Abstract:
A shaker movement permits an arbitrary path of motion in a shaker&#39;s shaking action. The shaker movement comprises independent control over the “X” and “Y” directions of the shaking actions by a pair of track assemblies, each track assembly comprising a pair of fixed rods and a pair of sliding rods that are interconnected with each other in a rectangular, grid-like pattern. Motion in both directions can be driven by a single motor utilizing independent pulley-and-belt systems or by two synchronized motors which are connected to a sliding rod of each track assembly. By altering the relative amplitude, phase angle, and frequency between the “X” and “Y” directions, the shaking action can follow a desired path. The shaker path can be varied from the traditional circular orbital motion or linear motion, to a new group of shaking patterns in which the direction of the shaking movement can reverse. The new patterns of shaker movement cause the liquid being shaken to be more thoroughly mixed, with less power input, and at a lower angular frequency than is practical with traditional paths of motion. This results in higher rates of gas transfer to and from the liquid, resulting in greater growth of a bacterial culture, and for higher rates of mass transfer at equivalent levels of energy input.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to shaking devices for flasks and other containers holding liquid mixtures which are used in biological and other applications, and more particularly to reversing rotatory shakers. 
     2. Description of the Prior Art 
     Shakers have been employed for many years for a variety of applications in the chemical, biological, metallurgical, and other industries. Shakers impart a mixing motion to a liquid which is contained in one or more flasks. The flasks, usually made of glass or a polymer, are attached to a platform on the top of the shaker. Because the flasks are so located, they are often referred to as “shake flasks”. 
     Shakers are sometimes enclosed in an environmental chamber held at a controlled temperature. The chamber often becomes an integral part of the shaker, but the device may also be placed in a controlled temperature room. Special lights may be incorporated in the shaker chamber when photosynthesis is desired. 
     One common application of shakers is to ensure that all components of the liquid are in intimate contact and are well mixed. Another common application is to effectuate mass transfer between liquid and gas by maximizing the boundary contact between these components. For this use, the shake flasks usually comprise Erlenmeyer flasks or some variant of Erlenmeyer flasks. The flask openings are covered with any of a variety of well-known closures which permit free exchange of gases between the flask and the ambient environment. For example, many biological applications require the transfer of oxygen from air to a liquid medium to encourage the growth of microorganisms. Simultaneously, carbon dioxide, a product of metabolism, must be removed from the liquid to prevent accumulation of this gas and inhibition of the growth process. 
     Prior art shakers accomplish these gas exchanges by imparting an external force to the flask, which in turn creates a vigorous shaking action in the liquid. Most commonly, the shaking action results from the shaker platform being moved in a circular pattern. Increasing the energy applied to the shaker platform increases the rotational speed of the platform and the vigorousness of the shaking action. Regardless, no matter how vigorous the shaking action, the entire body of fluid in the flask still rotates in a single angular direction around the center axis of the flask. Consequently, the motion of one element of liquid relative to another is poor. In fact, due to inertial and frictional considerations, the entire body of fluid tends to rotate as a unit on the walls of the flask. Thus, mixing is accomplished entirely by viscous action, and at high fluid viscosities, the quality of mixing may become quite poor. In short, large amounts of energy must be expended to realize the desired rate of gas exchange in a rotatory shaker. 
     Various tactics are currently employed to overcome this mixing limitation. One approach involves placing indentations on the walls of the flasks; another involves placing baffles in the flasks. These tactics are often helpful, but they do not solve the underlying problem, which is the mixing limitations inherent in the shaker&#39;s basic pattern of motion. 
     This mixing limitation has been addressed by utilizing a shaker platform motion that is a simple back-and-forth or reciprocating action. Reciprocating shakers can sometimes yield good mixing. However, these reciprocating designs suffer from excessive splashing even at relatively low shaker rates. This splashing is often unacceptable because it results in excessive spillage (from open containers) or contamination (from touching the stopper in closed containers). 
     Furthermore, there exists a fundamental limitation in these prior art shaker designs that cannot always be overcome either by more vigorous rotatory shaking or tolerating the inherent spillage/contamination in reciprocating shaking. In some instances, it is not possible to exchange gases rapidly enough, and the flask becomes “mass transfer limited”. Such operations are not reproducible. Thus, they may yield unreliable results. 
     An improved method of shaking which would overcome this and other problems associated with present shaker designs is desirable. 
     In short, prior art shaker designs offer either a circular motion or a linear reciprocating motion. The motion is always in a plane, and the plane is usually, but not necessarily, horizontal. All current designs frequently run at the limits of their capabilities. 
     SUMMARY OF THE INVENTION 
     A primary object of the instant invention is a rotatory shaker movement that permits shakers to utilize shaking motions other than circular or linear reciprocating. 
     Another object of this invention is a rotatory shaker movement that allows for more rapid mass transfer rates, thus overcoming “mass transfer limited” problems. 
     Another object of this invention is a rotatory shaker movement that produces better mixing at lower inputted energy levels. 
     Another object of this invention is a rotatory shaker movement that accommodates changeable shaking motions. 
     In short, this invention is a rotatory shaker movement which independently controls the horizontal and vertical motions of a shaker platform. The combination of these independent movements can produce an arbitrary path of motion in the shaking action, including, if desired the traditional circular and linear reciprocating ones. Thus, the shaking action can be optimized for each type of mixing application. The liquid being shaken can be more thoroughly mixed, with less power input, and at a lower angular frequency than is practical with prior art shakers. Also, this invention allows higher rates of mass transfer at equivalent levels of energy input. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 is a top view of the reversing rotatory shaker movement. 
     FIG. 2 is a cross-sectional view of the reversing rotatory shaker movement shown in FIG. 1 along line  2 — 2 . 
     FIG. 3 is a cross-sectional view of the reversing rotatory shaker movement shown in FIG. 1 along line  3 — 3 . 
     FIG. 4 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 1:1—x=sin(ωt), y=cos(ωt). 
     FIG. 5 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 2:3—x=sin(ωt), y=cos(3ωt/2). 
     FIG. 6 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 3:2—x=sin(ωt), y=cos(2ωt/3). 
     FIG. 7 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 2:1—x=sin(ωt), y=cos(ωt/2). 
     FIG. 8 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 3:1—x=sin(ωt), y=cos(ωt/3). 
     FIG. 9 is a representative plot of a motion path producible by the reversing rotatory shaker movement where the ratio of frequencies is 1:2—x=sin(ωt), y=cos(2ωt). 
     FIG. 10 is a top view of the reversing rotatory shaker movement comprising a system of gears. 
     FIG. 11 is a top view of the reversing rotatory shaker movement comprising a system of cams and slot plates. 
     FIG. 12 is a top view of the reversing rotatory shaker movement comprising a system of cams and springs. 
    
    
     DESCRIPTION OF PREFERRED EMBODIMENT 
     In its preferred embodiment, the rotatory shaker movement  1  for use inside a shaker frame  2  comprises two linear motion track assemblies: a first linear motion track assembly  11  and a second linear motion track assembly  12 . The two track assemblies  11 ,  12  are co-planar, but oriented orthogonal, to each other. 
     Each track  11 ,  12  is preferably manufactured from hardened steel cylindrical rods  111 ,  112 ,  113 ,  114 ,  121 ,  122 ,  123 ,  124  to prevent rod bending and length changes that can effect the operation of the shaker movement. 
     The first track  11  has two fixed rods  111 ,  112  which are secured to the frame of the shaker  2  preferably by large socket head screws  21  made of steel. This track  11  also has two sliding rods  113 ,  114  which are oriented orthogonally to the fixed rods  111 ,  112  with one end attached to each of the fixed rods via a slider block  115 . The slider block  115  comprises a structure made of aluminum having an opening the diameter of which is larger than the outer diameter of the fixed rods  111 ,  112 . The opening inside the slider block  115  has a bushing  116  made from a durable, but low-friction substance to provide a tight fit around the fixed rods  111 ,  112  but permitting the sliding rods  113 ,  114  to slide with minimal force along the fixed rods  111 ,  112 . Preferably, the bushing  116  is one of the well-known UHMW polyethylenes (ultra-high molecular weight) or similar low-friction polymer. Alternatively, a linear ball bearing structure may be used as the low-friction liner; linear ball bearing use is well known in the prior art. Thus, the sliding rods  113 ,  114  slide along the fixed rods  111 ,  112  easily and with minimal shimmying. Hereinafter, the direction of movement of the sliding rods  113 ,  114  of this first track  11  will be referred to as the “X” direction. 
     The “X” direction motion is controlled by a crank mechanism  13 . The crank mechanism  13  is driven by a single variable speed DC motor  15  via a system of pulleys and belts. The motor  15  has a metal drive shaft timing pulley  151  rigidly connected to the motor&#39;s drive shaft. A metal crank timing pulley  131  is rotatably connected to the bottom of the shaker  2 . The drive shaft timing pulley  151  is connected to the crank timing pulley  131  via an elastomer timing belt  132 . Preferably, crank timing pulley  131  has a diameter twice that of the drive shaft timing pulley  151 . 
     The crank timing pulley  131  is connected to an aluminum crank  133  via a well-known slot-and-key combination  134 . The crank  133  is further pinned to an aluminum connecting rod  135 . The slot-and-key  134  allows for variable positioning of the crank  133  to adjust the angle formed between the crank  133  and the connecting rod  135 . The connecting rod  135  is pinned to a clamping mechanism  136 ; the clamping mechanism  136  surrounds and is frictionally attached to a portion of sliding rod  114 ; such frictional attachments are well-known in the prior art. 
     The second track  12  also has two fixed rods  121 ,  122  which are threaded at all ends and two sliding rods  123 ,  124  oriented orthogonally to the fixed rods  121 ,  122 . The fixed rods  121 ,  122  pass through circular openings  127  in the sliding rods  123 ,  124 , and are secured to these sliding rods  123 ,  124  preferably by steel hex nuts  128 . This track  12  also has two sliding rods  123 ,  124  which are oriented orthogonally to the first track sliding rods  113 ,  114  with one end attached to each of these sliding rods  113 ,  114  via a slider block structure  125 . These slider blocks  125  are constructed similarly to slider blocks  115 , with a similar low-friction bushing  126 . Thus, the second track sliding rods  123 ,  124  slide along the first track slider rods  113 ,  114  easily and with minimal shimmying in a direction orthogonal to the “X” direction. Hereinafter, the direction of movement of the sliding rods  123 ,  124  of this second track  12  will be referred to as the “Y” direction. 
     The “Y” direction motion is also controlled by a crank mechanism  14 . The crank mechanism  14  is driven by the same motor  15  directly off the drive shaft timing pulley  151 . The drive shaft timing pulley  151  is connected to an aluminum crank  143  via a well-known slot-and-key combination  144 . The crank  143  is further pinned to an aluminum connecting rod  145 . The slot-and-key  144  allows for variable positioning of the crank  143  to adjust the angle formed between the crank  143  and the connecting rod  145 . The connecting rod  145  is pinned to directly to sliding rod  111 . 
     Each of the slider blocks  125  has in its top surface a platform hole  129 , a threaded screw hole to permit secure attachment of a flat, top-mounted shaker platform via screws. To further accommodate such attachment, the slider blocks  125  are preferably share common, flat top surfaces with sliding rods  123 ,  124 ; furthermore, the slider blocks  125  may be integral to sliding rods  123 ,  124 . 
     In use, the desired shaker motion is first described utilizing the well-known description of a path in a plane by specifying an “X” coordinate position and a “Y” coordinate position as a function of “T”, the time. Completely arbitrary motion can be achieved by controlling amplitude, phase angle, and frequency. (The subtractive difference between the magnitude of angles  136 ,  146  when the “X”-direction motion is at one extreme of its travel is commonly known as the “phase angle”.) The preferred embodiment, however, utilizes paths that result from altering the frequency but having a phase angle of π/2 radians (90°) and restricting the amplitude in each direction as a function of time to a sinusoidal waveform of fixed maximum amplitude, which is the same in the “X” and “Y” directions. Preferably, the frequencies of motion in each direction are expressed as a ratio of integers; but obviously, other ratios are possible. It can be easily seen that in the special case X=0 or Y=0 (movement in one direction not changing with time), the motion degenerates to simple translational mode. In the special case where X and Y have equal amplitudes and equal frequencies, the motion follows a circular path. FIGS. 4 through 9, inclusive, illustrate some sample motion patterns producible by the reversing rotatory shaker movement. 
     Illustratively, to produce the motion described by X=sin(ωt), Y=cos(ωt/2) (see FIG.  7 ), the angles  136 ,  146  respectively between crank  133  and connecting rod  135  and crank  143  and connecting rod  145  are set so that the connecting rods  135 ,  145  are out of phase by exactly π/2 radians (90°) when the “X” direction motion is at one extreme of its travel (phase angle of π/2 radians). This implementation will result in the “figure- 8 ” motion shown in FIG.  7 . 
     Next, the motor  15  is connected to a power source, typically commutated AC line voltage and a well-known motor controller which allows for reading and adjusting the motor speed. A shaker platform made of plastic or lightweight aluminum is connected to the top of the movement  1  by four screws inserted into the platform holes  129 . 
     The motor  15  is then activated, thereby turning the drive shaft timing pulley  151 . This timing pulley  151  in turn directly drives crank mechanism  14 , which moves the second track assembly  12  reciprocatingly in the “X” direction, and via the timing belt  132 , drives crank mechanism  13 , which drive the first track assembly  11  reciprocatingly in the “Y” direction. Because of the 1:2 relationship between the timing pulley diameters, the “X” direction movement occurs at frequency ω, the “Y” direction movement at frequency ω/2, or a frequency ratio of 2:1. 
     Altering the phase angle by changing angles  136 ,  146  results in a change in the path shape. Also, altering the relative sizes of the diameters of the timing pulleys  131 ,  151  results in changing the relative frequencies of the “X” and “Y” motions, thereby producing a change in the path shape. 
     Further variation of the shaker motion of the device could be obtained by varying the relative lengths of the cranks  133 ,  143 , thereby changing the relative amplitudes of the translational motions along the tracks  11 ,  12 , and thus changing the relative amplitudes of the “X” and “Y” motions. As the amplitude ratio becomes very large, the motion approaches purely linear in the direction with the larger amplitude (the X=0 or Y=0 described above). 
     The shaker movement  1  is then incorporated into a shaker setup that utilizes the present standard shaker equipment including prior art shaker enclosures, controls, platform, and shake flasks. The flasks containing liquid to be mixed are placed on the shaker platform. The shaker is activated at the desired speed and let run for the desired length of time. Once the shaker setup is assembled incorporating the instant invention, use of the shaker is the same as in prior art shakers. 
     An embodiment of the present invention shown in FIG. 10 comprises a shaker movement  500  in which the cranks are driven by a system of gears. A metal drive gear  171  having a plurality of teeth  172  on its outer surface is rigidly mounted on the drive shaft  152  of motor  15 . A metal driven gear  181  having a plurality of teeth  182  is rotatably connected to the bottom of the shaker  2 . The drive gear  171  and driven gear  181  are positioned such that their teeth engage and drive the shaker movement. Preferably, the pitch diameter of driven gear  181  is twice that of drive gear  171 . Another embodiment comprises a system of cams and slot plates to drive the shaker movement  600  (FIG.  11 ). Rod timing pulley  210  and cam  212  are rotatably mounted on a shaft  214  rotatably connected to the bottom of shaker  2 . Cam  202  is mounted on the drive shaft  152  of motor  15 . Shaft timing pulley  151 , mounted on drive shaft  152  of motor  15 , is connected to rod timing pulley  210  via an elastomer timing belt  132 . Slot plate  204  is attached to cam  202  via pin  208 . Slot plate  204  contains a central slot  206  which is disposed around pin  208 , such that slot plate  204  slides along pin  208 . 
     Slot plate  216  contains a central slot  218  disposed around pin  220 , such that slot plate  216  slides along pin  220 . Pin  220  is rigidly attached to cam  202 . 
     The rotation of cam  202  causes slot plate  204  to slide along pin  206 , cam  202  contacting sliding rod  124 , and cam  202  thereby driving sliding rod  124  in the “Y” direction. Belt  132  drives rod timing pulley  210  and cam  212 . The rotation of cam  212  causes slot plate  216  to slide along pin  220 , cam  212  contacting sliding rod  113 , and cam  212  driving sliding rod  113  in the “X” direction. Cams  202  and  212  can be similar, and are offset by N/2 where N is the diameter of the shaker orbit. 
     A further embodiment comprises a system of cams and springs to control shaker movement  700  (FIG.  12 ). Cam  302  is rigidly mounted on the drive shaft  152  of motor  15 . A coiled return spring  304  is disposed around an end of each of sliding rods  113  and  114  between slider blocks  115  and  125 , respectively. A second pair of coiled return springs  306  is disposed around an end of fixed rods  111  and  112 , between slider block  115  and shaker frame  2 . 
     Block  320  is rigidly mounted on rod  113  so that they will move as one unit. Rod timing pulley  310  and cam  312  are rotatably mounted on shaft  314 . Cam  312  makes frictional contact with block  320 . Shaft timing pulley  151  is mounted on drive shaft  152  of motor  15 . Drive shaft timing pulley  151  is connected to rod timing pulley  310  via an elastomer timing belt  132 . The rotation of cam  302  causes it to contact sliding rod  124 , and to urge bushings  126  against springs  304 , thereby driving the shaker movement in the “Y” direction. Springs  304  become compressed during the urging of the shaker movement in the “Y” direction, and as cam  302  rotates away from sliding rod  124  springs  304  decompress and cause sliding rod  124  to return to its prior position. Belt  132  drives rod timing pulley  310  and cam  312 . The rotation of cam  312  causes cam  312  to contact block  320 , and to urge bushings  116  against springs  306 , thereby driving the shaker movement in the “X” direction. Springs  306  become compressed during the urging of the shaker movement in the “X” direction, and as cam  312  rotates away from block  320  and sliding rod  113  springs  306  decompress and cause sliding rod  113  to return to its prior position. Cams  302  and  312  are similar, and are offset by N/2, where N is the diameter of the shaker orbit. 
     All of these paths result in a reversal of the direction of motion in the X,Y plane. The sense of the motion alternates repeatedly between clockwise and counterclockwise. Periodic reversal of the direction of motion forces the liquid in the flasks on the shaker platform to undergo an abrupt change of velocity relative to the flask in which it is contained. The outcome is higher shear forces in the liquid, which leads to better mixing. On average, each element of liquid moves from the surface to the interior of the liquid more readily than with prior art shakers. The higher shear forces also encourage each liquid element to break up and recombine with other elements more easily. Thus, there is improved mixing, increased turbulence, and superior gas-to-liquid mass transfer. 
     SAMPLE EXPERIMENTAL RESULTS 
     The results of using this invention were compared against a prior art conventional rotary movement shaker growing a strain of  Bacillus subtilis . This organism has a relatively high demand for oxygen. The experimental conditions were: 
       Bacillus subtilis  sp was used. 
     Concentrations were 50 ml of media in each 250 ml flask. 
     All flasks were fitted with cotton plugs. 
     The optical density of samples were measured with 1:10 dilution. 
     Ambient temperature was maintained at 25° C. 
     Experiment 1 
     Inoculum—5 ml of Washed Slant in Each Flask 
     In this experiment, both shakers were running at the same speed. 
     
       
         
               
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 Optical Density @ 590 nm 
                   
               
             
          
           
               
                   
                 Reversing 
                 Prior Art Rotary 
               
               
                 Time (Hours) 
                 Shaker (200 RPM) 
                 Shaker (200 RPM) 
               
               
                   
               
             
          
           
               
                 0 
                 0.2 
                 0.2 
               
               
                 14 
                 3.35 
                 1.25 
               
               
                 21 
                 6.4 
                 1.75 
               
               
                   
               
             
          
         
       
     
     Experiment 2 
     Inoculum—5% From Actively Growing Flask 
     In this experiment the prior art shaker was running at a higher rate than the shaker incorporating the instant invention. 
     
       
         
               
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 Optical Density @ 590 nm 
                   
               
             
          
           
               
                   
                 Reversing 
                 Prior Art Rotary 
               
               
                 Time (Hours) 
                 Shaker (200 RPM) 
                 Shaker (200 RPM) 
               
               
                   
               
             
          
           
               
                 0 
                 0.2 
                 0.2 
               
               
                 4 
                 2.69 
                 1.28 
               
               
                 6 
                 6.02 
                 2.52 
               
               
                 8 
                 6.78 
                 3.69 
               
               
                 10 
                 8.45 
                 4.1 
               
               
                 12 
                 9.75 
                 4.16 
               
               
                 14 
                 11.0 
                 4.6 
               
               
                 18 
                 11.5 
                 4.9 
               
               
                   
               
             
          
         
       
     
     Experiment 3 
     Inoculum—10% From Actively Growing Flask 
     In this experiment, the rate of shaking in the prior art shaker was higher than the previous experiment while the shaker setup incorporating the instant invention was kept at the same shaking rate. The inoculum was also increased to 10%. 
     
       
         
               
               
               
             
               
               
               
             
               
               
               
             
           
               
                   
                   
               
               
                   
                 Optical Density @ 590 nm 
                   
               
             
          
           
               
                   
                 Reversing 
                 Prior Art Rotary 
               
               
                 Time (Hours) 
                 Shaker (200 RPM) 
                 Shaker (200 RPM) 
               
               
                   
               
             
          
           
               
                 0 
                 0.2 
                 0.2 
               
               
                 2 
                 0.4 
                 0.31 
               
               
                 4 
                 0.7 
                 0.4 
               
               
                 6.5 
                 15.0 
                 12.0 
               
               
                 8 
                 25.0 
                 15.0 
               
               
                   
               
             
          
         
       
     
     Although this invention has been described with a certain degree of particularity, it is to be understood that the present disclosure has been made only by way of illustration and that numerous changes in the details of construction and arrangement of parts may be resorted to without departing from the spirit and scope of this invention. For example, separate synchronized motors could also be used to drive the cranks, allowing for arbitrary frequency ratios without the need to physically change pulleys. Also, gears could be used instead of belts and pulleys to control the cranks. Cams and slot plates or cams and springs would also be suitable. In fact, use of cams and springs would permit arbitrary amplitude of the shaker motion.