 5  shows an enlarged view of the periphery of the mist ejection head  32 . As shown in  FIG. 5 , the mist ejection heads  32 K,  32 C,  32 M and  32 Y of the mist ejection unit  32  are full line heads having a length corresponding to the maximum width of the recording paper  36  used with the image forming apparatus  30 , and comprising a plurality of nozzles for ejecting ink arranged on a nozzle surface through a length exceeding at least one edge of the maximum-size recording paper  36  (namely, the full width of the printable range). 
     The mist ejection heads  32 K,  32 C,  32 M and  32 Y are arranged in color order (black (K), cyan (C), magenta (M) and yellow (Y)) from the upstream side in the delivery direction of the recording paper  36 , and these mist ejection heads  32 K,  32 C,  32 M and  32 Y are fixed extending in a direction substantially perpendicular to the conveyance direction of the recording paper  36 . 
     A color image can be formed on the recording paper  36  by ejecting inks of different colors from the mist ejection heads  32 K,  12 C,  12 M and  12 Y, respectively, onto the recording paper  36  while the recording paper  36  is conveyed by the conveyance unit  42 . 
     By adopting a configuration in which the mist ejection heads  32 K,  32 C,  32 M and  32 Y having nozzle rows covering the full paper width are provided according to color in this way, it is possible to record an image on the full surface of the recording paper  36  by performing just one operation of moving the recording paper  36  and the mist ejection unit  32 , relatively, in the paper conveyance direction (the sub-scanning direction), (in other words, by means of one sub-scanning action). Higher-speed printing is thereby made possible and productivity can be improved in comparison with a shuttle type (serial type) head configuration in which mist ejection heads move reciprocally in a direction which is perpendicular to the paper conveyance direction. 
     Although a configuration with the four standard colors, K, C, M and Y, is described in the present embodiment, the combinations of the ink colors and the number of colors are not limited to these, and light and/or dark inks, or special color inks can be added as required. For example, a configuration is also possible in which mist ejection heads for ejecting light-colored inks such as light cyan and light magenta are added. Furthermore, there are no particular restrictions on the sequence in which the mist ejection heads of the respective colors are arranged. 
     The ejection determination unit  44  reads in a test pattern or an actual image formed by the mist ejection heads  32 K,  32 C,  32 M and  32 Y of the respective colors, and examines the ejection result. 
     Returning again to  FIG. 4 , a post-drying unit  60  is provided on the downstream side of the ejection determination unit  44 . The post-drying unit  60  is a device for drying the surface of the image formed on the recording paper  36 , and it may comprise, for example, a heating fan. 
     A heating/pressurizing unit  62  is disposed following the post-drying unit  60 . The heating/pressurizing unit  62  is a device to control the glossiness of the image surface, and the image surface is pressed with a pressure roller  63  having a predetermined uneven surface shape while the image surface is heated, and the uneven shape is transferred to the image surface. 
     The printed object generated in this manner is output via the paper output unit  46 . Desirably, the actual image that is to be printed (the printed copy of the desired image), and test images, are output separately. In the inkjet recording apparatus  30  according to the present embodiment, a sorting device (not shown) is provided for switching the outputting pathway in order to sort the printed matter with the target print and the printed matter with the test image, and to send them to output units  46 A and  46 B, respectively. If the main image and the test image are formed simultaneously in a parallel fashion, on a large piece of printing paper, then the portion corresponding to the test image is cut off by means of the cutter (second cutter)  64 . Although not shown in  FIG. 4 , the paper output unit  46 A for the target prints is provided with a sorter for collecting prints according to print orders. 
       FIG. 6  is a plan view perspective diagram showing one example of the mist ejection heads  32 K,  32 C,  32 M and  32 Y. The mist ejection heads  32 K,  32 C,  32 M and  32 Y all have the same structure, and therefore a representative example of the mist ejection heads is labeled here with the reference numeral  65 . 
     As shown in  FIG. 6 , the mist ejection head  65  has a structure in which a plurality of ink chamber units (mist ejection elements)  66 , each comprising a nozzle  66 A forming an ink spraying port, an ink chamber  66 B corresponding to the nozzle  66 A, and an individual supply channel  66 C, are arranged in the form of a two-dimensional matrix, and hence the effective nozzle interval (the projected nozzle pitch) as projected in the lengthwise direction of the mist ejection head  65  (the direction perpendicular to the paper conveyance direction) is reduced (high nozzle density is achieved). In  FIG. 6 , in order to simplify the drawing, a portion of the ink chamber units  66  is omitted from the drawing. 
     The ink chambers  66 B are connected to a common flow channel  68  via the individual supply channels  66 C. The common flow channel  68  is connected to an ink tank which acts as an ink source (not shown in  FIG. 6 ; equivalent to the ink storing and loading unit  34  shown in  FIG. 4 ) via the connection ports  68 A and  68 B, and the ink supplied from the ink tank is distributed and supplied to the ink chambers  66 B of the channels via the common flow channel  68  in  FIG. 6 . The reference numeral  68 C in  FIG. 6  indicates a main flow path of the common flow channel  68  and the reference numeral  68 D indicates a divergence flow path which branches from the main flow path  68 C. 
       FIG. 7  is a principal block diagram showing the system configuration of the image forming apparatus  30 . The image forming apparatus  30  comprises a communication interface  70 , a system controller  72 , an image memory  74 , a motor driver  76 , a heater driver  78 , a print controller  80 , an image buffer memory  82 , a head driver  84 , and the like. 
     The communication interface  70  is an interface unit for receiving image data sent from a host computer  86 . A serial interface such as USB, IEEE1394, Ethernet (registered trademark), wireless network, or a parallel interface such as a Centronics interface may be used as the communication interface  70 . A buffer memory (not shown) may be mounted in this portion in order to increase the communication speed. The image data sent from the host computer  86  is received by the image forming apparatus  30  through the communication interface  70 , and is temporarily stored in the image memory  74 . The image memory  74  is a storage device for temporarily storing images inputted through the communication interface  70 , and data is written and read to and from the image memory  74  through the system controller  72 . The image memory  74  is not limited to a memory composed of semiconductor elements, and a hard disk drive or another magnetic medium may be used. 
     The system controller  72  is a control unit for controlling the various sections, such as the communications interface  70 , the image memory  74 , the motor driver  76 , the heater driver  78 , and the like. The system controller  72  is constituted by a central processing unit (CPU) and peripheral circuits thereof, and the like, and in addition to controlling communications with the host computer  86  and controlling reading and writing from and to the image memory  74 , and the like, it also generates control signals for controlling the motor  88  of the conveyance system and the heater  89 . 
     The motor driver (drive circuit)  76  drives the motor  88  in accordance with commands from the system controller  72 . The heater driver (drive circuit)  78  drives the heater  89  of the post-drying unit  60  and the like in accordance with commands from the system controller  72 . 
     The print controller  80  has a signal processing function for performing various tasks, compensations, and other types of processing for generating print control signals from the image data stored in the image memory  74  in accordance with commands from the system controller  72  so as to supply the generated print control signal (print data) to the head driver  84 . Required signal processing is carried out in the print controller  80 , and the ejection amount and the ejection timing of the ink droplets from the mist ejection unit  32  are controlled via the head driver  84 , on the basis of the print data. By this means, desired dot size and dot positions can be achieved. 
     The print controller  80  is provided with the image buffer memory  82 ; and image data, parameters, and other data are temporarily stored in the image buffer memory  82  when image data is processed in the print controller  80 . The aspect shown in  FIG. 7  is one in which the image buffer memory  82  accompanies the print controller  80 ; however, the image memory  74  may also serve as the image buffer memory  82 . Also possible is an aspect in which the print controller  80  and the system controller  72  are integrated to form a single processor. 
     The head driver  84  drives the ultrasonic wave generating devices of the mist ejection unit  32 , on the basis of the print data supplied from the print controller  80 . A feedback control system for maintaining constant drive conditions for the heads may be included in the head driver  84 . 
     As shown in  FIG. 4 , the ejection determination unit  44  is a block including a line sensor (not illustrated), which reads in the image printed onto the recording paper  36 , performs various signal processing operations, and the like, and determines the print situation (presence/absence of ejection, variation in droplet ejection, and the like). The print determination unit  24  supplies these determination results to the print controller  80 . 
     According to requirements, the print controller  80  makes various corrections with respect to the mist ejection head  32  on the basis of information obtained from the ejection determination section  44 . 
     As described above, according to the present embodiment, since the portion of a parabola towards the side of the apex from the focal point is used as the reflector of the mist ejection head, then it is possible to restrict the diameter (outlet diameter) of the outlet side of the reflector, to the nozzle diameter at minimum, and furthermore, there is no consequent lengthening of the propagation distance of the ultrasonic wave. Therefore, it is possible to improve the effective focusing factor in comparison with the related art. 
     Moreover, by providing a mist ejection head of this kind in an image forming apparatus, it is possible to form images efficiently. 
     Mist ejection heads according to the present invention, and an image forming apparatus and liquid ejection apparatus comprising same, have been described in detail above, but the present invention is not limited to the aforementioned examples, and it is of course possible for improvements or modifications of various kinds to be implemented, within a range which does not deviate from the essence of the present invention. 
     It should be understood that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the invention is to cover all modifications, alternate constructions and equivalents falling within the spirit and scope of the invention as expressed in the appended claims.