Patent Publication Number: US-9839884-B2

Title: Method and apparatus for improved mixing of solid, liquid, or gaseous materials and combinations thereof

Description:
PRIORITY INFORMATION 
     The present application claims priority to U.S. Provisional Patent Application Ser. No. 61/702,465 of Regalbuto, et al. titled “Method and Apparatus for Improved Mixing of Solid, Liquid, or Gaseous Materials and Combinations Thereof” filed on Sep. 18, 2012, and to U.S. Provisional Patent Application Ser. No. 61/763,038 of Regalbuto, et al. titled “Method and Apparatus for Improved Mixing of Solid, Liquid, or Gaseous Materials and Combinations Thereof” filed on Feb. 11, 2013; the disclosures of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     When a reactor or mixing vessel uses a single impeller to agitate the fluid contents, a vortex is generally created. This vortex is inimical to proper mixing. In order to disrupt the formation of such a vortex, baffles have been included on the inside of the reactor/mixing vessel to prevent the formation of a vortex by disrupting the flow of the contents. Alternatively, scrapers could be associated with the mixing apparatus and inserted into the reactor/mixing vessel to prevent the formation of a vortex by disrupting the flow of the contents. Such scrapers can be stationary and/or rotating. 
     After prolonged use, however, deposits of materials can collect unevenly on the baffles. These deposits should be removed for consistent performance, leading to downtime and subsequent loss of production output and higher production costs. 
     Additionally, the use of baffles and/or scrapers requires higher torque from the mixing motor. Higher torque requires, in turn, larger and more expensive motors, resulting in higher capital costs as well as higher operating costs. This higher torque can also create enough force to cause the vessel to begin to rotate if not held in place, creating additional work and/or a dangerous environment. Similarly, the impellers can push up into a cowling (when present) that creates a suction force against the user, which can be particularly difficult to handle on a hand-held mixer. 
     As such, a need exists for a method and apparatus that allows for proper mixing of fluids without baffles, while still eliminating vortex formation in the reaction/mixing vessel and minimizing torque and power consumption. 
     SUMMARY 
     Objects and advantages of the invention will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the invention. 
     Mixer apparatus is generally provided that is configured to mix the contents of a vessel without the formation of a vortex. Methods are also generally provided for mixing a fluid within a mixing vessel using any of the presently described mixer apparatus, particularly without a baffle or scrapper. 
     In one embodiment, the mixer apparatus includes a rotational mechanism; a gearbox attached to the rotational mechanism; a first shaft attached to the gearbox; a second shaft attached to the gearbox; a first rotor configured to be rotated by the first shaft; and a second rotor configured to be rotated by the second shaft. The first shaft can be coaxial with the second shaft, and the gearbox can be configured to rotate the first shaft and the second shaft in opposite directions. In one particular embodiment, the first rotor and the second rotor are configured to be rotated in opposite directions. 
     In another embodiment, the mixer apparatus includes a rotational mechanism; a first gearbox attached to the rotational mechanism; a second gearbox attached to the rotational mechanism; a first shaft attached to the first gearbox; a second shaft attached to the second gearbox; a first rotor configured to rotated by the first shaft; and a second rotor configured to be rotated by the second shaft. The first shaft can be coaxial with the second shaft, and the first rotor and the second rotor can be configured to be rotated in opposite directions. 
     In yet another embodiment, the mixer apparatus includes a rotational mechanism; a gearbox attached to the rotational mechanism; a shaft attached to the gearbox; a first rotor configured to rotated by the shaft; and a second rotor configured to be rotated by the shaft, wherein the first rotor and the second rotor are configured to be rotated in the same direction. 
     Other features and aspects of the present invention are discussed in greater detail below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       A full and enabling disclosure of the present invention, including the best mode thereof to one skilled in the art, is set forth more particularly in the remainder of the specification, which includes reference to the accompanying figures, in which: 
         FIG. 1  shows an exemplary mixer apparatus utilizing contra-rotating rotors; 
         FIG. 2  shows a top view looking below the gearboxes of the exemplary mixer apparatus of  FIG. 1 ; 
         FIG. 3  shows another exemplary mixer apparatus utilizing contra-rotating rotors; 
         FIG. 4  shows another exemplary mixer apparatus, similar to that shown in  FIG. 1 , within a mixing vessel; 
         FIG. 5  shows an exemplary mixer apparatus having a single gearbox configured to rotate both rotors in opposite directions; 
         FIG. 6  shows an cut away of an exemplary gearbox of the exemplary mixer apparatus shown in  FIG. 5 ; 
         FIG. 7  shows a cut away of another exemplary gearbox of the exemplary mixer apparatus shown in  FIG. 5 ; 
         FIGS. 8A-8H  show diagrams of various configurations that are particularly suitable for mixing the contents of a reaction/mixing vessel; 
         FIGS. 9A and 9B  show alternative embodiments that include a hand-powered mixer, instead of a motor-powered mixer, as the rotational mechanism; 
         FIGS. 10A-10D  show a plot of the torque mixing study of comparative mixer apparatus having a single shaft with a single impeller, with and without a baffle present, performed according to the comparative examples; 
         FIGS. 11A-11D  show a plot of the torque mixing study of exemplary mixer apparatus having a single shaft with a dual impellers, with and without a baffle present, performed according to the examples; 
         FIG. 12  shows a plot of the torque mixing study of exemplary mixer apparatus having a contra-rotating shafts with a dual impellers performed according to the examples; and 
         FIG. 13  shows the power (in Watts, W) needed for uniform mixing for the nine examples in which uniform suspensions were observed. 
     
    
    
     Repeat use of reference characters in the present specification and drawings is intended to represent the same or analogous features or elements of the present invention. 
     DETAILED DESCRIPTION 
     Reference now will be made to the embodiments of the invention, one or more examples of which are set forth below. Each example is provided by way of an explanation of the invention, not as a limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as one embodiment can be used on another embodiment to yield still a further embodiment. Thus, it is intended that the present invention cover such modifications and variations as come within the scope of the appended claims and their equivalents. It is to be understood by one of ordinary skill in the art that the present discussion is a description of exemplary embodiments only, and is not intended as limiting the broader aspects of the present invention, which broader aspects are embodied exemplary constructions. 
     Apparatus and methods are generally provided for mixing the contents of a reaction/mixing vessel utilizing multiple rotors turned by a rotational mechanism (e.g., a motor, a push-operated lever, etc.). Various configurations are provided that utilize using opposing toroidal flow or matching toroidal flow, which can be created by contra-rotating rotors or dual rotors in conjunction with suitable rotor blades.  FIGS. 8A-8H  show diagrams of various configurations that are particularly suitable for mixing the contents of a reaction/mixing vessel. 
       FIG. 8A  shows an embodiment with opposing toroidal flow directed inward created by contra-rotating rotors. Conversely,  FIG. 8B  shows an embodiment with opposing toroidal flow directed outward created by contra-rotating rotors. 
       FIG. 8C  shows an embodiment with matching toroidal flow directed upward created by contra-rotating rotors. On the other hand,  FIG. 8D  shows an embodiment with matching toroidal flow directed downward created by contra-rotating rotors. 
       FIG. 8E  shows an embodiment with opposing toroidal flow directed inward created by dual-rotating rotors. To the contrary,  FIG. 8F  shows an embodiment with opposing toroidal flow directed outward created by dual-rotating rotors. 
       FIG. 8G  shows an embodiment with matching toroidal flow directed upward created by dual-rotating rotors. Conversely,  FIG. 8H  shows an embodiment with matching toroidal flow directed downward created by dual-rotating rotors. 
     In the embodiments shown in  FIGS. 8A-8H  and the above descriptions, the direction of rotation of both rotors in each embodiment, along with the angle of the respective blades, can be reversed. That is, referring to  FIG. 8A  as an example (viewed from the top), though the upper rotor is shown moving clock-wise while the lower rotor is shown moving counter clock-wise to achieve the opposing toroidal flow directed inward, it is understood that the opposing toroidal flow directed inward can be achieved by the upper rotor moving counter clock-wise while the lower rotor moves clock-wise and appropriately angling the respective rotor blades. Such an opposite rotational direction can be applied to each of the shown embodiments in  FIGS. 8A-8H . 
     Each of these configurations is discussed in greater detail in the following descriptions. 
     I. Opposing Toroidal Flow, Contra-Rotating Rotors 
     In one embodiment, apparatus and methods are generally provided for mixing the contents of a reaction/mixing vessel using opposing toroidal flow created by contra-rotating rotors. The mixing apparatus generally includes two coaxial shafts, one within another (e.g., an inner shaft and an outer shaft), rotating in opposite directions. Rotors with angled rotor blades are attached to each shaft in axial proximity to each other such that the axis of rotation of the two shafts is substantially aligned with the vertical axis of the reaction/mixing vessel (e.g., a cylindrical vessel). 
       FIGS. 1 and 2  show one particular embodiment of a mixer apparatus  10 . The mixer apparatus  10  generally includes a motor  12  (as the rotational mechanism) and a pair of gearboxes  14 ,  15 . The gearboxes  14 ,  15  are coupled to a pair of coaxial shafts  16 ,  17 . As shown, the outer shaft  16  defines a hollow center  18  where the inner shaft  17  is located. Thus, the inner shaft  17  is independently rotatable within the hollow center  18  of the outer shaft  16 . A lubricant (e.g., grease) can be included within the hollow center  18  of the outer shaft  16  to ensure minimal friction between the coaxial shafts  16 ,  17  during operation. As such, the inner shaft  17  can rotate opposite to the outer shaft  16  (i.e., one shaft rotates clockwise and the other shaft rotates counter-clockwise). 
     Although shown having two gearboxes  14 ,  15  in the embodiments of  FIGS. 1 and 3-4 , a single gearbox can be utilized to rotate the inner shaft  17  and the outer shaft  16  in opposite directions. For example,  FIG. 5  shows a single gearbox  14  that is configured to rotate both the inner shaft  17  and the outer shaft  16  in opposite directions. Thus, the second gearbox shown in  FIGS. 1 and 3-4  is optional, depending on the design of the motor and/or gearbox  14 . 
     In such an embodiment, the use of a single gearbox generally rotates the inner shaft  17  and the outer shaft  16  in opposite directions at a fixed speed ratio. In one particular embodiment, the use of a single gearbox generally rotates the inner shaft  17  and the outer shaft  16  in opposite directions at substantially the same speed. 
     Each of  FIGS. 6 and 7  show an exemplary gearbox  14  that is configured to rotate the inner shaft  17  and the outer shaft  16  in opposite directions. In these embodiments, the motor  12  rotates the motor shaft  60  in one direction. The first gear  62  contacts and rotates the transmission gear  64 . The transmission gear  64  in turn contacts and rotates the second gear  66  in an opposite direction of the first gear  62 . The second gear  66  is connected to the outer shaft  16  (which defines a hollow center  18  through which the inner shaft  17  extends). Thus, the outer shaft  16  rotates in an opposite direction than the inner shaft  17 . 
     As shown, the motor shaft  60  is connected to a first gear  62  and to the inner shaft  17 . However, it is to be understood that the motor shaft  60  could be connected to the outer shaft  16  in other embodiments. Likewise, the second gear  66  could be connected to the inner shaft  17 . 
     As known in the art, the first gear  62 , the transmission gear  64 , and/or the second gear  66  can have teeth or cogs, which mesh with a toothed/cogged of an adjacent gear in order to transmit torque. 
     No matter the particular configuration of the gearbox, each of the shafts  16 ,  17  are coupled to a rotor  20 ,  22 , respectively. Due to the counter-rotation of the shafts  16 ,  17 , the rotors  20 ,  22  are configured to rotate in opposite directions (i.e., contra-rotating). The rotors  20 ,  22  are shown vertically arranged, with the upper rotor  20  positioned closest to the gearboxes  14 ,  15  and above the lower rotor  22 . 
     The rotors  20 ,  22  are connected to a plurality of rotor blades  21 ,  23 , respectively. Although shown having four rotor blades  21 ,  23 , any suitable number of rotor blades  21 ,  23  can be attached to the rotors  20 ,  22  (e.g., about two blades to about eight blades). The rotor blades  21 ,  23  can be curved and/or angled to help force the contents of the vessel in the direction desired. As show, the rotors  20 ,  22  with the rotor blades  21 ,  23  can be described as a propeller. In another embodiment, the rotors  20 ,  22  with the rotor blades  21 ,  23  can be an impeller with a casing (not shown) surrounding the outer edges of the rotor blades  21 ,  23 . 
     The rotational speed of each rotor  20 ,  22  (and their rotor blades  21 ,  23 ) and the speed ratio between the two rotors  20 ,  22  can be controlled to create the desired mixing motion of the contents of the vessel. For example, in one embodiment, the rotors  20 ,  22  are rotating at the same speed, but in opposite directions. In this embodiment, if the rotors  20 ,  22  and blades  21 ,  23  are substantially the same size, the contra-rotating rotors  20 ,  22  can serve to substantially eliminate torque applied to the contents/vessel during use. In alternative embodiments, the rotors  20 ,  22  are rotating at differing speeds and in opposite directions. 
     In the embodiment of  FIGS. 1 and 2 , the angle of the blades and/or rotation direction of the upper rotor are such that the contents of the vessel are directed downward (toward the lower rotor), while the angle of the blades and/or rotation direction of the lower rotor are such that the contents are directed upward (toward the upper rotor). Thus, in this embodiment, the rotors are configured to direct the contents toward each other. 
     In an alternative shown in  FIG. 3 , the angle of the blades and/or rotation direction of the upper rotor are such that the contents of the vessel are directed upward (away from the lower rotor), while the angle of the blades and/or rotation direction of the lower rotor are such that the contents are directed downward (away from the upper rotor). Thus, in this embodiment, the rotors are configured to direct the contents away each other. 
     The direction of rotation can be reversed in both the embodiments shown in  FIGS. 1 and 3 , respectively. For example,  FIG. 8A  shows an exemplary embodiment having the opposite rotational direction of both the upper rotor  20  and the lower rotor  22 , respectively, than that shown in  FIG. 1 , along with suitably angled rotor blades  21 ,  23 . Such a reversed embodiment can be applied to each of the embodiments shown in  FIGS. 8A-8H . 
     Additional variables are associated with the design of the rotor blades  21 ,  23  and can be adjusted to achieve the desired mixing motion of the contents of the vessel, such as their angle, their cross-sectional shape, their aspect ratio, etc. Likewise, the solidity (defined as the ratio of the total projected area of the blades  21 ,  23  divided by the area swept by the rotor  20 ,  22 /blades  21 ,  23 ) of the rotors  20 ,  22  can be controlled as desired. 
     The spacing between the upper rotor  20  and the lower rotor  22  can also be adjusted as desired. In most embodiments, however, distance between the rotors  20 ,  22  (referred to as D R  in  FIGS. 1 and 3 ) can be less than the average length (referred to as L B  in  FIGS. 1 and 3 ) of the individual rotor blades  21  and/or  23  on the rotors  20 ,  22  respectively. For example, the distance D R  can be about 10% to about 50% of the average length L B  of the rotor blades  21  and/or  23 . As such, the rotor blades  21 ,  23  affect a relatively wide diameter within the mixing vessel, while mixing within a relatively small space between the rotors  20 ,  22 . 
       FIG. 4  shows an exemplary mixer apparatus  10 , similar to that shown in  FIG. 1 , utilized to mix the contents  42  of a mixing vessel  40 . The mixing vessel  40  has an inner surface  41  that is substantially smooth and/or free from baffles. Although shown in a liquid form, it is understood that the contents  42  can be a solid (e.g., a plurality of solid particles), a liquid, a gas, or a mixture thereof. 
     In the embodiment of  FIG. 4 , handles  30  are attached to the motor housing  13  of the motor  12  to allow a user to manually control the mixer apparatus  10  as desired. In other embodiments, the mixing apparatus  10  can be fixed in place (e.g., in a manufacturing setting). Also in this embodiment, an extension  32  is positioned below the lower rotor  22  such that the lower rotor  22  is protected from contacting the bottom surface of the vessel  40 . Although not shown, a casing can be positioned around the ends of the rotor blades  21 ,  23  and attached to the mixing apparatus  12  to prevent the edges of the blades  21 ,  23  from contacting the inner surface  41  of the vessel  40 . 
     The shaft length L S  of the shafts  16 ,  17 , measured from the gearboxes  14 ,  15  to the upper rotor  20 , can be any suitable length depending on the size of the vessel  40  and the depth of the contents  42 . Generally, however, the shaft length L S  can be greater than the average length L B  of the rotor blades  21  and/or  23  in most embodiments. 
     II. Parallel Toroidal Flow, Contra-Rotating Rotors 
     In another embodiment, apparatus and methods are generally provided for mixing the contents of a reaction/mixing vessel using similar (e.g., parallel) toroidal flow created by contra-rotating rotors. As discussed above, the mixing apparatus generally includes two coaxial shafts, one within another (e.g., an inner shaft and an outer shaft), rotating in opposite directions. Rotors with angled rotor blades are attached to each shaft in axial proximity to each other such that the axis of rotation of the two shafts is substantially aligned with the vertical axis of the reaction/mixing vessel (e.g., a cylindrical vessel). 
     Referring to  FIG. 8C , an embodiment is shown having matching toroidal flow directed upward created by contra-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . On the other hand,  FIG. 8D  shows an embodiment with matching toroidal flow directed downward created by contra-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . 
     III. Opposing Toroidal Flow, Dual Rotors 
     In yet another embodiment, apparatus and methods are generally provided for mixing the contents of a reaction/mixing vessel using opposing toroidal flow created by dual rotors rotating in the same direction (e.g., matching-rotating rotors).  FIG. 8E  shows an embodiment with opposing toroidal flow directed inward created by dual-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . To the contrary,  FIG. 8F  shows an embodiment with opposing toroidal flow directed outward created by dual-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . 
     In such an embodiment, the mixing apparatus generally can includes two coaxial shafts (as shown in  FIGS. 1-7 ), one within another, rotating in the same direction. As such, the rotors  20 ,  22  can be rotated at the same or different speeds. Alternatively, the rotors  20 ,  22  can be attached to a single shaft  16 , since their rotation is in the same direction. 
     IV. Parallel Toroidal Flow, Dual Rotors 
     In yet another embodiment, apparatus and methods are generally provided for mixing the contents of a reaction/mixing vessel using matching (e.g., parallel) toroidal flow created by dual rotors rotating in the same direction (e.g., matching-rotating rotors).  FIG. 8G  shows an embodiment with matching toroidal flow directed upward created by dual-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . Conversely,  FIG. 8H  shows an embodiment with matching toroidal flow directed downward created by dual-rotating rotors  20 ,  22  and suitably angled blades  21 ,  23 . 
     In such an embodiment, the mixing apparatus generally can includes two coaxial shafts (as shown in  FIGS. 1-7 ), one within another, rotating in the same direction. As such, the rotors  20 ,  22  can be rotated at the same or different speeds. Alternatively, the rotors  20 ,  22  can be attached to a single shaft  16 , since their rotation is in the same direction. 
     V. Manual Operation 
       FIGS. 9A and 9B  show an alternative embodiment that includes a hand-powered mixer, instead of a motor-powered mixer, as the rotational mechanism. In this embodiment, the push-operated mechanism  90  powers the rotation of the shafts  16  and/or  17  on the down stroke and/or the return stroke (powered by the return spring) of the handle shaft  92  within the housing  94 . For example, the user can push down on the handle  96 , causing the handle shaft  92  to slide into the housing  94 . As the handle shaft  92  enters the housing  94 , the internal screw mechanism  98  is rotated. 
     The rotation of the internal screw mechanism  98  causes, in conjunction with the workings of the gearbox  14 , rotation of shafts  16  and/or  17  as described above with respect to  FIGS. 1-8  (i.e., substituting the motor  12  for the push-operated mechanism  90 ). As such, any combination of rotation of the upper rotor  20  and lower rotor  22  can be utilized (e.g., as shown in  FIGS. 8A-8H ). 
     COMPARATIVE EXAMPLES 
     For comparison, four different mixer apparatus were made with each mixer apparatus having a single impeller. 
     Comparative Example 1 
     A mixer apparatus was made with a single impeller with rotor blades situated 8 inches from the tank bottom that, in use, are configured to force fluid flow up.  FIG. 10A  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. A uniform suspension was not observed at any rpm or torque, with or without baffles present. 
     Comparative Example 2 
     A mixer apparatus was made with a single impeller with rotor blades situated 4 inches from the tank bottom that, in use, are configured to force fluid flow up.  FIG. 10B  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 550 rpm and a torque of 9 N-cm (circled in  FIG. 10B ). 
     Comparative Example 3 
     A mixer apparatus was made with a single impeller with rotor blades situated 4 inches from the tank bottom that, in use, are configured to force fluid flow down.  FIG. 100  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 550 rpm and a torque of 10 N-cm (circled in  FIG. 10C ). 
     Comparative Example 4 
     A mixer apparatus was made with a single impeller with rotor blades situated 8 inches from the tank bottom that, in use, are configured to force fluid flow down.  FIG. 10D  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 550 rpm and a torque of 8 N-cm (circled in  FIG. 10D ). 
     EXAMPLES 
     Mixer apparatus were made having various two rotor configurations (i.e., dual impellers).  FIGS. 11A-11D  show a plot of the torque mixing study of exemplary mixer apparatus having a single shaft with dual impellers, with and without a baffle present, performed according to the examples.  FIG. 12  shows a plot of the torque mixing study of exemplary mixer apparatus having contra-rotating shafts with dual impellers performed according to the examples. 
     Example 1 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in the same direction (e.g., a single shaft). In use, the top impeller was configured to force fluid flow down (toward the bottom impeller), and the bottom impeller was configured to force fluid flow up (toward the top impeller).  FIG. 8E  shows a general schematic of this dual impellers configuration. 
       FIG. 11A  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 450 rpm and a torque of 12.5 N-cm (circled in  FIG. 11A ). 
     Example 2 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in the same direction (e.g., a single shaft). In use, the top impeller was configured to force fluid flow down (toward the bottom impeller), and the bottom impeller was configured to force fluid flow down (away from the top impeller).  FIG. 8H  shows a general schematic of this dual impellers configuration. 
       FIG. 11B  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 400 rpm and a torque of 8 N-cm (circled in  FIG. 11B ). 
     Example 3 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in the same direction (e.g., a single shaft). In use, the top impeller was configured to force fluid flow up (away from the bottom impeller), and the bottom impeller was configured to force fluid flow down (away the top impeller).  FIG. 8F  shows a general schematic of this dual impellers configuration. 
       FIG. 11C  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. The minimum rpm for a uniform suspension was observed with baffles at 450 rpm and a torque of 12 N-cm (circled in  FIG. 11C ). 
     Example 4 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in the same direction (e.g., a single shaft). In use, the top impeller was configured to force fluid flow up (away from the bottom impeller), and the bottom impeller was configured to force fluid flow up (toward the top impeller).  FIG. 8G  shows a general schematic of this dual impellers configuration. 
       FIG. 11D  shows the amount of torque created at various rotations per minute (RPM) of the impeller, with baffles present and absent in the mixing vessel. A uniform suspension was not observed at any rpm or torque, with or without baffles. 
     Example 5 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in opposite directions (e.g., a dual shaft). In use, the top impeller was configured to force fluid flow up (away from the bottom impeller), and the bottom impeller was configured to force fluid flow down (away from the top impeller). No baffles were used.  FIG. 8B  shows a general schematic of this dual impellers configuration. 
       FIG. 12  shows the amount of torque created at various rotations per minute (RPM) of the impeller, represented by the solid line with diamond data points. The minimum rpm for a uniform suspension was observed at 350 rpm and a torque of 10 N-cm (indicated in  FIG. 12 ). 
     Example 6 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in opposite directions (e.g., a dual shaft). In use, the top impeller was configured to force fluid flow down (toward the bottom impeller), and the bottom impeller was configured to force fluid flow up (toward the top impeller). No baffles were used.  FIG. 8A  shows a general schematic of this dual impellers configuration. 
       FIG. 12  shows the amount of torque created at various rotations per minute (RPM) of the impeller, represented by the solid line with square data points. The minimum rpm for a uniform suspension was observed at 350 rpm and a torque of 11 N-cm (indicated in  FIG. 12 ). 
     Example 7 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in opposite directions (e.g., a dual shaft). In use, the top impeller was configured to force fluid flow down (toward the bottom impeller), and the bottom impeller was configured to force fluid flow down (away the top impeller). No baffles were used.  FIG. 8D  shows a general schematic of this dual impellers configuration. 
       FIG. 12  shows the amount of torque created at various rotations per minute (RPM) of the impeller, represented by the solid line with triangle data points. The minimum rpm for a uniform suspension was observed at 300 rpm and a torque of 9 N-cm (indicated in  FIG. 12 ). 
     Example 8 
     A mixer apparatus was made with dual impellers situated 4 and 8 inches from the tank bottom that are aligned with one over the other and configured to rotate in opposite directions (e.g., a dual shaft). In use, the top impeller was configured to force fluid flow up (away from the bottom impeller), and the bottom impeller was configured to force fluid flow up (toward the top impeller). No baffles were used.  FIG. 8C  shows a general schematic of this dual impellers configuration. 
       FIG. 12  shows the amount of torque created at various rotations per minute (RPM) of the impeller, represented by the solid line with “X” data points. A uniform suspension was not observed at any rpm or torque. 
     Summary of Examples 
     The product of RPM and torque is power. The power (in Watts, W) needed for uniform mixing for the nine cases in which uniform suspensions were observed is summarized in  FIG. 13 . In general, the power required by the contra-rotating impellers was less than that for the single or dual impellers on one shaft. The lowest value of required power, 0.45 W for the contra down/down configuration, was 15% lower than the minimum power (0.53 W) of the single shaft configurations (dual down/down). 
     These and other modifications and variations to the present invention may be practiced by those of ordinary skill in the art, without departing from the spirit and scope of the present invention, which is more particularly set forth in the appended claims. In addition, it should be understood the aspects of the various embodiments may be interchanged both in whole or in part. Furthermore, those of ordinary skill in the art will appreciate that the foregoing description is by way of example only, and is not intended to limit the invention so further described in the appended claims.