Static mixer

An improved static mixer is disclosed which is capable of efficient mixing and is of a construction which allows relatively inexpensive manufacture. A pair of flow channels are provided for respectively receiving the fluids to be mixed at respective ends thereof. The flow channels have at least one common wall element therebetween, the common wall element having an undulating shape which alternately enlarges and restricts one of the channels while simultaneously alternately restricting and enlarging the other of the channels in opposing relationship. The common wall has openings therein at about the peaks and valleys of the undulations. In operation, two fluids to be mixed are introduced to the respective flow channels. At each peak or valley of the undulating wall element, the opposing enlargement and restriction of the two channels causes a pressure difference and results in a cross flow through the openings in the common wall element. In one form of the disclosed mixer, the common wall element comprises an undulating sheet separating side-by-side flow channels. In another form of the disclosed mixer, the common wall element comprises an undulating annulus separating concentric flow channels.

BACKGROUND OF THE INVENTION 
This invention relates to the mixing of fluids and, more particularly, to a 
motionless mixer apparatus which operates on a multiple venturi principle. 
In industrial mixing two or more materials are blended together to yield a 
homogeneous product. Devices that employ propellers or turbines to cause 
mixing by agitation are quite common. These "dynamic" type mixers, while 
quite effective, involve the use of power driven elements and other moving 
parts which tend to make them relatively expensive to manufacture, 
install, operate and maintain. Motionless or "static" mixers are 
advantageous in that they have no moving parts, but mixing action is not 
always adequate. The simplest device of the static type is a straight 
length of pipe 50 to 100 diameters in length. Various more complicated 
static mixers are described, for example, in U.S. Pat. Nos. 2,025,974, 
2,784,530, 3,051,453, 3,239,197, 3,286,992, 3,459,407, 3,775,063, 
3,908,702, 4,040,256, and 4,043,539. 
In one well known type of mixer (see e.g. U.S. Pat. No. 3,286,992) a series 
of short helical divider elements are mounted in a pipe. Each helical 
element divides the fluid stream into two parts and causes it to rotate 
through 180.degree. before it is passed to the next element whose leading 
edge is oriented at 90.degree. with respect to the final edge of the prior 
helical element. For n elements there are 2.sup.n divisions and 
recombinations of fluid which is somewhat analagous to cutting a deck of 
cards 2.sup.n times. While this and certain other static mixers are 
capable of acceptable performance, the nature of the structures involved 
often does not lend itself well to inexpensive manufacture. 
It is an object of the present invention to provide a static mixer which 
both exhibits good performance and can be fabricated relatively 
inexpensively from a minimum of parts. 
SUMMARY OF THE INVENTION 
The present invention is directed to an improved static mixer which is 
capable of efficient mixing and is of a construction which allows 
relatively inexpensive manufacture. A first elongated enclosure is 
provided, this first enclosure defining a first flow channel. A second 
elongated enclosure is provided adjacent to the first enclosure and has a 
wall element in common therewith. This second enclosure has an undulating 
cross-section that defines a second flow channel which is an undulating 
flow channel. Preferably, although not necessarily, the first enclosure 
also has an undulating cross-section such that the first flow channel 
undulates in alternating relationship to the undulations of the second 
flow channel. This means that the first row channel alternately enlarges 
and restricts in opposing relationship to the restriction and enlargement, 
respectively, in the adjacent second flow channel. The common wall element 
has openings therein at about longitudinal positions thereof corresponding 
to the peaks and valleys of the undulations of the first and second flow 
channels. 
In operation, two fluids to be mixed are introduced to the respective flow 
channels. At positions corresponding to each peak or valley of the 
undulations, the opposing enlargement and restriction of the two channels 
causes a pressure difference and results in a cross-flow through the 
openings in the common wall element. This cross-flow is due to the venturi 
effect and is perpendicular to the main flow in each channel. This 
produces turbulence and good mixing between stages of the mixer. The 
number of stages (i.e., the number of waves in the undulating structure) 
will depend upon the degree of mixing desired. 
In one form of the invention, the common wall element comprises an 
undulating sheet separating side-by-side channels. In another form of the 
invention, the common wall element comprises an undulating annulus 
separating concentric flow channels. In the latter form of the invention, 
inner and outer substantially concentric spaced pipes are provided. A 
central pipe, in the form of an undulating annulus, is mounted between the 
inner and outer pipes and in spaced concentric relation thereto. The 
central pipe has openings therein at about the peaks and valleys of its 
undulations. An outer flow channel is defined by the region between the 
central and outer pipes, and an inner flow channel is defined by the 
region between the central and inner pipes. In still further forms of the 
invention, the undulations of the first and/or second enclosures are 
defined by one or more wall elements of the enclosures other than the 
common wall element. 
In the preferred embodiment of the invention, the openings comprise 
multiple perforations at each of the peaks and valleys of the common wall 
element. The size and number of perforations at each peak and valley are 
selected in accordance with the expected pressure differential at the peak 
or valley. 
Further features and advantages of the invention will become more readily 
apparent from the following detailed description when taken in conjunction 
with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring to FIGS. 1 and 2, there is shown an embodiment of a motionless 
mixer 100 in accordance with an embodiment of the invention. An elongated 
enclosure 120 is divided into flow channels designated f1 and f2 by a 
common wall element 150 (FIGS. 2 and 3) which is secured to the top and 
bottom of enclosure 120 by any suitable fluid-tight means (not shown). A 
pair of inlet pipes 121 and 122 communicate with channels f1 and f2, 
respectively, at an inlet end of enclosure 120. An outlet pipe 123 
communicates with both flow channels at an outlet end of enclosure 120. 
The enclosure 120, wall element 150, and inlet and outlet pipes may be 
formed of any suitable material such as metal or plastic. 
The common wall element 150, shown in further detail in FIG. 3, is seen to 
have an undulating shape, and in the present embodiment it is an 
undulating sheet of uniform thickness. The wall element 150 is seen to 
alternately enlarge and then restrict the flow channel f1 while 
simultaneously alternately restricting and enlarging the flow channel f2. 
For ease of explanation, the beginning of the wall element 150, which 
starts equidistant from the side walls of enclosure 120 in this 
embodiment, is designated "station 0" and then successive valleys and 
peaks are designated as "station 1", "station 2" etc. A plurality of 
perforations are located at about each peak and valley of the wall element 
150; i.e., at the stations 1, 2, 3 . . . n thereof. The perforations in 
this embodiment are in a row that is normal to the direction of fluid 
flow. 
In operation, two fluids to be mixed, designated A and B, are introduced to 
channels f1 and f2, respectively, via inlet pipes 121 and 122. As the 
fluid A approaches station 1, its velocity decreases and its pressure 
increases. Just the reverse happens to fluid B as it approaches station 1. 
The resulting pressure difference causes fluid to flow from channel f1 to 
channel f2 through the perforations at station 1. As the fluid flows from 
station 1 to station 2, the pressure difference developed is in the 
opposite direction and causes fluid to flow from f2 to f1 through the 
perforations at station 2. Thus, each time a peak or valley (i.e., a 
mixing stage) of the undulating common wall element 150 is encountered, 
fluid flows transversely to the axis of mixer 100. Since the cross flow is 
at right angles to the main flow in each channel, this produces turbulence 
and good mixing between stages. The number of stages required will depend 
upon the degree of mixing desired. 
The operation of mixer 100 can be better understood with reference to an 
example. Consider two pure liquids A and B entering the mixer with 100 
parts by volume of A entering f1 and 100 parts by volume of B entering f2. 
Assume that the perforations of stations, 1, 2 . . . n, are sufficient in 
size and number to allow 25% cross flow at each station with the 
pertaining pressure difference. Table I shows the number of particles of A 
and B to be expected at each station for channels f1 and f2. The last 
column of Table I shows the difference between A and B in channel f2 at 
each station. It is clear from this table that to insure perfect mixing, 
an infinite number of stations would be required. 
TABLE I 
______________________________________ 
Channel f1 Channel f2 
Station No. 
A B .SIGMA. 
A B .SIGMA. 
.vertline.A-B.vertline. 
______________________________________ 
0 100 0 100 0 100 100 100 
1 75 0 75 25 100 125 75 
2 81.25 25 106.25 
18.75 
75 93.75 56 
3 60.94 18.75 79.69 39.06 
81.25 
120.31 
42 
4 70.71 39.06 109.77 
29.30 
60.94 
90.24 32 
5 53.03 29.30 82.33 46.98 
70.71 
117.69 
24 
6 64.78 46.98 111.76 
35.24 
53.03 
88.27 18 
7 48.59 35.24 83.83 51.44 
64.78 
116.22 
13 
8 61.45 51.44 112.89 
38.58 
48.58 
87.16 10 
9 46.09 38.58 84.67 53.94 
61.44 
115.38 
7.5 
10 59.58 53.94 113.52 
40.46 
46.09 
86.55 5.6 
11 44.69 40.46 85.15 55.36 
59.58 
114.04 
4.2 
12 58.53 55.36 113.89 
41.52 
44.69 
86.21 3.2 
13 43.90 41.52 85.42 56.15 
58.53 
114.68 
2.4 
14 57.94 56.15 114.09 
42.11 
43.90 
86.01 1.8 
15 43.46 42.11 85.57 56.60 
57.94 
114.54 
1.3 
16 57.61 56.60 114.21 
42.45 
43.46 
84.91 1.0 
17 43.21 42.45 85.66 56.85 
57.61 
114.46 
0.7 
18 57.42 56.85 114.27 
42.64 
43.21 
85.85 0.5 
19 43.07 42.64 85.71 57.00 
57.42 
114.42 
0.4 
20 57.32 57.00 114.32 
42.75 
43.07 
85.82 0.3 
______________________________________ 
However, we might consider practically perfect mixing to correspond to the 
situation where 50.+-.0.5% of A and B are present in both channels. This 
corresponds to the situation where .vertline.A-B.vertline. in Table I 
equals 1, which is seen to occur after 16 stations have been traversed in 
this example. 
The total transverse area required for the desired cross flow will depend 
upon the pressure difference (.DELTA.p) which, in turn, will depend upon 
the ratio of maximum to minimum axial area. For present purposes viscous 
losses will be ignored since they play the same role on each side of the 
mixer. Again, an example can be used to illustrate parameters of the 
mixing system. Assume the ratio of maximum to minimum axial area at each 
station; i.e., the enlargement-to-restriction ratio, is made 3:1. If the 
areas of f1 and f2 at station 0 are both equal to A.sub.o, then the areas 
of f1 and f2 at station 1, designated A.sub.1f1 and A.sub.1f2, are: 
EQU A.sub.1f1 =1.5A.sub.o (1) 
EQU A.sub.1f2 =0.5A.sub.o (2) 
By continuity, if the velocity at station 0 is V.sub.o in both channels, 
the velocities at station 1 are: 
EQU V.sub.1f1 =1/3V.sub.o (3) 
EQU V.sub.1f2 =2V.sub.o (4) 
Assuming no loss between stations 0 and 1 and negligible change in 
elevation, then by Bernouilli's equation, the difference in pressure at 
station 1, designated .DELTA.P.sub.1, will be 
EQU .DELTA.p.sub.1 =.rho./2(V.sup.2.sub.1f2 -V.sup.2.sub.1f1) (5) 
where .rho. is the mass density of the fluid. 
The flow rate through the sharp edged transverse orifices can be 
represented by the following equation, for high Reynold's numbers: 
##EQU1## 
where A.sup.'.sub.1 is the total area of transverse perforations at 
station 1 (see e.g. "Unit Operations of Chemical Engineering" by McCabe & 
Smith, published by McGraw Hill). Substituting the expression for 
.DELTA.p.sub.1 from (5) into (6) gives 
##EQU2## 
For a cross-flow Q.sup.'.sub.1 equal to (1/4)A.sub.o V.sub.o, as in the 
example of Table I, we have 
##EQU3## 
or 
##EQU4## 
Thus, for the desired cross-flow, the perforation area is 0.22 times the 
flow channel area at station 0. To compute the total perforation area at 
station 2, we first set forth the axial flow rates at station 1, taking 
into account the fluid gained or lost (i.e., 1/4 A.sub.o V.sub.o) due to 
the cross-flow at station 1: 
EQU Q.sub.1f1 =3/4A.sub.o V.sub.o (10) 
EQU Q.sub.1f2 =5/4A.sub.o V.sub.o (11) 
Now, the velocities at station 2, can be computed by dividing by the areas 
at station 2: 
##EQU5## 
From (7), we then have, for the cross-flow: 
##EQU6## 
For a 25% cross-flow, Q.sup.'.sub.2 =(0.25) (1.25)A.sub.o V.sub.o, so: 
##EQU7## 
Similarly, to compute the total perforation area at station 3: 
EQU V.sub.3f1 =1.06(2/3)V.sub.o =0.71V.sub.o (16) 
EQU V.sub.3f2 =0.94(2)V.sub.o =1.88V.sub.o (17) 
EQU Q.sup.'.sub.3 =0.61A.sup.'.sub.3 V.sub.o .LAMBDA.3.01 (18) 
For a 25% cross-flow, Q.sup.'.sub.3 =(0.25) (1.06)A.sub.o V.sub.o, so: 
##EQU8## 
The perforation area at subsequent stations can be computed in the same 
manner. 
Referring to FIG. 4, there is shown a motionless mixer 200 in accordance 
with another embodiment of the invention. An outer pipe 210 defines the 
outside wall of an outer flow channel fo. A central pipe 250 is in the 
form of an undulating annulus. The pipe 250 serves as a common wall 
element between outer flow channel fo and an inner flow channel fi; i.e., 
it is the inside wall of outer flow channel fo and it is the outside wall 
of inner flow channel fi. An inner pipe 270, through which no fluid need 
flow in this embodiment, serves as the inside wall of the inner flow 
channel fi. It will be understood, however, that the inner pipe 270 can, 
if desired, be utilized as an auxiliary flow pipe or to carry heating or 
cooling fluid. As in the previous embodiment, a plurality of openings or 
perforations are located at about the peaks and valleys of the common wall 
member; i.e., at about the maximum and minimum of the undulating annulus 
250. The undulating annulus 250 may be held between pipes 210 and 270 by a 
spider mount (not shown) or other suitable mounting means. 
Referring to FIG. 7, there is shown a cross-sectional view of a motionless 
mixer 300 in accordance with still another embodiment of the invention. In 
the embodiment of FIG. 7, adjacent elongated undulating enclosures 301 and 
302 form flow channels f1 and f2. A common wall member 303 is flat in this 
embodiment. The outer wall members 304 and 305 have undulating shapes and 
are arranged so that the undulations of the two flow channels are in 
opposing relationship; i.e., flow channel f1 is restricted when flow 
channel f2 is enlarged, and vice versa. The common wall element 303 has 
perforations at positions corresponding to the peaks and valleys of the 
undulations, as shown in FIG. 7. In operation, fluids to be mixed are 
injected into inlet pipes 321 and 322, which communicate with flow 
channels f1 and f2, respectively. Mixed fluids are received at outlet pipe 
323. The opposing restrictions and enlargements of the flow channels cause 
mixing due to the venturi effect, as described in conjunction with 
previous embodiments. 
FIG. 8 is similar to FIG. 7, but in this case a mixer 400 has an undulating 
enclosure 401 and a non-undulating enclosure 402. Thus, only flow channel 
f1 undulates while flow channel f2 does not. However, mixing occurs due to 
enlargements and restrictions of f1 and the resultant cross-flow through 
perforations in common wall element 403. 
It will be understood that cylindrical versions of the FIG. 7 or FIG. 8 
embodiments (analagous to the FIG. 5 embodiment) could be implemented 
using one or more undulating annuli (of the type illustrated in FIG. 6) 
with no perforations, and a conventional cylindrical pipe, with 
perforations in the cylindrical pipe at positions corresponding to peaks 
and valleys of the indulations. 
There are various ways in which the apparatus of the present invention can 
be manufactured at relatively low cost. For example, with regard to the 
embodiment of FIG. 1, the undulating common wall element can be made as 
follows: The perforations are first punched in a flat metal sheet. The 
sheet is then passed through cammed rolling members adapted to form 
indentations in the sheet at the positions of the perforations; i.e., at 
the positions which are to become the peaks and valleys of the element. 
The sheet is then placed on a mandrel and buckled to obtain desired 
undulating shape. For the embodiments of FIGS. 7 or 8, the construction 
technique would be the same, except for the perforations. In the case of 
the embodiment of FIG. 4, the perforated sheet with indentations thereon 
is first roll welded in the manner in which tubing is conventionally 
formed, and then buckled from the ends to obtain the desired undulating 
annulus. The shapes described herein could alternatively be obtained using 
moldable materials in conjunction with known molding techniques.