Apparatus and method for controlling fluid flow
11181132 · 2021-11-23
Assignee
Inventors
- Anna Galea (Stow, MA)
- Joseph Beuford Parse (Stow, MA, US)
- Kylie Stengel (Allston, MA, US)
- Kristen LeRoy (Waltham, MA, US)
- Minh Duong (Worcester, MA, US)
- Samuel Harrington Warner (Brighton, MA, US)
- Andrew Evan Kamholz (Brookline, MA, US)
- Brandon Johnson (Somerville, MA, US)
Cpc classification
F15D1/025
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
A61M2206/16
HUMAN NECESSITIES
A61M1/36
HUMAN NECESSITIES
B01L2300/165
PERFORMING OPERATIONS; TRANSPORTING
B01L3/502776
PERFORMING OPERATIONS; TRANSPORTING
F15D1/06
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
A61M2205/12
HUMAN NECESSITIES
B01L2300/0816
PERFORMING OPERATIONS; TRANSPORTING
B01L2200/0636
PERFORMING OPERATIONS; TRANSPORTING
International classification
F15B21/06
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
F15D1/06
MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
Abstract
Apparatuses for flowing multiple fluids in a single channel while substantially maintaining fluid separation are disclosed. In one configuration, the apparatus includes a first internal surface portion with an affinity to a first fluid and a second internal surface portion with an affinity to a second fluid. In another configuration, the apparatus includes a first fluid channel portion, a second fluid channel portion wrapped helically around the first fluid channel portion, and an opening therebetween. Also disclosed is an apparatus for maintaining substantially even fluid flow in fluid pathways having a first flow resistor portion, a second flow resistor portion, and a fluid channel therebetween.
Claims
1. An apparatus for flowing multiple fluids in a single channel while substantially maintaining fluid separation, comprising: a fluid channel configured to receive a first fluid and a second fluid, wherein at least a portion of the fluid channel has a first internal surface portion and a second internal surface portion, wherein the first internal surface portion is configured to have an affinity to the first fluid and the second internal surface portion is configured to have an affinity to the second fluid, and the first internal surface portion and the second internal surface portion have different fluid affinities, wherein the at least a portion of the fluid channel, including the first internal surface portion and the second internal surface portion, is configured to maintain substantially stable flow of the first fluid and the second fluid within the at least a portion of the fluid channel; and wherein the fluid channel is configured to allow equal volumetric flow rates of the first fluid and the second fluid in the at least a portion of the fluid channel, and a relationship between a dynamic viscosity of the first fluid u.sub.1 and a dynamic viscosity of the second fluid u.sub.2 satisfies the condition of u.sub.1<2 u.sub.2.
2. The apparatus according to claim 1, wherein the first internal surface portion is one of oleophobic and hydrophobic, and the second internal surface portion is the other of oleophobic and hydrophobic.
3. The apparatus according to claim 1, wherein the first internal surface portion is one of hydrophilic and hydrophobic, and the second internal surface portion is the other of hydrophilic and hydrophobic.
4. The apparatus according to claim 1, further comprising: a first coating applied to at least a portion of the fluid channel to provide the first internal surface portion; and a second coating applied to at least a portion of the fluid channel to provide the second internal surface portion.
5. The apparatus according to claim 1, wherein the at least a portion of the fluid channel has a width w and a height h, and a ratio of the width w and the height h is within a range of 1:2 to 10:1.
6. The apparatus according to claim 5, the ratio of the width w and the height h is substantially 2:1.
7. An apparatus for flowing multiple fluids in a single channel while substantially maintaining fluid separation, comprising: a fluid channel comprising: a first fluid channel portion configured to receive a first fluid; a second fluid channel portion configured to wrap helically around the first fluid channel portion and configured to receive a second fluid; and an opening configured to allow for fluid contact between the first fluid flowing through the first fluid channel portion and the second fluid flowing through the second fluid channel portion.
8. The apparatus according to claim 7, wherein the fluid channel is configured to maintain substantially stable flow of the first fluid and the second fluid within the fluid channel.
9. The apparatus according to claim 7, wherein the first fluid channel portion is substantially straight.
10. The apparatus according to claim 7, wherein the first fluid channel portion and the second fluid channel portion each have a substantially circular cross-section.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
DETAILED DESCRIPTION
(21) Referring generally to the FIGURES, apparatuses are shown and described for flowing multiple fluids in a single fluid channel to facilitate molecular transport between the fluids while substantially maintaining fluid separation. Also, an apparatus is shown and described that equilibrates fluid flow in multiple channels.
I. First Embodiment of an Apparatus for Flowing Multiple Fluids in a Single Channel
(22) A. Overview
(23) Disclosed herein are embodiments of an apparatus for flowing multiple fluids, preferably immiscible, in a single channel while substantially maintaining fluid separation. The multiple immiscible fluids may be, for example, blood and a second fluid (e.g., perflourodecalin), but may be other fluids such as oil and water. An apparatus for flowing blood and second fluid is significant because of a need for molecular transport between the blood and the second fluid (e.g., transport of oxygen molecules into the blood and carbon dioxide molecules out of the blood) in a sanitary environment (e.g., avoiding contaminating the blood or biofouling a fluid membrane).
(24) Stable or laminar flow refers to fluid flow in which layers of fluid within a flow slip smoothly over one another without causing disruptions between the fluid layers. In other words, laminar flow is characterized as orderly and predictable fluid flow. In contrast, turbulent flow refers to fluid flow in which layers of fluid disrupt each other in a manner which renders the flow difficult to describe precisely because such flow is characterized as irregular, random, and chaotic. In the apparatus disclosed herein, preferably fluid flow within the apparatus is characterized by a Reynold's number of about 10.
(25) Such fluid flow can be obtained, for example, by unique millifluidic (or mesofluidic) configurations. Millifluidics (or mesofluidics) involves manipulating and controlling fluids, usually in the range of milliliters (10.sup.−3), in networks of channels with cross-sectional dimensions typically of about 0.75 to 1.5 millimeters. Because of the small scale in millifluidics, the dominant force acting within the small channels is surface tension. In such cases, the volumetric flow rates and the relative viscosity of immiscible fluids flowing in the same channel determine the total amount of a cross section of the channel that each fluid will occupy within the channel. If an interface between the multiple fluids does not reach across the channel (i.e., from one side of the channel to a second, opposite side of the channel), stable fluid flow can be maintained in the channel because fluid separation will be substantially maintained due to the fluid interface acting as a pseudo-membrane. The pseudo-membrane stores energy associated with a surface area of the pseudo-membrane and creates a pressure differential between the multiple fluids related to a curvature of the pseudo-membrane. The pressure differential causes the interface to bow in and out away from an edge of the channel that subtends the interface.
(26) It has been determined that stable fluid flow in a single channel can be obtained by configuring internal surfaces to have different affinities to different, immiscible fluids. Accordingly, a first immiscible fluid flows along a first internal surface or surfaces to which the first fluid has an affinity and a second immiscible fluid flows along a second internal surface or surfaces to which the second fluid has an affinity.
(27) B. Housing
(28)
(29) The housing 30 also can support structure for supplying fluids to the fluid channel 21. For example, a first fluid input 22A and a second fluid input 22B can be in fluid communication with an input channel 24A and an input channel 24B, respectively. In turn, the input channel 24A and the input channel 24B are in fluid communication with the fluid channel 21.
(30) Each of inputs 22A and 22B can be configured, by conventional means, for connection with a respective fluid source (not shown) (e.g., an IV bag, etc.), such that fluid inputs 22A and 22B receive a first fluid and a second fluid, respectively, from the fluid sources. As shown in
(31) The housing 30 also can support structure for receiving fluids from the fluid channel 21. For example, an output channel 25A and an output channel 25B are in fluid communication with the fluid channel 21. In turn, the output channel 25A and the output channel 25B are in fluid communication with a first fluid output 23A and a second fluid output 23B.
(32) As shown in
(33) Preferably, the housing 30 supports the fluid channel 21 such that fluid can be pumped to flow through the fluid channel such that the system (and specifically the fluid flow) is unaffected by gravity.
(34) C. Fluid Channel
(35) The fluid channel 21 is configured to allow flow of multiple fluids (e.g., the first and second fluids) while substantially maintaining fluid separation. Thus, molecular transport can be facilitated between the two fluids without fluid intermixture occurring.
(36) The fluid channel 21 can be formed in a variety of configurations. For example, it can be a flexible or rigid channel. Additionally, it can have a variety of cross-sectional shapes, but a rectangular cross-sectional shape with four sides is preferred. The fluid channel 21 can be formed of any suitable material for transporting biomaterials.
(37)
(38) The at least one first internal surface 31 has an affinity to a first fluid, and the at least one second internal surface 32 has an affinity to a second fluid. The affinity of the internal surfaces 32 can be established in a variety of ways. For example, the affinity can be established by the material of the corresponding portion of the fluid channel 21. For example, a hydrophilic surface could be made of hydrogels, polyamides, or hydroxylated polyurethanes. As another example, a hydrophobic surface could be made of polytetrafluoroethylene or polymethylene. Alternatively, the affinity can be established by a treatment, such as a coating, applied to the interior of the fluid channel 21. Such treatments include plasma or corona treatments or coating a surface with hydrogels, polyamides, or hydroxylated polyurethanes (to create a hydrophilic surface) or coating a surface with polytetrafluoroethylene or polymethylene (to create a hydrophobic surface. For example, the affinity of each internal surface can be established by applying a first coating on the at least one first internal surface and applying a second coating to the at least one second internal surface. As a more specific example, the above substances can be applied in any suitable order, with appropriate masking (e.g., apply or coat a first coating on the first internal surface, mask the first coating, and apply or coat a second coating on the second internal surface).
(39) As one example of the affinities of the surfaces for the fluids, the at least one first internal surface 31 can be configured to be one of oleophobic and hydrophobic and the at least one second internal surface 32 can be configured to be the other of oleophobic and hydrophobic. In a further example, the at least one first internal surface 31 can be configured to be one of hydrophilic and hydrophobic and the second internal surface can be configured to be the other of hydrophilic and hydrophobic 32. For example, for hydrophilicity a contact angle with water of no more than 50 degrees is preferred, and for hydrophobicity a contact angle with water of more than 110 degrees is preferred.
(40) When multiple immiscible fluids flow in fluid channel 21, a fluid interface 38 is created by a first fluid and a second fluid. Depending on parameters, such as the configuration of the fluid channel 21, the flow rates, and the fluids used, the fluid interface may occur at different locations within the fluid channel 21. For example, the parameters may cause the fluid interface 38A to exist at the location in the fluid channel 21A shown in
(41) The shape of fluid interface 38 approximates a segment of a circle. However, using a parabolic shape to estimate an extent to which the first fluid extends into the second fluid will overestimate the height of the fluid interface because the height of the segment from the chord that subtends the circle is less than the height of the parabola. Accordingly, such an approach will provide an additional margin to prevent the fluid interface from reaching across the fluid channel.
(42) The shape of a parabola is generally defined by relationship (1): y=ƒ(x), where the function ƒ(x) is generally of the form given such that relationship (2) defines the shape of a parabola:
(43) y=Cx.sup.2−h, with respect to the dimensions in
(44) As a result, the shape of the interface (as estimated by a parabolic shape is described by relationship (4):
y=h(4x.sup.2/w.sup.2−1)
Thus, an area of the first fluid that lies within the parabola (that is, in the area of fluid channel 21 that is above fluid interface 38 and below internal surface portion 31) is given by relationship (5):
A.sub.1=⅔hw
The second fluid therefore occupies the remaining space in fluid channel 21 and this area is described by relationship (6):
A.sub.2=Hw−⅔hw
(45) Assuming equal volumetric flow rates (a volumetric flow rate of the first fluid is equal to a volumetric flow rate of the second fluid), the ratio of areas occupied by the first fluid and the second fluid in fluid channel 21 is determined by a viscosity of the first fluid and a viscosity of the second fluid, with a relatively more viscous fluid taking up a proportionally greater amount of area. This can be expressed by relationship (7):
A.sub.1/u.sub.1=A.sub.2/u.sub.2
(46) Using relationship (7) to relate relationship (5) to relationship (6) yields the following derivation for relationship (8):
⅔hw/u.sub.1=Hw/u.sub.2−⅔hw/u.sub.2
and relationship (9):
h/u.sub.1=3/2(H/u.sub.2−⅔h/u.sub.2)=3/2H/u.sub.2−h/u.sub.2
and relationship(10):
h(1/u.sub.1+1/u.sub.2)=3/2H/u.sub.2
(47) Solving for the height h 34 of the fluid interface yields relationship (11):
h=3/2H u.sub.1/(u.sub.1+u.sub.2)
(48) Therefore, the height h 34 of the fluid interface is equal to the channel height H 37 when relationship (12) holds:
3/2u.sub.1/(u.sub.1+u.sub.2)−1=0
(49) Relationship (12) holds when relationship (13) is true: u.sub.1=2u.sub.2. In other words, the fluid interface 38 will reach from one side to an opposite side of the fluid channel 21 when a dynamic viscosity of the first fluid is equal to twice a dynamic viscosity of the second fluid.
(50) Assuming, therefore that a volumetric flow rate of the first fluid is equal to a volumetric flow rate of the second fluid, the fluid interface will remain substantially stable (i.e., the fluid interface will not reach across the fluid channel) as long as a dynamic viscosity of the first fluid is less than twice a dynamic viscosity of the second fluid, that is, the relationship of the dynamic viscosities of the two fluids satisfies the condition of u.sub.1<2u.sub.2, where u.sub.1 is the dynamic viscosity of the first fluid and u.sub.2 is the dynamic viscosity of the second fluid.
(51)
(52)
(53) Because the first fluid and the second fluid are immiscible, the first internal surface portion and the second internal surface portion have different fluid affinities. Further, the first internal surface portion and the second internal surface portion are configured to substantially maintain stable fluid flow of the two immiscible fluids in the fluid channel.
(54) According to the embodiment illustrated in
(55) According to the embodiment illustrated in
(56) According to the embodiment illustrated in
(57) As described herein, embodiments can be constructed in which multiple fluids are flowed in a single channel 21, while substantially maintaining fluid separation. While it is desired to maintain 100% fluid separation, it is understood that sufficient fluid separation can be an amount of separation that may be less than 100% fluid separation, while still being acceptable commercially or for the particular application. In some embodiments, there can be at least 90% fluid separation. In some embodiments, there can be at least 95% fluid separation. In some embodiments, there can be at least 98% fluid separation. In some embodiments, there can be at least 99% fluid separation.
II. Second Embodiment of an Apparatus for Flowing Multiple Fluids in a Single Channel
(58) A. Overview
(59) Disclosed herein is an embodiment of an apparatus for flowing multiple fluids, preferably immiscible, in a single fluid channel while substantially maintaining fluid separation. The multiple immiscible fluids may be, for example, blood and a second fluid (e.g., perflourodecalin), but may be other fluids such as oil and water. An apparatus for flowing blood and the second fluid is significant because of a need for molecular transport between the blood and the second fluid (e.g., transport of oxygen molecules into the blood and carbon dioxide molecules out of the blood) in a sanitary environment (e.g., avoiding contaminating the blood or biofouling a fluid membrane).
(60) Separate fluid flow of two immiscible fluids (one of which preferably is blood) can be maintained in a single fluid channel by configuring the physical structure of the fluid channel to take advantage of the unusual fluid characteristics of blood flow due to RBCs in the blood (e.g., the deformation and tumbling of RBCs during flow and the tumbling of RBCs away from regions of high shear). The fluid channel is configured to employ helical flow such that a first fluid flows in an inner, central straight path and a second fluid flows in an outer, helical path around the inner, central straight path. For example, the first fluid is blood and fluid separation between the blood and the second fluid is substantially maintained because RBCs in the blood will tend to tumble to the middle of the flow in the central, straight path. In a further example, the second fluid is blood and fluid separation between the blood and the first fluid is substantially maintained because a rotational flow of RBCs in the blood in the outer, helical path, will tend to tumble towards the outside of the outer flow path and away from the first fluid.
(61) Such an apparatus can be useful for hemodialysis and blood oxygenation because of the need to prevent RBCs from intermixing with another fluid without using a physical membrane.
(62) B. Housing
(63)
(64) The housing 130 also can support structure for supplying fluids to the fluid channel 75. For example, a first fluid input 72A and a second fluid input 72B can be in fluid communication with an input channel 71 and an input channel 73, respectively. In turn, the input channel 71 and the input channel 73 are in fluid communication with the fluid channel 75.
(65) Each of first and second fluid inputs 72A and 72B can be configured, by conventional means, for connection with a respective fluid source (not shown) (e.g., an IV bag, etc.), such that fluid inputs 72A and 72B receive a first fluid and a second fluid, respectively, from the fluid sources. As shown in
(66) The housing 130 also can support structure for receiving fluids from the fluid channel 75. For example, an output channel 83 and an output channel 84 are in fluid communication with the fluid channel 75. In turn, the output channel 83 and the output channel 84 are in fluid communication with a first fluid output 74A and a second fluid output 74B.
(67) As shown in
(68) Preferably, the housing 130 supports the fluid channel 75 such that fluid can be pumped to flow through the first channel such that the system (and specifically the fluid flow) is unaffected by gravity.
(69) C. Fluid Channel
(70) The fluid channel 75 is configured to allow flow of multiple fluids (e.g., the first and second fluids) while substantially maintaining fluid separation. Thus, molecular transport can be facilitated between the two fluids without fluid intermixture occurring. The fluid channel 75 can include a first fluid channel portion 75′ and a second fluid channel portion 75″.
(71) 1. First Fluid Channel Portion
(72)
(73) Preferably, the first fluid channel portion 75′ is substantially straight. As shown in
(74) The first fluid channel portion 75′ is configured to receive a first fluid from the input channel 71. The first fluid channel portion 75′ is configured such that a portion of the first fluid channel portion 75′ is in fluid communication with the second fluid channel portion 75″ through the opening 81. The first fluid channel portion 75′ directs the first fluid to flow into the output channel 83 to exit the apparatus.
(75) 2. Second Fluid Channel Portion
(76)
(77) As shown in
(78) The second fluid channel portion 75″ is configured to receive a second fluid, which is different from the first fluid, from the input channel 73. The second fluid channel portion 75″ is configured such that the opening 81 of the second fluid channel portion 75″ is in fluid communication with the first fluid channel portion 75′. The second fluid channel 75″ directs the second fluid to flow into the output channel 84 to exit the apparatus.
(79) As shown in
(80) 3. Opening
(81) As shown in
(82) With reference to
(83) TABLE-US-00001 TABLE 1 Angle Diameter Diameter Length Width 76 D.sub.1 D.sub.2 L W Design 1 45° 0.6 mm 0.6 mm 50 mm 0.4 mm Design 2 30° 0.4 mm 0.6 mm 50 mm 0.25 mm
(84) As described herein, embodiments can be constructed in which multiple fluids are flowed in a single channel 75, while substantially maintaining fluid separation. While it is desired to maintain 100% fluid separation, it is understood that sufficient fluid separation can be an amount of separation that may be less than 100% fluid separation, while still being acceptable commercially or for the particular application.
III. Embodiment of an Apparatus for Maintaining Substantially Even Fluid Flow in Fluid Pathways
(85) A. Overview
(86) To increase throughput, it can be desirable to provide an apparatus having a number of fluid pathways that preferably each include, for example, the fluid channels 21 and 75 described above. To supply fluid to such fluid channels, it can be efficient to feed the fluid into an input and spread the fluid to each of the fluid channels via the separate fluid pathways.
(87) To maintain substantially even fluid flow across the fluid pathways, an apparatus for equilibrating fluid flow is disclosed. Generally, in fluid systems, uneven levels of flow in parallel fluid pathways result due to different levels of fluid resistance present in each fluid pathway. A fluid pathway having a lesser fluid resistance will enable a greater flow rate, and, conversely, a fluid pathway having a greater fluid resistance will have a lower flow rate.
(88) In the apparatus disclosed herein, flow resistor portions are provided in each of the fluid pathways. The flow resistor portions can equalize the levels of fluid resistance present in each fluid pathway, thereby maintaining substantially even fluid flow across the fluid pathways. For example the flow resistor portions can add a pressure drop to the fluid flow in each of the fluid pathways.
(89) The apparatus may have more than one set of fluid pathways. An embodiment will be described having two sets of fluid pathways. The first set of fluid pathways will be described in detail, with it being understood that the second set of fluid pathways can be configured to have essentially the same structure. Alternatively, the second set of fluid pathways can be configured to have a different structure, as described in more detail below. Each set of fluid pathways can receive a respective fluid. For example, the first set of fluid pathways can receive a first fluid and the second set of fluid pathways may receive a second fluid. According to a preferred embodiment, the first fluid may be blood and the second fluid may be a perfluorocarbon. Each fluid pathway of the first set of fluid pathways may have a fluid channel that coincides with a corresponding fluid channel of a fluid pathway in the second set of fluid pathways to facilitate molecular transport between fluids in the first and second sets of fluid pathways.
(90) B. Housing
(91)
(92) Preferably, the housings 230, 230′ support the fluid pathways such that fluid can be pumped to flow through the fluid pathways such that the system (and specifically the fluid flow) is unaffected by gravity.
(93) C. Fluid Input(s)
(94) Apparatus 90 has fluid inputs 91 and 91′ that are configured to receive fluid from external sources. Each of fluid inputs 91 and 91′ can be configured, by conventional means, for connection with a respective fluid source (not shown) (e.g., an IV bag, etc.), such that fluid inputs 91 and 91′ receive a first fluid and a second fluid, respectively, from the fluid sources.
(95) Fluid inputs 91 and 91′ are in fluid communication with the first and second set of fluid pathways, respectively.
(96) D. First Set of Fluid Pathways
(97)
(98) 1. First Flow Resistor Portions
(99) The first flow resistor portions 95A, 95B, 95C are configured to increase fluid resistance in the fluid pathways. In the illustrated embodiment, each of the first flow resistor portions 95A, 95B, 95C increases fluid resistance by changing the direction of the flow in the fluid pathway. For example, the first flow resistor portions 95A, 95B, 95C can have a serpentine shape, which changes the direction of fluid flow and increases a length of a fluid pathway. Preferably, each first flow resistor portion 95A, 95B, 95C is configured to avoid excessive shear rates in any turn or change of direction. Preferably, each first flow resistor portion 95A, 95B, 95C is configured to maintain shear rates less than 2000 inverse seconds (s.sup.−1).
(100) In some embodiments, the first flow resistor portions 95A, 95B, 95C can have an approximately square cross-sectional shape, but other appropriate cross-sectional shapes could be utilized. Preferably, each of the first flow resistor portions 95A, 95B, 95C has a width and a height in the range of 0.4 to 1.0 mm, and more preferably a width of about 0.8 mm and a height of about 0.75 mm high. However, other suitable dimensions could be used, as appropriate.
(101) 2. Fluid Channels
(102) Fluid channels 97A, 97B, 97C are in fluid communication with and positioned downstream to receive fluid from the first flow resistor portions 95A, 95B, 95C.
(103) The fluid channels 97A, 97B, 97C each can be fully enclosed channels to contain fluid. However, in the illustrated embodiment (see
(104) 3. Second Flow Resistor Portions
(105) The second flow resistor portions 99A, 99B, 99C are configured to increase fluid resistance in the fluid pathways. Preferably the second flow resistor portions 99A, 99B, 99C are in fluid communication with and positioned downstream to receive fluid from the fluid channels 97A, 97B, 97C.
(106) In some embodiments, the second flow resistor portions 99A, 99B, 99C can have an approximately square cross-sectional shape, but other appropriate cross-sectional shapes could be utilized. Preferably, each of the second flow resistor portions 99A, 99B, 99C has a width and a height in the range of 0.4 to 1.0 mm, and more preferably a width of about 0.8 mm and a height of about 0.75 mm high. However, other suitable dimensions could be used, as appropriate.
(107) E. Fluid Output(s)
(108) Apparatus 90 can have a single fluid output for each of the first and second set of fluid pathways. In a more preferred embodiment shown in
(109) F. Second Set of Fluid Pathways
(110)
(111) G. Configurations of Flow Resistor Portions
(112) In the embodiments described above, a fluid pathway in the first set of fluid pathways and a corresponding fluid pathway in the second set of fluid pathways may have the same configuration, e.g., both of the corresponding fluid pathways will have the same configuration for the first flow resistor portion, fluid channel, and second flow resistor portion. However, it is contemplated that the corresponding fluid pathways may have different configurations, e.g., differences in the flow resistor portions, to achieve balanced and/or desired flow across corresponding fluid pathways. Some contemplated embodiments are more specifically described below.
(113) For example,
(114) However, if the second fluid is more viscous than the first fluid, that configuration may be less than optimal. For example, if the fluid output 103A is set at atmospheric pressure (that is, the fluid output 103A is open to the atmosphere), then the following relationship (14) holds:
P.sub.4=0
and relationship (15):
P.sub.3=P.sub.4+ΔP.sub.3
and relationship (16):
P.sub.5=P.sub.3−ΔP.sub.4.
Substituting relationships (14) and (15) into relationship (16) yields relationship (17):
P.sub.5=P.sub.4+ΔP.sub.3−ΔP.sub.4−ΔP.sub.3−ΔP.sub.4.
Because the second fluid is more viscous than the first fluid, then relationship (18) also holds:
ΔP.sub.4>ΔP.sub.3.
Given relationship (18), then relationship (19) follows:
P.sub.5<0,
thereby indicating that the fluid output 103A′ of the fluid pathway of the second set of fluid pathways is in a vacuum. It is undesirable to have the fluid output 103A′ in a vacuum because, particularly when each fluid pathway includes a flexible tubing, the tubing may pinch when subjected to a vacuum.
(115) To avoid the problems associated with having the fluid output 103A′ under a vacuum, a smaller resistor portion may be used for the fluid pathway in which the second fluid flows. For example, as shown in
(116) Another alternative to avoiding the problems associated with having the fluid output 103A′ under a vacuum, the fluid pathway in which the second fluid flows may omit the second flow resistor portion 99A′ entirely. For example, as shown in
(117) The construction and arrangement of the apparatuses and methods as shown in the various exemplary embodiments are illustrative only. Although only a few embodiments have been described in detail in this disclosure, many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.). For example, the position of elements may be reversed or otherwise varied and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of the present disclosure. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present disclosure.