Apparatus and method for mixing small volumes of liquid

An apparatus for mixing small volumes of liquids using a submerged permanent magnet impeller and a programmable electromagnet driver with variable frequency and magnetic field strength and field gradient. These variables and the duration of their application are controllable by a computer programmed with specific algorithms. The electromagnet driver has no moving mechanical parts. In a typical embodiment a small permanent magnet impeller is submerged in a solution to be mixed while contained in, say, a 1.5 mL Eppendorf conical tube or in a well of a multiwell plate. The tube or well to be mixed is placed above and in close proximity to the electromagnet driver. An operator inputs the frequency, field, gradient, and duration using a graphical user interface. The magnetic field applied to the impeller magnet via the driver electromagnet causes the impeller to undergo rapid motion in all planes thereby transferring momentum vertically in the solution.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT While the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which particular embodiments and methods are shown, it is to be understood from the outset that persons of ordinary skill in the art may modify the invention herein described while achieving the functions and results of this invention. Accordingly, the descriptions which follow are to be understood as illustrative and exemplary of specific embodiments within the broad scope of the present invention and not as limiting the scope of the invention. In the following descriptions, like numbers refer to similar features or like elements throughout. FIGS. 1 a and 1 b illustrate a conventional magnetic impeller mixing apparatus 10 and an apparatus 20 according to one embodiment of the present invention, respectively. In a conventional magnetic-impeller mixing apparatus 10 , a rotating motor 12 rotates a permanent magnet 14 , the field of which couples with that of a permanent magnet impeller 16 submerged in a solution 18 to be mixed. A vortex 19 is commonly formed in solution 18 which transfers momentum vertically or axially within solution 18 to effect mixing in all dimensions. This vertical or axial transfer of momentum is critical to the mixing process and is, in conventional mixing, dependent on macroscopic vortex formation, that is, formation of vortex 19 . The volume of solution 18 represented in beaker 11 in the diagram is typically 50 mL. FIG. 1 b illustrates a preferred single station embodiment of the present invention. The apparatus 20 comprises electromagnet driver 22 which is powered by a signal generator 24 , the frequency and current of which can be controlled by an operator 100 (not shown), typically via computer programs. The signal generated by signal generator 24 is typically a sinusoidal wave, but can be generally any wave type suitable for the purpose of powering electromagnet drivers, including, but not limited to, saw-tooth wave forms and square wave forms. Those skilled in the art will understand that an infinite number of possible wave forms may be generated by computer or electronically for use in the present invention. Electromagnet driver 22 creates a rapidly rising and falling electromagnetic field that couples to that of a permanent magnet impeller 26 located within a small volume of liquid, or liquid sample 28 , that is contained in a liquid sample container 27 . Liquid sample container 27 can take many forms, including but not limited to, test tubes, Eppendorf tubes, beakers, graduated cylinders, wells in standard multi-well plates, and any other vessel suitable for housing liquids. This changing electromagnetic field, along with viscous forces in the liquid sample 28 , causes translation of impeller 26 in multiple directions in all planes. This motion, spurred by modulated magnetic field produced by electromagnet driver 22 , mixes the liquid sample 28 , using the submerged permanent magnet impeller 26 . It is this motion of permanent magnet impeller 26 , in contrast to the conventional mixers, that provides the desired vertical (axial) momentum transfer. Electromagnet driver 22 advantageously has no moving parts. The liquid sample 28 represented in the tube in the diagram is typically 1 mL. FIG. 2 illustrates a typical arrangement for the major components of the present invention. One or a plurality of electromagnet drivers 22 receive(s) a power signal of programmed frequency and current from signal generator 24 . Signal generator 24 receives electrical power from DC power supply 34 and commands from electronic controller 32 . The electronic controller 32 produces a conditioned electronic signal established by the output of computer 30 controlled by a graphical user interface (GUI) or similar laboratory interface software. FIG. 3 illustrates a flow diagram for an operating program usable in conjunction with a computer to operate the present invention. A significant feature of the immediate invention is the ability to program the electromagnetic drivers 22 . The operator 100 has at least three options. First, operator 100 may use menu 110 to enter at 120 the viscosity and density of the solution and the diffusivity of the solute. Second, operator 100 may enter at 130 the identity of a liquid or solution by selecting from a menu. Third, operator 100 may enter at 140 the desired electromagnet current, frequency, and duration of mixing. The first and second options incorporate algorithms derived from the theory of homogeneous isotropic turbulence, from which required power levels and mixing times can be calculated on the basis of solution and solute properties. The algorithms are used to calculate these outputs and signal the electronic controller 32 accordingly. At 150 , the operator 100 has an opportunity to enter parameters for different samples if operator 100 chooses to vary the parameters among samples. After operator 100 has made an entry or chosen not to make an entry at 150 , the operator 100 proceeds to activation step 160 , and appropriate signals are passed from the computer 30 to the controller 32 . FIG. 4 a illustrates an embodiment of the invention wherein an upper plate 40 has a first ring of cavities 42 defined around the circumference of the upper plate 40 at a distance from the center of the upper plate 40 ; and a lower plate 50 has a second ring of cavities 52 similarly defined therein. First ring of cavities 42 have openings 44 facing openings 54 in second ring of cavities 52 , as best shown in FIG. 5 . First and second rings of cavities 42 serve the function of a plurality of small volumes of liquid 28 . Each of the individual cavities 52 houses a permanent magnet impeller 26 which, in this embodiment, is held in place by an axle 46 about which the magnet impeller 26 is free to rotate. The upper plate 40 and lower plate 50 are positioned in proximity to electromagnet drivers 22 which activate each magnetic impeller 26 . After mixing (and demixing in the case of immiscible liquids) lower plate 50 rotates about a common axis with respect to upper plate 40 (or vice versa), thereby separating the upper half of each of the plurality of cavities 42 from its corresponding lower half 52 , and subsequently contacting the upper half of cavities 42 with the next lower half of cavities 52 in the ring. The magnetic mixing process and intervening fluid transfers can be repeated up to 22 times in the embodiment shown, which is also known as “BISEP” biphasic multistage extractor. However, it will be understood that any number of repetitions may be employed, depending on the size of the plates 40 ; the number of cavities 42 therein; and the number of steps needed to achieve mixing, demixing, purification, and so forth. The sample size of liquid sample 28 in this embodiment is less than 1.0 mL, and the number of electromagnet drivers 22 is twenty-two. FIG. 4 b shows a detail of one of magnetic impeller 26 rotatable about axle 46 . In this embodiment, rather than random motion of the impeller 26 , simple rotation about axle 46 is employed. Referring again to FIGS. 4 and 5 , a method of countercurrent extraction utilizing the present invention is shown. In countercurrent extraction, separands 45 (species of dissolved molecules or suspended particles) are transferred between phases for the purpose of their purification. FIG. 5 a illustrates lower immiscible liquid sample 28 initially contains separands 45 to be separated by extraction into upper phase liquid sample 29 . Lower immiscible phase liquid sample 28 is initially contained in a plurality of cavities 52 in lower plate 50 , and one of these cavities contains a starting mixture of separands 45 . Upper immiscible phase liquid sample 29 is initially contained in a plurality of inverted cavities 42 in upper plate 40 . FIG. 5 b illustrates the contacting of the two immiscible phases by the sliding (rotation) of lower plate 50 and the formation of an interface between the two immiscible phases of liquid samples 29 . These phases 29 are next mixed vigorously using an embodiment of the present invention, as best shown in FIG. 5 c . As can be seen, the apparatus 20 allows the transfer of mass between the two immiscible liquid samples 29 . Mixing is terminated and particles distribute themselves between the phases on the basis of thermodynamic equilibrium, as indicated in FIG. 5 d . This process is repeated until all top phases 29 have been combined with bottom phases 28 to the right, and all bottom phases 28 have been contacted with top phases to the left 29 , hence the name “countercurrent distribution” of separands. The present invention replaces the conventional mixing method in which mass transfer was achieved by shaking the entire assembly illustrated in FIG. 4 . Additional embodiments are depicted in FIG. 6 . FIG. 6 a is a multiple station embodiment of the single station embodiment of FIG. 1 b . FIG. 6 b shows a portion of a typical 96-well plate system (12×8), which is the most common embodiment of such plates used in the art. Persons of ordinary skill in the art will recognize that any number of wells are possible with this invention, and other common sizes are 24-well and 72-well plates. Referring now to FIG. 6 a , the liquid sample containers 29 are Eppendorf tubes 60 having a capacity of approximately 1.5 mL are shown captured in the wells 62 of a reaction block 64 . Said reaction blocks 64 are typically used to polymerize specific sequences of nucleic acids or peptides by a variety of synthetic methods involving enzymes and/or artificial substrates, and/or catalysts and/or immobilizing agents. Well-known applications of such reaction blocks 64 include, but are not limited to, enzymatic amplification of limited quantities of a gene sequence (also known as polymerase chain reaction—PCR), randomized amplification of nucleic acid or peptide sequences in combinatorial chemistry, and semi-solid synthesis of nucleic acids and peptides. A permanent magnet impeller 26 is submerged in the liquid sample 28 in each Eppendorf tube 60 , and the plurality of Eppendorf tubes 60 in their wells 62 in rectangular array is placed atop a corresponding rectangular array of electromagnet drivers 22 . FIG. 6 b illustrates an alternative embodiment wherein the liquid sample containers 29 comprise a rectangular array of a plurality of fixed wells 72 in rectangular array in a single plate 70 . The plate 70 may typically contain 96 or 24 wells, and typically has a single cover 74 for the entire array of wells 72 . Beneath each of the wells 72 , on its own platform, is a corresponding rectangular array 76 of a plurality of electromagnetic drivers 22 , one beneath each well 72 . Electromagnetic drivers 22 couple with the permanent magnet impellers 26 (also known, in this case, as “fleas”) in each corresponding well 72 . A typical volume per well 72 is 0.25 mL. Various embodiments of the present invention have been tested, and one of these will be described in the following example. 
 EXAMPLE FIG. 4 , as explained above, illustrates an embodiment of the present invention that works extremely well for its intended purpose. In particular, a criterion for complete mixing was established in the serial transfer mode provided by the embodiment shown in FIG. 4 . The details of a single transfer cycle using the embodiment of FIG. 4 are shown in FIG. 5 . All twenty-two upper liquid sample containers, cavities 42 , were filled with pure water, and twenty-one of the lower liquid sample containers, cavities 52 , were filled with pure water. One lower liquid sample container cavity 52 , called the first liquid sample container, was filled with a solution consisting of 0.4% trypan blue dye (or any clearly visible dye) and 99.6% pure water. Referring to FIG. 5 , upper and lower liquid containers were brought into contact and mixed for ten seconds by magnet impeller 26 driven at 500 cycles per minute, and the upper and lower volumes of liquid were again separated from one another. This process was repeated twenty-two times using plates 40 and 50 each having twenty-two liquid sample containers. A mathematical relationship predicts that, after twenty-two transfers of the type shown in FIG. 5 , the highest concentration of dye should appear in the 11 th upper liquid sample container from said first liquid sample container, and the amount of dye in all other containers is also predicted. When mixing was complete, the dye concentration was distributed in this predicted fashion. After twenty-two countercurrent transfers in the device of FIG. 4 , solute concentration was measured in all twenty-two cavities and found to be as predicted on the basis of complete mixing. Thus twenty-two tests of the immediate invention were performed in a single experiment, which was repeated several times with identical results. Furthermore, this test was performed in the absence of gravity during a space shuttle flight, and it was further demonstrated that complete mixing by the invention is independent of the gravity vector. That is, the invention should function in any orientation that allows the magnetic field of the electromagnet driver to couple with that of the permanent magnet impeller. This means that the invention works even in the absence of inertial forces, in closed or open containers. Successful mixing is achieved by the embodiments of the present invention as a result of, and dependent upon, assumptions of the homogeneous isotropic turbulence model. In this model an impeller must generate turbulent flow, which is assumed to produce eddies. Each eddy is assumed to consist of a small unstirred stagnant volume having a specified diameter and being surrounded by a fully-mixed dispersion. Mixing is assumed to be complete when the dispersed phase has had time to diffuse across an eddy. Turbulence is judged by the magnitude of Reynolds number (Re) using the relationship Re&equals;&rgr;lv/&eegr; where &rgr;&equals;density of fluid; l&equals;length of impeller; v&equals;velocity of rotation; and &eegr;&equals;viscosity of the fluid. If Re>2,000 turbulence is commonly assumed. In a typical embodiment of the present invention, Re&equals;3,000; therefore, turbulence is assumed. In the theory of homogeneous isotropic turbulence the diameter of stagnant zones is calculated from the impeller power density (Power/Volume) and the viscosity and mass density of the dispersion. This diameter is also known as Kolmogoroff length, thus: Kolmogoroff length&equals; f (viscosity, density, P/V ). Furthermore, the time required for complete mixing is calculated as the time required for a dissolved molecule or suspended particle to diffuse a distance equal to the Kolmogoroff length by Brownian diffusion using the Einstein diffusion equation: Mixing time&equals;&lsqb;Kolmogoroff length&rsqb; 2 /4&lsqb;diffusion coefficient&rsqb; In a typical embodiment of the immediate invention, mixing time for a dissolved solute in water is of the order of 10 s. Some additional background and sample calculations are useful. In a fully enclosed cylinder with no vapor space, such as is required in orbital spacecraft and often in the mixing of hazardous liquids, a stir bar rotating at about 500 rpm at the bottom of the vessel will typically input a power density of 1,000 W/m 3 . At the top of the closed vessel, owing to the no-slip boundary condition, this is zero. Assuming Couette Flow, the rotational velocity should reduce linearly from 500 rpm at the bottom to zero rpm at the top. Power density goes as the square of rotational velocity &lsqb;(rpm) 2 &rsqb;. This means, for example, that ¾ of the way up the vessel, power density is {fraction (1/16)} that at the bottom, and the required mixing time, according to the theory of homogeneous isotropic turbulence, is about 60 times as long at this position as at the bottom of the vessel. Typical mixing times at this velocity would be about 10 s at the bottom and 10 min at the top. For some reactions this would be too much heterogeneity, and for some processes this would be too much time. The transfer of momentum randomly, including vertically at 500 rpm, on the other hand, eliminates the heterogeneous distribution of mixing times. A vortex, in the classical sense, cannot form in a fully enclosed liquid with no vapor phase, except in exceptional cases in which the fluid is compressed causing cavitation. In most practical terms, performing experiments in low gravity requires that the entire contents of a container be liquid and no vapor phase is present. This requirement presents the mixing problem discussed above, and also eliminates the possibility of forming a classical vortex. Expanding upon the homogeneous isotropic turbulence model discussed previously indicates the effects on mixing created by a random impeller. Any object moving through a fluid at high Reynolds number (that is, Re>2,000) causes fluid motion in its vicinity by destabilizing its own laminar streamline and shedding vortices, also known as eddies. If turbulent flow is indicated on the basis of Reynolds number, then, to a good approximation the theory of homogeneous isotropic turbulence can be applied to the evaluation of mixing. In this theory, the Kolmogoroff length, as discussed above (which is a characteristic length), is calculated on the basis of the power density of the impeller (Watts/m 3 ) and the density and viscosity of the fluid. This length is taken as the diameter of a characteristic unmixed zone over which complete homogenization of a solute or suspension of particles requires diffusion. So, in a sample calculation, an impeller may impart 1,000 Watts/m 3 to a tank, and the resulting Kolmogoroff length is 10 −5 cm, then a solute with a diffusion coefficient of 10 −6 cm 2 /s will require 10 −5 cm/10 6 cm 2 /s&equals;10 s to be fully mixed. Thus the idea of turbulent mixing is to reduce the distance, and hence the time, required for solutes or suspended particles to become homogeneously dispersed by diffusion. On the basis of the above typical numbers, the need for vigorous mixing of particle suspensions is made clear. Some particles have diffusion coefficients as low as 10 −9 cm 2 /s or even less. This means, in the example just explained, the complete mixing time would be 10 4 s or 3 hours. However, simply doubling the rpm reduces the time required to several minutes. The present invention is capable of numerous mixing rates between about 50 and about 2000 rpm. The algorithms involved in the embodiment, as stated above, can allow operators at least three options to perform proper mixing. One option involves having an empirical formula provided in the computer algorithm so the operator need enter only the viscosity and molecular weight (or density of solution or diffusivity of solute) of the species to be fully mixed. A second option allows the operator simply to select from a menu list of most-frequently-used solutions' names, which include, but are not limited to, the following: tissue culture medium with 10% serum; buffer solution with 50% phenol extractant; phosphate buffered saline; physiological saline; human blood, undiluted; human blood diluted 50%; 20% solution of PEG 8,000; 1% protein solution in neutral buffer; 10% protein solution in neutral buffer; 50% protein solution in neutral buffer; 1% nucleic acid solution in aqueous buffer; peptide synthesis reagent; 1% nucleic acid solution in ethanol; suspension of 10 9 bacteria/mL broth; suspension of 10 6 animal cells/mL broth. And, as stated above, a third option allows the operator simply to input the desired electromagnet current, frequency, and duration of mixing. Subsequently the device is then activated to commence the mixing operation. While there has been described and illustrated particular embodiments of a novel device and method for efficiently mixing small volumes of liquid, it will be apparent to those skilled in the art that variations and modifications are possible without deviating from the broad spirit and principle of the present invention, which shall be limited solely by the scope of the claims appended hereto.