Adaptive self-sealing microfluidic gear pump

Abstract

A microfluidic pumping system configured to prevent backflow from an outlet of the system toward an inlet of the system. The microfluidic pumping system comprising a gear housing that has an inlet and an outlet and that houses a drive gear, an idler gear and a drive shaft. The system further includes a front end plate that is coupled to a first surface of the gear housing and a rear end plate that is coupled to a second, different surface of the gear housing. Also coupled to the gear housing is a first and second Halbach magnet arrays that is disposed between the front end plate and the rear end plate. The first and second Halbach magnet arrays include one or more solenoids and the first Halbach magnet array is disposed proximate to the drive gear and the second Halbach magnet array is disposed proximate to the idler gear.

Claims

1. A micro-fluidic pumping system comprising: a gear housing having an inlet and an outlet, wherein a drive gear, an idler gear and a drive shaft are disposed within the gear housing; a magneto-rheological (MR) fluid disposed in the housing; a front end plate coupled to a first surface of the gear housing; a rear end plate coupled to a second, different surface of the gear housing; and first and second Halbach magnet arrays coupled to the gear housing and disposed between the front end plate and the rear end plate, wherein the first and second Halbach magnet arrays include one or more solenoids and the first Halbach magnet array is disposed proximate to the drive gear and the second Halbach magnet array is disposed proximate to the idler gear.

2. The system of claim 1, wherein the gear housing is disposed between the front end plate and the rear end plate.

3. The systems of claim 1, wherein the first Halbach magnet array is disposed on an upper surface of the gear housing and the second Halbach magnet array is disposed on a lower surface of the gear housing.

4. The system of claim 3, wherein the upper surface and the lower surface of the gear housing have an arc shape.

5. The system of claim 1, wherein a clearance between the drive gear and the idler gear forms a channel coupling the inlet to the outlet.

6. The system of claim 5, wherein a flowrate of the magneto-rheological (MR) fluid through the channel corresponds to dimensions of at least one of or a combination of: the gear housing, the drive gear, the idler gear, a rotational speed of the drive gear, a rotational speed of the idler gear, or a magnetic field intensity of the first and second Halbach magnet arrays.

7. The system of claim 5, wherein a back flow rate of the channel corresponds to dimensions of at least one of or a combination of: the gear housing, the drive gear, the idler gear, a rotational speed of the drive gear, a rotational speed of the idler gear, or a magnetic field intensity of the first and second Halbach magnet arrays.

8. The system of claim 1, wherein the gear housing, the front end plate and the rear end plate include non-ferromagnetic material.

9. The system of claim 1, wherein the first and second Halbach magnet arrays comprise a top Halbach array scaffold, a bottom Halbach array scaffold, five ferromagnetic blocks, a plurality of wires and two independent resonant-power-transfer supplies.

10. The system of claim 9, wherein each of the five ferromagnetic blocks have a ring shape with a rectangular cross-section with a direction of one or more sides orthogonal to a radial direction.

11. The system of claim 9, wherein each of the five ferromagnetic blocks have a counter-bored hole.

12. The system of claim 9, wherein each of the five ferromagnetic blocks include ferromagnetic material.

13. The system of claim 9, wherein the top Halbach array scaffold has threaded holes and through-holes.

14. The system of claim 9, wherein the plurality of wires are routed on the five ferromagnetic blocks and the bottom Halbach scaffold.

15. A micro-fluidic pumping system comprising: means for housing a drive gear, an idler gear and a drive shaft; means for providing a container for a magneto rheological (MR) fluid, the container having an inlet and an outlet; a means for coupling a front end plate to a first surface of the gear housing; a means for coupling a rear end plate to a second, different surface of the gear housing; and a means for coupling a first and second Halbach magnet arrays to the gear housing, wherein the first Halbach magnet array is disposed proximate to the drive gear and the second Halbach magnet array is disposed proximate to the idler gear.

16. The system of claim 15, further comprising a means for preventing backflow.

17. The system of claim 15, further comprising a means for coupling the inlet to the outlet.

18. The system of claim 17, wherein a fluid dynamic of the magneto-rheological (MR) fluid through the inlet or outlet corresponds to at least one of or a combination of a pressure applied to the MR fluid through the inlet, a flow velocity of the MR fluid, a rotational speed of the drive gear, a rotational speed of the idler gear, or a magnetic field intensity of at least one of the first and second Halbach magnet arrays.

19. A micro-fluidic pumping system comprising: a gear housing having an inlet and an outlet, wherein a drive gear, an idler gear and a drive shaft are disposed within the gear housing; a magneto-rheological (MR) fluid disposed in the housing; a front end plate coupled to a first surface of the gear housing; a rear end plate coupled to a second, different surface of the gear housing; and first and second Halbach magnet arrays coupled to the gear housing and disposed between the front end plate and the rear end plate, wherein the first and second Halbach magnet arrays include one or more solenoids and the first Halbach magnet array is disposed proximate to the drive gear and the second Halbach magnet array is disposed proximate to the idler gear, wherein the first and second Halbach magnet arrays generate a magnetic field causing the MR fluid to create dipoles within a gap between the gear housing and one of the drive gear and the idler gear.

20. The micro-fluidic pumping system of claim 19, wherein the magnetic field causes the MR fluid to create dipoles within a gap between the gear housing and the drive gear, and a second gap between the gear housing and the idler gear.

21. The micro-fluidic pumping system of claim 19, wherein the magnetic field causes the MR fluid to create dipoles within a gap between the gear housing and the front end plate.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The foregoing features may be more fully understood from the following description of the drawings in which:

(2) FIG. 1 is a plot of efficiency vs. pressure which illustrates a prior art graphical depiction of a measure of efficiency versus maximum pressure for conventional small-scale pumping strategies.

(3) FIG. 2A is a cross-sectional view of a portion of an external gear pump.

(4) FIGS. 2B-2C are magnified (or enlarged) views of a portion of the external gear pump illustrated in FIG. 2A.

(5) FIG. 3A is an isometric view of an adaptive microfluidic system having portions thereof removed to reveal a portion of a gear.

(6) FIG. 3B is an exploded view of the adaptive microfluidic system of FIG. 3A.

(7) FIG. 4A is an isometric view of an array of solenoids arranged in a Halbach configuration to provide a magnet array.

(8) FIG. 4B is an exploded view of the Halbach array of solenoids of FIG. 4A

(9) FIG. 5 is an illustration of the magnetic fields generated by the Halbach array of solenoids

(10) FIG. 6A is a top (or front) view of a portion of an external gear pump.

(11) FIG. 6B is a cross-sectional view taken along lines A=A of the portion of the external gear pump shown in FIG. 6A.

(12) FIG. 6C is an enlarged view of a portion of the external gear pump illustrated in FIG. 6A taken along lines B-B in FIG. 6B.

(13) FIG. 6D is an enlarged view of a portion of the external gear pump illustrated in FIG. 6A taken along lines C-C in FIG. 6B. sealing between FIG. 7A is an isometric view of a portion of a shaft and housing of an external gear pump.

(14) FIG. 7B is a cross-section view of a portion of a rotating shaft and a housing with a conventional sealing mechanism.

(15) FIG. 7C is a cross-section view of a portion of a rotating shaft and housing which may be the same as or similar to the shaft and housing of FIG. 7A and which includes a dynamic sealing mechanism using magnetorheological (MR) fluids.

(16) FIG. 8A is a plot of volumetric loss vs. flow rate which illustrates ratio of volumetric loss to the normal flow rate of a gear pump having an MR sealing mechanism.

(17) FIG. 8B is a plot friction factor vs. flow rate which illustrates a friction factor.

(18) FIG. 9 is a plot of average pressure gradient vs. rotational speed of a gear which illustrates efficiencies for a variety of different magnetic field intensities.

DETAILED DESCRIPTION

(19) Various embodiments of the concepts systems and techniques are described herein with reference to the related drawings. Alternative embodiments can be devised without departing from the scope of the described concepts. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the following description and in the drawings. These connections and/or positional relationships, unless specified otherwise, can be direct or indirect, and the present disclosure is not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship. As an example of an indirect positional relationship, references in the present description to element or structure “A” over element or structure “B” include situations in which one or more intermediate elements or structures (e.g., element “C”) is between element “A” and element “B” regardless of whether the characteristics and functionalities of element “A” and element “B” are substantially changed by the intermediate element(s).

(20) Additionally, the term “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment or design described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms “one or more” and “one or more” are understood to include any integer number greater than or equal to one, i.e. one, two, three, four, etc. The terms “a plurality” are understood to include any integer number greater than or equal to two, i.e. two, three, four, five, etc. The term “connection” can include an indirect “connection” and a direct “connection”.

(21) References in the specification to “one embodiment,” “an embodiment,” “an example embodiment,” or variants of such phrases indicate that the embodiment described can include particular features, structures, or characteristics, but every embodiment can include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment. Further, when a particular feature, structure, or characteristic is described in connection knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

(22) Furthermore, it should be appreciated that relative, directional or reference terms (e.g. such as “above,” “below,” “left,” “right,” “top,” “bottom,” “vertical,” “horizontal,” “front,” “back,” “rearward,” “forward,” etc.) and derivatives thereof are used only to promote clarity in the description of the figures. Such terms are not intended as, and should not be construed as, limiting. Such terms may simply be used to facilitate discussion of the drawings and may be used, where applicable, to promote clarity of description when dealing with relative relationships, particularly with respect to the illustrated embodiments. Such terms are not, however, intended to imply absolute relationships, positions, and/or orientations. For example, with respect to an object or structure, an “upper” surface can become a “lower” surface simply by turning the object over. Nevertheless, it is still the same surface and the object remains the same. Also, as used herein, “and/or” means “and” or “or”, as well as “and” and “or.” Moreover, all patent and non-patent literature cited herein is hereby incorporated by references in its entirety for all purposes.

(23) The terms “disposed over,” “overlying,” “atop,” “on top,” “positioned on” or “positioned atop” mean that a first element, such as a first structure, is present on a second element, such as a second structure, where intervening elements or structures (such as an interface structure) may or may not be present between the first element and the second element. The term “direct contact” means that a first element, such as a first structure, and a second element, such as a second structure, are connected without any intermediary elements or structures between the interface of the two elements.

(24) As used herein, the term “fluid” may be used to refer to a liquid, a liquid comprising solid matter, a gas or any other material that deforms when shear stress is applied thereto.

(25) The term “fluid dynamic” may be used to refer to characteristics or properties of a fluid flow (i.e. the flow of a fluid), for example fluid dynamic can refer to the velocity, direction or pressure at which a fluid flows, or the temperature or density of a fluid.

(26) The term “magnetorheological (MR) fluids” refers to materials that exhibit a reversible change in rheological properties with the application of an external magnetic field, which can result in a rich range of physical properties. Typical operational modes for MR fluid application are the pressure driven flow mode and the direct shear mode.

(27) Illustrated in FIG. 2A is an external gear pump 10 having two gears 25a-b with gear teeth 15. The first gear 25a turns in a first direction D1, while the second gear 25b turns in a second direction D2. The gears 25a-b are housed in a housing 20 with an inlet 22 and an outlet 24. An area of the external gear pump 10 during operation is circled in FIG. 2A and labeled “A”, FIGS. 2B and 2C illustrate a magnified portion of this area “A”.

(28) Fluid flows through the inlet 22 of the housing with a first fluid dynamic 30a and out of the outlet 24 of the housing 20 with a second fluid dynamic 30b. In some embodiments the first fluid dynamic 30a can be substantially equal to the second fluid dynamic 30b, while in other embodiments, the two dynamics 30a-b can differ from each other. For example, the fluid can flow through the inlet 22 with a first fluid dynamic 30a having a first velocity, however the fluid can flow out of the outlet 24 with a second fluid dynamic 30b having a second different velocity.

(29) In this example, the velocity of the second fluid dynamic 30b can be higher or lower depending on the rotational speed of the gears 25a-b. In another example, the fluid can flow into the inlet 22 with a first fluid dynamic 30a that has a first pressure, and out of the outlet 24 with a second fluid dynamic 30b that a second pressure that is larger than the first pressure. When fluid dynamic 30b at the outlet has a higher pressure than the fluid dynamic 30a at the inlet 22, fluid can flow in an opposite direction to the first and second fluid dynamic 30a-b, otherwise referred to as backflow. In this example, the backflow is a Poiseuille flow caused by the pressure gradient created between the difference in pressure of the fluid dynamic 30a at the inlet 22 and the fluid dynamic 30b at the outlet 24. While backflow can be a Poiseuille flow cause by a pressure differential, it can also be a Poiseuille flow caused by a high shear stress caused by a large exerted force.

(30) FIG. 2B illustrates a magnified view of a portion (i.e., the portion of FIG. 2A circled and labeled “A”) of the external gear pump 10 during operation and when the pressure of the fluid at the inlet 22 is less than the pressure of the fluid at the outlet 24. The difference in pressure between the first and second fluid dynamic 30a-b can cause backflow across a gap 40 between a surface of housing 20 and a surface of gear tooth 15. To promote clarity and conciseness in the description and drawings, this is illustrated for a single gear tooth, however backflow may occur in a gap between a surface of the housing and a surface of any gear tooth. This backflow can be characterized as having a direction D3 that is opposite to the direction of movement of the gear 25a, i.e. D1. Fluid that backflows across the gap 40 can have a third fluid dynamic with its own flow velocity, pressure and direction. This third fluid dynamic can differ from the fluid dynamic 30a at the inlet 22 and the fluid dynamic 30b at the outlet 24. Flow through the gap 40 can be characterized as Couette flow which is a laminar, circular flow of fluid between a static surface and a rotating surface. In this instance, the Couette flow of the fluid through the gap 40 flows between a static surface (e.g. a surface of the static housing 20) and a surface that rotates relative to the static surface (e.g. a surface of the movable gear tooth 15).

(31) FIG. 2C is an enlarged (or magnified) view of a portion (i.e., the portion of FIG. 2A circled and labeled “A”) of the external gear pump 10 during operation and while using MR fluid that has a fluid dynamic 50 generated by applying an external magnetic field 45 to the MR fluid. In the illustrative embodiment of FIG. 2C, applying the magnetic field 45 to the MR fluid causes magnetically induced dipoles to aggregate in the vicinity of the housing 20 and specifically in the gap 40. The existence of the magnetic dipoles in the gap 40 prevents backflow of the MR fluid. That is, the characteristics of the MR fluid are such that the MR fluid will not flow in a direction opposite the movement of the gear (e.g. gear 25a) in the presence of the magnetic dipole. Thus, using the MR fluid and applying an external magnetic field 45 controls flow of fluid through aspects of the external gear pump 10 without requiring modified manufacturing methods.

(32) Further referring to FIG. 2C and in more detail, the MR fluid can be any MR fluid, or in some instances be a commercially available MR fluid such as those manufactured by the LORD corporation, e.g. LORD MRF-140CG Magneto-Rheological Fluid. Other MR fluids may, of course, also be used. In particular, the MR fluid can be a homogeneous or non-homogeneous mixture of fluid or medium with MR particles suspended therein. The volume fraction of MR particles within the MR fluid can be within a range of 1% to 10%. When a magnetic field is applied to a microfluidic system with a micropump and the flow velocity or flow rate through a portion of a micropump is lower than a predetermined threshold, the MR particles within the MR fluid can form dipole chains that aggregate in bunches. When a magnetic field is applied to a microfluidic system with a micropump and the flow velocity or flow rate through a portion of a micropump is lower than a predetermined threshold, the dipole chains of MR particles begin to deform and eventually collapse.

(33) Illustrated in FIG. 3A is a microfluidic system 100 that uses a sealed micropump. Aspects of the microfluidic system 100 are further demonstrated in the exploded view of FIG. 3A illustrated in FIG. 3B. The microfluidic system 100 includes a front end plate 102 mechanically coupled to a gear housing 120 and a rear end plate 104 using on or more mechanical fasteners 106. Coupling the front end plate 102 to the gear housing 120 encloses one or more gears 122a-b within the gear housing 120. Each gear 122a-b has one or more gear teeth 124. At least one gear 122a rotates about a drive shaft 126 that extends through the gear housing 120, the rear end plate 104 and mechanically couples to a rear housing 108 with a drive shaft support 112 that at least partially supports the drive shaft 126. Included within the gear housing 120 is a pressure port 118 and disposed on either end of the gear housing are solenoid arrays 150a-b.

(34) Further referring to FIGS. 3A and 3B, and in more detail, the front end plate 102 can be mechanically coupled to the gear housing 120 via one or more fasteners 106. These fasteners can be screws, nails, pegs or any other type of mechanical fastening means. In some embodiments, the front end plate 102 can be coupled to the gear housing 120 via an adhesive, while in other embodiments the front end plate 102 can be permanently fastened to the gear housing 120.

(35) The gears 122a-b can function similarly to the gears 25a-b illustrated in FIGS. 2A-2C.

(36) Each gear 122a-b can have a plurality of gear teeth 124. A first gear 122a can be a drive gear 122a mounted on a drive shaft 126 such that the drive gear 122a can rotate about the drive shaft 126. A second drive gear 122b can be an idler gear 122b that rotates about a fixed shaft 128. The gear teeth 124 of the drive gear 122a can engage the gear teeth 124 of the idler gear 122b to rotate the idler gear 122b in a direction opposite of the direction of movement of the drive gear 122a. For example, when the drive shaft 126 rotates the drive gear 122a in a clockwise direction, the gear teeth 124 of the drive gear 122a engage the gear teeth 124 of the idler gear 122b to rotate the idler gear 122b in a counterclockwise direction. These directions can correspond to the directions illustrated in FIG. 2A such that the drive gear 122a (25a in FIG. 2A) moves in a clockwise direction (D1 in FIG. 2A) which causes the idler gear 122b (25b in FIG. 2A) to move in a counter-clockwise direction (D2 in FIG. 2A).

(37) The drive shaft 126 controls movement of the drive gear 122a which in turn controls movement of the idler gear 122b. Thus, the drive shaft 126 controls the rotational speed of the drive gear 122a and in turn the rotational speed of the idler gear 122b. In some embodiments, the drive shaft 126 can be movably manipulated and controlled by a motor (not shown).

(38) Included within the gear housing 120 is a pressure port 118 which can include a hole bored through the surface of the gear housing 120. An identical port, a suction port 118′ (not shown), can be located on the opposite surface of the gear housing 120. The suction port 118′ can be an inlet such as the previously discussed inlet (22 in FIG. 2A) that has a first fluid dynamic (30a in FIG. 2A), and the pressure port 118 can be an outlet such as the previously discussed outlet (24 in FIG. 2A) that has a second fluid dynamic (30b in FIG. 2A). In an embodiment, the sealed micropump of the microfluidic system 10 can be used to pump magneto-rheological (MR) fluid from the suction port 118′ to the pressure port 118 by applying a rotational speed to the gears 122a-b via the drive shaft 126.

(39) Disposed between the front end plate 102 and the rear end plate 104 and located on either end of the gear housing 120 are two solenoid arrays 150a-b. These solenoid arrays 150a-b can include a Halbach magnet array of solenoids. In some embodiments, each Halbach magnet array 150a-b can be attached to either end of the gear housing 120 such that one Halbach magnet array 150a is attached to the top of the gear housing 120 or proximate to the drive gear 122a, while the second Halbach magnet array 150b is attached to the bottom of the gear housing 120 or proximate to the idler gear 122b. The first Halbach magnet array 150a may be disposed on an upper surface 121 of the gear housing and the second Halbach magnet array 150b may be disposed on a lower surface 123 of the gear housing.

(40) The Halbach magnet arrays 150a-b can be powered by one or more power supplies (not shown) that supply a current and/or potential to the Halbach magnet arrays 150a-b to cause each array to generate a magnetic field. These power supplies (not shown) can be charged using resonant power transfer. In response to receiving current and/or potential from the external power supplies, the Halbach magnet arrays 150a-b generate a magnetic field having a direction perpendicular to a direction of backflow. The direction of the generated magnetic field can be substantially similar to the direction of the magnetic field illustrated in FIG. 2A (45 in FIG. 2A). Just as the external magnetic field 45 illustrated in FIG. 2A caused the MR fluid particles to aggregate in the vicinity of the gear teeth or more specifically the gap 40, and reduce the backflow, when the Halbach magnet arrays 150a-b generate the magnetic field across the clearance (i.e. the gap 40 illustrated in FIG. 2B) formed between the gear housing 120 and the gear teeth 124, the magnetic particles in the magneto-rheological (MR) fluid aggregate to adjust and prevent the back-flow driven by the pressure gradient between the suction port 118′ and the pressure port 118. The power source or supplies (not shown) can control the magnetic field intensity of the magnetic field generated by the Halbach magnet arrays 150a-b by controlling an amount of current applied to the arrays 150a-b.

(41) Illustrated in FIG. 4A is a Halbach magnet array of solenoids 150 and illustrated in FIG. 4B is an exploded view of the Halbach magnet array of solenoids 150 of FIG. 4A. While FIGS. 4A-4B illustrate a single Halbach magnet array 150, it should be understood that as shown in FIGS. 3A-3B, more than one Halbach magnet array 150 can be included in a micropump of a microfluidic system 100. The Halbach magnet array of solenoids 150 includes a top Halbach array scaffold 160, a bottom Halbach array scaffold 162, five ferromagnetic blocks 164a-e, routed wires 170, two independent resonant-power-transfer supplies 168a-b, and mounting screws 172. Each block 164a-e is a section of a ring with a rectangular cross-section, and each block 164a-e has a counter-bored hole 173 for mounting on the bottom scaffold 162 with screws 172. The wires 170 are routed in the way which can generate magnetic field illustrated in FIG. 5, and after the ferromagnetic blocks 164a-e are mounted on the bottom scaffold 162.

(42) In one embodiment, the bottom scaffold 162 has nine threaded holes 163 used to mount the ferromagnetic blocks 164a-e with screws 172, the resonant-power-transfer supply 168a-b, and the top Halbach array scaffold 160 respectively. The bottom scaffold 162 also has two unthreaded holes 165 (which may also be referred to as through-holes) used for screws to secure the front end plate 102, Halbach magnet array of solenoids 150 and rear end plate 104. In an embodiment, the two independent power supplies 168a-b power the Halbach array of solenoids 150 alternately, and charge via the two resonant-power-transfer supplies 168a-b alternately and during a vacant period.

(43) Referring to FIG. 5, the diagram 200 depicts the magnetic field intensity and direction generated by the Halbach array scaffold 160, 162 as a result of the ferromagnetic blocks 164a-e. Each block can have associated therewith a set of two-dimensional axes illustrating a positive and negative X and y direction. The magnitude and the direction of the arrows indicate the magnitude and direction of the magnetic field respectively. For example, the two outer ferromagnetic blocks 164a, 164e generate a magnetic field of similar intensity and pointing in the direction of the positive X direction. One ferromagnetic block 164b generates a magnetic field pointing in the negative y direction, while ferromagnetic block 164d has a magnetic field with a similar intensity to the one produced by ferromagnetic block 168b but pointing in the positive y direction. Ferromagnetic block 164c generates a magnetic field pointing in the negative X direction. This

(44) Halbach array 150 generates magnetic fields in the vicinity of the inner side of the array 150 stronger than that of the outer side. The normal direction of the two side surfaces of the ferromagnetic blocks are orthogonal to the radial direction.

(45) In an alternative embodiment, the architecture may be used to provide a sealing mechanism between the gear sides and the housing 120. The architecture of the Halbach magnet array of solenoids 150a-b can also be applied for sealing between the gear sides 250, 255 and the housing (FIG. 6A) when MR fluids are used. As shown in FIG. 6B, volumetric loss also happens at position B-B and C-C, though this leakage is much less significant than the loss between the gear teeth and the housing. Using an approach similar to the ones discussed herein, a magnetic field supplied by the Halbach magnet arrays 150a-b to the MR fluid can seal the gear sides 250, 255 to mitigate volumetric loss.

(46) In a further embodiment, additional sealing may be provided between the rotating shaft 270 and the static housing 275 in various types of pumps, e.g., as shown in FIG. 7A. The traditional sealing approach is to apply an oil-resistant O-ring (e.g., as shown in FIG. 7B).

(47) Alternatively, the Halbach magnet array of solenoids may be applied using MR fluid (see, e.g., FIG. 7C). One advantage of this approach is that the magnetic field intensity can be tuned adaptively according to the working condition of the pump. In this embodiment, additional magnetic arrays 260, 265 are incorporated into the static housing to supply a magnetic field to the MR fluid to seal the area between the rotating shaft 270 and the static housing 275.

Example 1

(48) A microfluidic system includes a network of microchannels in fluid communication with each other and having a width of approximately 0.7 mm or 70 micrometers. Flowing through the channels of the microchannel network is a mixture containing a magneto-rheological

(49) (MR) fluid that has a volume fraction of MR particles diluted to be 1%. The MR fluid can have a carrier fluid of silicone oil and the MR particles can have a surface field of 1895 Gauss (NdFeB, Grade N42, 2.44 oz.). Within this microfluidic system, Couette flow and Poiseuille flow of the MR fluid are observed as a result of two slots moving in parallel with respect to each other and in the presence of various magnetic field intensities. Within this system, the Reynolds

(50) ${\mathrm{Re}}_{\delta }=\frac{pU\delta }{\mu }=0.05<<1,$

(51) number or ratio of viscous forces to inertial forces is less than one (1), thus the inertia of the MR fluid in this example is negligible. Given the low Reynolds number of the system, the conservation of momentum equation for steady, laminar flow, in the x-direction, reduces to:

(52) $\frac{\mathrm{dp}}{\mathrm{dx}}=\frac{d{\tau }_{\mathrm{yx}}}{\mathrm{dy}},$
where p is the mechanical pressure, τ.sub.yx is the shear stress. The MR fluid can be modeled as a Bingham fluid, and because of the distribution of the magnetic field intensity, the yield stress is larger in the slot closer to the magnet than that in the further one. The constitutive relationship can be expressed as:

(53) ${\tau }_{\mathrm{yx}}=\left(\mu +\frac{{\tau }_y}{.Math.\gamma .Math.}\right)\gamma ;.Math.\tau .Math.>{\tau }_y$$\gamma =0;.Math.\tau .Math.\le {\tau }_y,$
where μ is the viscosity of the MR fluid, T.sub.y is the yield stress, and y is the shear rate. The following boundary conditions on the inner and outer walls of the channel apply:
v.sub.x|y=0=U
v.sub.x|y=δ=0,
where v.sub.x is the velocity of the fluid in x-direction and U is the velocity of the inner wall.

(54) In this Example 1, the behavior of the dipole chains can be defined by two Mason numbers. A first Mason number that is the ratio between the shear forces and the magnetic interaction forces in Poiseuille flow, and a second Mason number one for Couette flow. The magnetic interaction forces are characterized by the yield stress τ.sub.y.

(55) $\mathrm{Mn}\left(p\right)=\frac{\delta }{{\tau }_y}\left(-\frac{\mathrm{dp}}{\mathrm{dx}}\right)$$\mathrm{Mn}\left(\Omega \right)=\frac{{\tau }_y\delta }{\mu R\Omega }$
Other dimensionless variables are defined as follows:

(56) $y^{*}=\frac{y}{\delta };{\tau }^{*}=\frac{{\tau }_{\mathrm{yx}}}{{\tau }_y};v^{*}=\frac{v_x}{R\Omega };U^{*}=\frac{R\Omega }{.Math.R\Omega .Math.}.$
Substituting the dimensionless variables into the conservation of momentum equation and constitutive equation yields:

(57) $\frac{d_{\tau *}}{d_{\tau *}}+\mathrm{Mn}\left(p\right)=0;$${\tau }^{*}=\frac{1}{\mathrm{Mn}\left(\Omega \right)}\frac{\mathrm{dv}*}{\mathrm{dy}*}+\mathrm{sgn}\left(\frac{\mathrm{dv}*}{\mathrm{dy}*}\right);.Math.{\tau }^{*}.Math.>1$$\frac{\mathrm{dv}*}{\mathrm{dy}*}=0;.Math.{\tau }^{*}.Math.\le 1.$
The boundary conditions in this Example 1 become:
v*|.sub.y*=0=U*;v*|.sub.y*=1=0.

(58) The velocity profiles of various fluid dynamics can be computed from the governing equation and the associated boundary conditions and can be categorized into three modes: (i) a one-region mode, (ii) a two-region mode and (iii) a three-region mode. The one-region mode occurs when the pressure gradient between the inlet and the outlet is small and the velocity of the boundary is relatively large. In this mode, the fluid stress is larger than the yield stress of the Bingham fluid across the system, so chains of MR particles cannot form. The velocity profile in the one-region mode can be identical to that of a Newtonian fluid in Poiseuille Couette flow. The two-region mode occurs as the pressure gradient between the inlet and outlet increases, which in turn causes an increase in the slope of the stress distribution. In the region where the fluid stress is smaller than the yield stress, a plug zone will occur, where MR particle chains form and the velocity profile can resemble plug flow. In two-region mode, the plug zone is anchored to the surface nearest the magnet, whereas in the region at the opposing surface the MR particles are prevented from aggregating, similarly to one-region mode. Finally, the three-region mode occurs as the pressure gradient between the inlet and outlet increases even further. Under such conditions, the plug zone will detach from the wall and move to the middle of the channel, surrounded by Newtonian regions on either side.

(59) The average velocity of the fluid in the one-region mode is given by:

(60) ${\stackrel{\_}{v}}^{*}=\frac{1}{12}\mathrm{Mn}\left(\Omega \right)\mathrm{Mn}\left(p\right)+\frac{1}{2}{U}^{*}.$
The average velocity of the fluid in the two-region mode is given by:

(61) ${\stackrel{\_}{v}}^{*}=\frac{U^{*}}{3}\sqrt{\frac{-2U^{*}}{\mathrm{Mn}\left(\Omega \right)\mathrm{Mn}\left(p\right)}}.$
The average velocity of the fluid in the three-region mode is given by:

(62) ${\stackrel{\_}{v}}^{*}=\frac{1}{12}\mathrm{Mn}\left(\Omega \right)\mathrm{Mn}\left(p\right)\left(1-\frac{3}{.Math.\mathrm{Mn}\left(p\right).Math.}+\frac{4}{{.Math.\mathrm{Mn}\left(p\right).Math.}^3}\right)+\frac{U^{*}}{2}\pm \frac{1}{\mathrm{Mn}\left(\Omega \right){\left(2\mp \mathrm{Mn}\left(p\right)\right)}^2}.$
The transition pressure from one-region mode to two-region mode and from two-region mode to three-region mode can also be computed and are found to be quantities Mn(p).sub.R1 and Mn(p).sub.R2 respectively:

(63) 0${\mathrm{Mn}\left(p\right)}_{R1}=\frac{2}{\mathrm{Mn}\left(\Omega \right)}$${\mathrm{Mn}\left(p\right)}_{R2}=2+\frac{1}{\mathrm{Mn}\left(\Omega \right)}+\sqrt{\frac{1}{{\mathrm{Mn}\left(\Omega \right)}^2}+\frac{4}{\mathrm{Mn}\left(\Omega \right)}}.$

(64) In terms of the design and application for external gear pumps, two performance metrics may be considered which evaluate the performance of dynamic seals. The first performance metric is given by the ratio of volumetric flow rate loss to the nominal volumetric flow rate of the gear pump.

(65) The nominal volumetric flow rate is proportional to the angular speed of the gear. Therefore, the dimensionless group

(66) $u^{*}=\frac{v}{R\Omega }$
can be used to characterize the sealing effectiveness of MR fluid, where v is the average velocity of the back-flow rate in the clearance of the gear pump, RΩ is proportional to the volumetric flow rate pumped by the gear pump. FIG. 8A depicts a graphical depiction illustrating ratio of volumetric loss to the normal flow rate of a gear pump. As shown in FIG. 8A, the ratio of volumetric loss to the nominal flow rate of a gear pump is a function of Mn(p), for Mn(Ω) equal 0.5, 1, 1.5, 2, 2.5. The arrow indicates the direction Mn(Ω) increases.

(67) As shown in FIG. 8A, to achieve higher effectiveness, u* should be designed to be as small as possible. Mn(p).sub.R1 is the transition point of the velocity profile from one-region mode to two-region mode for both slots, because Mn(p).sub.RS1 equals Mn(p).sub.RL1. Mn(p).sub.SR2, Mn(p).sub.LR2 are the transition points of the velocity profile from two-region mode to three-region mode for the slots in the presence of larger and smaller magnetic field intensity respectively. When Mn(p) is larger than Mn(p).sub.SR2, u* dramatically increases. Thus, to ensure a small volumetric loss, Mn(p) should be smaller than Mn(p).sub.SR2. The second performance metric comes from the energy loss in both of the slots, which can be characterized by the friction factor

(68) $f=\frac{p}{\frac{1}{2}{\mathrm{pv}}^2}.$
To achieve the optimal sealing performance, the friction factor is maximized, indicating that the back-flow between the gear teeth 124 and the housing 120 will experience as much energy loss as possible. As shown in FIG. 8B, a friction factor is a function of Mn(p), for Mn(Ω) equal 0.5, 1, 1.5, 2, 2.5. The arrow indicates the direction Mn(Ω) increases. i: one-region mode; ii: two-region mode; iii: three-region mode. The dot lines indicate the transition for the velocity profile to transit from one mode to another. Further, as shown in FIG. 8B, the maximum friction factor can be achieved around Mn(p).sub.SR2, which is the Mn(p) of the transition point from two-region mode to three-region mode for the slot in presence of the smaller magnetic field intensity.

(69) Upon considering the two performance metrics mentioned above, the optimal sealing performance can be achieved at the transition of two-region mode to three-region mode. Thus, at any given nominal work condition of external gear pump, the magnetic field intensity can be tuned to make the yield stress satisfy the equation described above, namely:

(70) ${\mathrm{Mn}\left(p\right)}_{R1}=\frac{2}{\mathrm{Mn}\left(\Omega \right)}$${\mathrm{Mn}\left(p\right)}_{R2}=2+\frac{1}{\mathrm{Mn}\left(\Omega \right)}+\sqrt{\frac{1}{{\mathrm{Mn}\left(\Omega \right)}^2}+\frac{4}{\mathrm{Mn}\left(\Omega \right)}}.$
This equation reflects the condition for the MR fluid to transit from the two-region mode to the three-region mode, and can be expressed explicitly by the following equation:

(71) ${\tau }_y=\frac{1}{2}\frac{{\left(\frac{\mathrm{dp}}{\mathrm{dx}}\delta \right)}^2-2\mu \frac{\mathrm{dp}}{\mathrm{dx}}R\Omega }{\frac{\mathrm{dp}}{\mathrm{dx}}\delta -\sqrt{2\mu \frac{\mathrm{dp}}{\mathrm{dx}}R\Omega }}.$
The relationship between magnetic field intensity (B) and yield stress (Pa) of MR fluid is expressed as:

(72) $\lg B=\frac{4}{7}\lg {\tau }_y+\frac{4}{7}\lg \left(9\times {10}^{-4}\right),$
where B is the magnetic field intensity, τ.sub.y is the yield stress.
A ratio Φ is defined as a metric for the effectiveness of dynamic seals using MR fluid:

(73) $\Phi =\frac{Q_{\mathrm{Oil}}-Q_{MR}}{Q_{\mathrm{Oil}}},$
where Q.sub.Oil is the volumetric loss using general pump oil, Q.sub.MR is the volumetric loss using MR fluid with the same viscosity as the general pump oil.

(74) The optimal magnetic field intensity (T) is shown in FIG. 9. The solid line indicates the magnetic field intensity distribution from 0.01 T to 0.03 T at given specific condition. The shaded area indicates the percentage of the reduction in volumetric loss from Φ=90% (white) to 0% (black). This indicates that dynamic sealing using rheological fluid will achieve the optimal sealing effectiveness under a high pressure gradient between the inlet and the outlet and relatively low rotational speed, which would reduce the volumetric loss to over 90%.

(75) As indicated above, volumetric loss accounts for the extremely low efficiency of small-scale gear pumps. In order to reduce the volumetric loss without introducing larger friction, tighter manufacturing tolerances, or vulnerability to vibrations, the above-described techniques provide for activation of magnetorheological fluid in the vicinity of the clearance between gear and housing to create a dynamic seal.

(76) For purposes of illustrating the present embodiment, the disclosed embodiments are described as embodied in a specific configuration and using special logical arrangements, but one skilled in the art will appreciate that the device is not limited to the specific configuration but rather only by the claims included with this specification. In addition, it is expected that during the life of a patent maturing from this application, many relevant technologies will be developed, and the scopes of the corresponding terms are intended to include all such new technologies a priori.