Elastically turbulent compositions and systems

Abstract

A fluid composition capable of exhibiting elastic turbulence when pumped through a flow path that forces a change of direction of a flow line, and comprising a solution of two or more two classes of flexible linear polymers. The first class has an average molecular weight of at least 10 mega Daltons and the second class has an average molecular weight in the range of 0.25 to 5 mega Daltons. The concentration of the first polymer is sufficient to achieve elastic turbulence regardless of the presence of the second class. The concentration of the second class is greater than the concentration of the first class. When flowing to or out of the chamber at low shear, the flow path will cause elastic turbulence, and the second polymer will reduce elastic instability and pressure drop resulting therefrom, thereby reducing pumping energy requirements.

Description

Cross-reference to related applications

[0001] The disclosure of this subject matter claims priority to UK Patent Application No. GB2314051.0, filed on 14 September 2023, which is incorporated herein by reference in its entirety. Technical Field

[0002] This disclosure relates to compositions capable of exhibiting elastic turbulence, as well as methods and systems for using elastic turbulence. Background Technology

[0003] This disclosure utilizes the phenomenon of elastic turbulence. It is well known that Newtonian fluids such as water can undergo both laminar and turbulent flow. This type of turbulence is called inertial turbulence. The states of laminar and turbulent flow are usually expressed using the Reynolds number, which is the ratio of inertial forces to viscous forces within the fluid. The Reynolds number is dimensionless because it is a ratio. When the Reynolds number exceeds approximately 2000, the fluid exhibits inertial turbulence. When the Reynolds number is below approximately 1500, the Newtonian fluid is in a laminar state.

[0004] Elastic turbulence is a distinct physical phenomenon discovered in the late 20th century. Observed at low flow velocities, it involves low Reynolds numbers, and Newtonian fluids will be in a laminar state. Some early observations of elastic turbulence used the older term "elastic instability." However, this term is more general and encompasses other forms of instability in flow. Elastic turbulence occurs in solution fluids containing dissolved molecules that have one or more flexible, long chains that can entangle with other such molecules. Elastic turbulence is observed when a fluid flows at a sufficient velocity along a flow path, causing the streamlines to change direction. Numerous studies have mentioned the potential applications of elastic turbulence in microfluidics, where the size of the flow path and the flow velocity are so small that the device volume does not exceed 10 ml, and the Reynolds number is very small, well below one. Summary of the Invention

[0005] This summary is provided to introduce concepts that will be further elaborated and described in the detailed description below. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid to limiting the scope of the claimed subject matter.

[0006] A previously unrecognized problem involves the flow of fluids containing dissolved polymers that can induce elastic turbulence, which does not occur when the fluid flows at low speeds and therefore under low shear conditions. This can happen, for example, when fluid is pumped through a pipe to the inlet of a device where elastic turbulence is expected. The strong elasticity of the dissolved polymer does not induce elastic turbulence in the pipe, but it does introduce some flow instability, increasing pressure drop and requiring a more powerful pump that consumes more energy.

[0007] We have now discovered that elasticity under low shear conditions can be reduced by using blends of polymers.

[0008] A first aspect of this disclosure is a fluid composition capable of exhibiting elastic turbulence when flowing, the fluid composition being a solution of two or more polymers, the solution comprising: at least one dissolved first polymer, which is a linear polymer with a weight-average molecular weight of at least 10 megadaltons; and at least one dissolved second polymer, which is a linear polymer with a weight-average molecular weight in the range of 0.25 to 5 megadaltons; wherein the amount of the higher molecular weight polymer is in the range of 0.05 to 5% by weight of the solution and is sufficient to enable the solution containing the first higher molecular weight polymer but not the second lower molecular weight polymer to exhibit elastic turbulence, and wherein the amount of the second polymer is greater than the amount of the first polymer but does not exceed 10% by weight of the solution.

[0009] As disclosed herein, it has been found that including a lower molecular weight second polymer reduces overall elasticity under low shear conditions. It also affects the temperature range in which elastic turbulence may occur.

[0010] Another aspect of this disclosure is a system comprising a fluid containment structure defining a fluid flow path, the fluid containment structure including: a chamber with an inlet and an outlet and internal barriers to force a streamline of fluid flow to change direction, and conduits leading to the inlet and the outlet of the chamber, wherein the system further includes at least one pump for propelling fluid through the conduits and the chamber, and wherein the structure contains a fluid composition according to the first aspect above. The internal barriers may be an array with regular spacing.

[0011] Fluid flow paths can be loops. Pipes can transport fluid from a storage container to an inlet, and can also transport fluid from an outlet back to the same storage container or another storage container.

[0012] A third aspect of this disclosure is a method of operating the system described above, the method comprising pumping the fluid through the conduit and the chamber at a certain flow rate, such that the fluid is in laminar flow without elastic turbulence in the conduit leading to the chamber, and in an elastic turbulent state within the chamber. The viscosity of the fluid, the flow rate of the fluid within the chamber, and the gap width between internal obstacles can yield a flow Reynolds number (Re) in the range of 1 to 1000.

[0013] One possibility for the above system and method is that the chamber can be part of a heat exchanger, wherein the wall of the chamber in contact with the fluid flowing through the chamber is an interface through which heat is conducted to or from the fluid flowing through the chamber, and elastic turbulence within the chamber increases the rate at which heat energy enters or leaves the fluid flowing through the chamber.

[0014] Another possibility for the above system and method is that the chamber can be part of an electrochemical cell, and the fluid contains at least one chemical substance capable of undergoing an electrochemical reaction at the electrodes of the cell. The chamber may be, or can surround, a porous electrode, or the electrode may be in contact with the fluid flowing through the chamber. Elastic turbulence then enhances the transport of the active material to the electrode surface. Alternatively or additionally, elastic turbulence enhances the transport of electrochemical reaction products away from the electrode. Attached Figure Description

[0015] In the following detailed description, the subject matter disclosure is further described with reference to the several accompanying drawings, which are labeled with non-limiting examples of the subject matter disclosure, wherein the same reference numerals denote similar parts throughout the several views of the drawings, and wherein: Figure 1 This is a diagram showing the experimental results of the onset of elastic turbulence; Figure 2 This is a graph showing the relationship between repptation time and shear rate; Figure 3 This is a schematic view of a heat transfer system, which has two devices for heat transfer, both of which are shown in cross-section. Figure 4 It shows Figure 3 Part of the support array in the heat transfer device; Figure 5 It is along Figure 3 A cross-section of a heat transfer device taken by the AA line; Figure 6 yes Figure 5 A magnified view of a portion; Figure 7 Is with Figure 6 A similar view shows pillars with different cross-sections; Figure 8 This is a schematic diagram showing the components of a flow battery; Figure 9 It is along Figure 8 The view taken from the BB line shows the circulation path of the electrolyte fluid through the porous electrode. Figure 10 This is a diagram showing the components of another flow battery; Figure 11 yes Figure 10 Perspective view of the current-conducting components used in the battery; Figure 12 It shows Figure 10 The five connections in the flow battery form a battery stack; Figure 13 This is a diagram showing the components of a fuel cell; Figure 14 It is a graphical view of the equipment used to determine the system's operating parameters; and Figure 15 and 16 Experimental results obtained using an implementation of such a device are shown. Detailed Implementation

[0016] The details shown herein are merely illustrative and for the purpose of explaining embodiments of the subject matter disclosure only, and are presented in the manner that is considered most useful and readily understood in terms of the principles and concepts of the subject matter disclosure. In this regard, no attempt is made to show structural details in more detail than is necessary for a basic understanding of the subject matter disclosure, and the description, taken in conjunction with the accompanying drawings, will be readily apparent to those skilled in the art as to how various forms of the subject matter disclosure may be manifested in practice. Furthermore, the same reference numerals and symbols in the various drawings indicate the same elements.

[0017] This specific embodiment relates to embodiments of this disclosure and the possibilities that can be used. It should be understood that the features or possibilities described in combination may be used individually, if doing so is feasible. Furthermore, any feature or possibility described in any embodiment may be used in any other embodiment, whenever possible.

[0018] The compositions according to this disclosure are solutions containing two classes of soluble polymers defined by molecular weight and chain length. The first class is a high molecular weight polymer with a molecular weight of at least 10 megadaltons (i.e., at least 10,000,000 g / mol) and containing at least one flexible linear chain. This chain can have a chain length of at least 5,000 monomer units linked together sequentially by single chemical bonds. Single chemical bonds allow rotation at the bond, while double bonds do not. One or more polymers of this class are capable of achieving elastic turbulence. This first class of polymers can contain at least one linear chain with a length of at least 20,000 monomer residues linked by single bonds, and the chain length can be significantly greater, such as at least 50,000 or at least 100,000 monomer residues. This first class of polymers can comprise a single linear chain with a length of 250,000 or more monomer units, but may also have some chain branches connecting the long linear chains. The weight-average molecular weight of this first class of polymers can be at least 15 megadaltons or at least 16 or 17 megadaltons. It may even be higher, such as at least 23 megadaltons. The concentration of this high molecular weight polymer in the solution may not exceed 5% by weight, for example, in the range of 0.05% or 0.1% to 1% or 2% by weight.

[0019] The second type of polymer also contains at least one flexible linear chain. These polymers have low molecular weights, with a weight-average molecular weight in the range of 0.25 megadaltons to 5 megadaltons. In some embodiments, the molecular weight of this type of polymer is at least 0.5 megadaltons or at least 1 megadalton. This type of polymer may contain at least one linear chain consisting of at least 2,000 monomer residues linked by a single chemical bond. The length of a single linear chain in this type of polymer can be much greater than 2,000 or 5,000 monomer units, while still meeting the requirement that the average molecular weight is not greater than 5 megadaltons.

[0020] The concentration of the second type of polymer should be greater than that of the first type of polymer. The concentration of one or more second type of polymers may not exceed 10% by weight of the fluid, and may also not exceed 7% by weight or 5% by weight. The concentration of one or more second type of polymers may be at least twice the concentration of the first type of polymer, and may be at least three times or at least four times the concentration of the first type of polymer.

[0021] Both types of polymers described above contain linear chains of monomer units. These monomer units can be linked together by single chemical bonds to allow rotation. The polymer chains can be homopolymers derived from a single monomer, or the chains can be copolymers of more than one monomer, such as linear block copolymers. The polymer can also contain side chains attached to long-chain monomer units, which are linked together by single covalent bonds. If the chains contain units that are themselves oligomers, such as in block copolymers, the oligomer units can rotate more freely relative to each other than the monomer residues within the oligomer units. The polymer can contain some chain branching, for example at branching points where three or more linear chains are linked together, with each linear chain having at least 1000 monomer units, and possibly at least 2000 or 5000 monomer units.

[0022] The flexibility of polymer chains allows polymer molecules to entangle. This flexibility can be described using mathematical models. The free-linked chain model is commonly used, and the flexibility of a particular polymer can be represented by the parameters of an equivalent free-linked chain (which is itself a mathematical model). This approach was described by Rubinstein and Colby in Chapter 2 of *Polymer Physics*, published by Oxford University Press in 2003. The equivalent free-linked chain has the same mean-square end-to-end distance and the same maximum end-to-end distance as the actual polymer, but is thought to contain so-called Kuhn monomers that can rotate freely relative to each other. These model monomers have a length and molar mass called the Kuhn length.

[0023] The aforementioned Class I polymer may contain at least one flexible polymer chain whose length and composition correspond to at least 5,000 Kuhn monomers, with a Kuhn length not exceeding 100 angstroms (10 nm) and possibly not exceeding 50 angstroms. If the Class I polymer is a single unbranched chain, its length may correspond to at least 20,000 Kuhn monomers, and possibly even at least 50,000 Kuhn monomers.

[0024] The length and composition of the aforementioned second type of polymer may correspond to at least 100 Kuhn monomers, possibly at least 250 or at least 500 Kuhn monomers, and the Kuhn length may not exceed 100 angstroms and may not exceed 50 angstroms.

[0025] Elastic turbulence has been observed in solutions of several different long-chain polymers. One of these polymers is polyacrylamide, which can be hydrolyzed or partially hydrolyzed. Groisman and Steinberg provided experimental evidence for elastic turbulence in high molecular weight polyacrylamide solutions in their article "Elastic Turbulence in a polymer solution flow" published in Nature (Vol. 45, p. 53, 2000). Other examples of long-chain polymers reported to be capable of inducing elastic turbulence include: polyisobutylene with a molecular weight of 4 to 6 megadaltons dissolved in organic solvents (Dris and Shaqfeh, *J. Non-Newtonian Fluid Mech.*, Vol. 80, pp. 1–58, 1998); polystyrene with a molecular weight of 18 megadaltons dissolved in organic solvents (Magda and Larson, *J. Non-Newtonian Fluid Mech.*, Vol. 30, pp. 1–19, 1988); and polyoxyethylene with a molecular weight of 4 megadaltons dissolved in aqueous solution (Davoodi et al., *J. Fluid Mech.*, Vol. 857, pp. 823–850, 2018). Rubinstein and Colby give the Kuhn lengths of polystyrene and polyoxyethylene as 18 Å and 11 Å, respectively, on page 53. The Kuhn length of polyacrylamide has been reported to be 15 to 25 angstroms (Fetters, Lohse and Colby, Chain Dimensions and Entanglement Spacings, in Mark, JE, ed., In Physical Properties of Polymers Handbook, pp. 447–454, Springer, New York, 2007).

[0026] The first type of polymer can be a single polymer or a mixture of polymers. Similarly, the second type of polymer can be a single polymer or a mixture. These two types of polymers can be polymers of the same monomers that differ only in length, or they can be polymers of different monomers. For example, the first type could be partially hydrolyzed polyacrylamide, while the second type could be polyethylene glycol.

[0027] When using long-chain polymers to achieve elastic turbulence, it is best to include biocides to protect the polymer from biodegradation.

[0028] When a solution contains substances capable of inducing elastic turbulence, elastic turbulence occurs if the solution flows at a sufficient velocity (possibly low) and the flow path causes the streamlines to bend. Therefore, one known possibility for a flow path inducing elastic turbulence is a serpentine channel. Another possibility is described below with reference to the accompanying figures. Elastic turbulence is discussed in detail by Steinberg in *Annual Review of Fluid Mechanics*, Volume 53, pp. 27-58 (2021).

[0029] According to this disclosure, compositions containing two types of polymers and compositions not containing one or more of the second type of polymers can both exhibit elastic turbulence under similar flow conditions. Under low-shear conditions without elastic turbulence, one or more of the first type of polymers will increase the viscosity of the composition. It has been found that, according to this disclosure, containing one or more of the second type of polymers with lower molecular weights can reduce the viscosity under low shear.

[0030] The ability of solutions to exhibit elastic turbulence can be experimentally demonstrated. In a cone-plate rheometer, the elastic instability begins to manifest as a significant increase in viscosity at a specific shear rate with increasing shear force, which is associated with a sudden increase in noise in the measured torque signal. This has been described by DO Olagunju in "The relaxation time of entangled HPAM solutions in flow" (published in Z Angew Math Phys, Vol. 46, pp. 224-238 (1995)) and by E. Tran and A. Clarke in "The relaxation time of entangled HPAM solutions in flow" (published in Journal of Non-Newtonian Fluid Mechanics, Vol. 311, pp. 104954 (2023)). The significant increase in viscosity can be viewed as a change in the slope (sometimes referred to as an increase) in the viscosity versus shear rate graph. Figure 1 The results of experimental tests conducted using a laboratory rheometer are shown, measuring at both increasing and decreasing shear rates. This is a graph showing the dynamic viscosity versus increasing shear rate for four aqueous solutions, all containing 0.456 wt% sodium chloride, a small amount of linearly partially hydrolyzed polyacrylamide, and a few drops of a biocide composed of isopropanol and thiourea. The polyacrylamide in the solutions is: a) (Solid circle) 0.24% by weight of Flopaam 3630, which is 30% hydrolyzed polyacrylamide with an average molecular weight between 18 and 20 megadaltons. b) (Hollow circle) 0.2% by weight of Flopaam 6040, which is 40% hydrolyzed polyacrylamide with an average molecular weight between 25 and 30 megadaltons. c) (Hollow rhombus) 1.24% by weight of Flopaam 3130, which is 30% hydrolyzed polyacrylamide with an average molecular weight of 3.6 megadaltons. d) (Solid cube) A mixture of 1.24% by weight of Flopaam 3130 and 0.2% by weight of Flopaam 6040.

[0031] These Flopaam partially hydrolyzed polyacrylamides are available from SNF Floerger, headquartered in André-Dreyjoy, France.

[0032] The polymers used in solutions (a) and (b) both meet the requirements of the first category mentioned above. For solutions (a) and (b), the onset of elastic turbulence with increasing shear rate can be considered as the curve being plotted at approximately 150 s. -1 The slope change at the point. The polymer used in solution (c) meets the requirements of the second category described above. No elastic turbulence was observed within the tested shear rate range, but it is possible that this polymer could induce elastic turbulence at higher shear rates than the rheometer used here. Solution (d) contains a mixture of polymers that meet the requirements of this disclosure. The initiation of elastic turbulence in solution (d) occurs at shear rates similar to those of solutions (a) and (b). Therefore, at the higher shear rates required for the initiation of elastic turbulence, the elastic properties are dominated by the high molecular weight polymer of the first category.

[0033] Characteristic times indicating the relaxation time of elastic polymers or polymer blends can be derived by fitting measurements to a model (such as the Carreau-Yasuda model, which is a mathematical equation relating multiple parameters). Tools for fitting data to equations are available in both general-purpose and specialized software (such as Matlab, Excel, and Python). Figure 2 This is a crawling time plot of a solution (a) containing Flopaam 3630 and a solution (d) containing a mixture of Flopaam 6040 and Flopaam 3130 at shear rates below the initiation of elastic turbulence. The crawling time is a characteristic time indicating relaxation under low shear conditions. At 0.01 sec... -1 At the lowest shear rate, the crawling time for solution (a) was 9.5 seconds, while the repeating time for solution (d) was only 0.2 seconds. Furthermore, at 0.01 sec... -1 At the given shear rate, the creep time of solution (b) is 28.5 seconds. Therefore, under low shear conditions, the elastic properties of the solution are mainly dominated by the less elastic polymer in the second class.

[0034] These findings indicate that, according to the present disclosure, solutions containing polymer mixtures will generate elastic turbulence under flow rates and shear conditions similar to those required for solutions containing only the first type of polymers (excluding the second type of lower molecular weight polymers); however, under low shear conditions, the polymer mixtures will exhibit less elastic properties, thereby mitigating elastic instability and reducing pressure drop during low-shear flow.

[0035] Another effect of including the polymers in the second class is a change in the effect of temperature on the initiation of elastic turbulence. For the fluid containing Flopaam 3630 (a), the initiation of elastic turbulence shifts towards slightly higher shear rates with increasing temperature. For the fluid containing a mixture of the two types of polymers (d), the shift of the initiation of elastic turbulence towards higher shear rates is more pronounced with increasing temperature.

[0036] The compositions according to this disclosure can be used in various systems in which fluid is pumped into and through a chamber in which the fluid exhibits elastic turbulence. The reduced elastic properties under low shear conditions can decrease pressure drop as the fluid is pumped along a pipe, conduit, or any other form of flow path to the chamber inlet and as the fluid is pumped along a pipe, conduit, or other flow path out of the chamber outlet.

[0037] Figures 3 to 7 This illustrates the use of a fluid containing a polymer mixture when the fluid is the working fluid of a heat transfer loop, wherein the walls of a chamber with elastic turbulence are the interfaces through which heat is transferred to or from the working fluid.

[0038] Figures 8 to 12 The use of a fluid containing a polymer mixture in an electrochemical half-cell is shown, wherein the fluid is an electrolyte pumped through the half-cell and generates elastic turbulence upon contact with the electrodes.

[0039] As an example embodiment of this disclosure, Figure 3 A heat transfer system is shown for transferring thermal energy from a heat source to a given volume of water. Figure 3 The device 10 on the left is exposed to the sun so that it can be heated. Figure 1 The device 12 on the right is submerged in water. The two devices 10 and 12 are connected by a pipe 14 for circulating a working fluid, which is pumped around the loop by a pump 16. The pipe section conveying the hot working fluid is surrounded by insulation 24. Devices 10 and 12, together with pipe 14 and pump 16, form a heat exchange loop for transferring solar energy received at the surface 20 of device 10 to the water surrounding device 12.

[0040] The device 10 has a cuboid outer shell defining a chamber through which the working fluid is pumped. The outer shell surface 20, exposed to solar heat, is the interface between the working fluid within the shell and the heat source. This is made of a thermally conductive material, such as copper or aluminum. The opposing surface 22 has an insulating layer 24 abutting it to reduce heat loss.

[0041] Inside the housing of device 10 is a strut array 30 formed by rods extending from the housing surface 20 through the internal chamber to the opposite surface 24. Figure 4 The arrangement of such pillars 30 is shown in a perspective view from one side, without the enclosed outer shell 20 in the figure. Figure 5 For along Figure 3 The cross-section along centerline AA also shows the arrangement of support column 30. (As shown) Figure 5 and Figure 6 As shown in the enlarged view, the support column 30 has a square cross-section, the cross-section having a flat surface 32 that intersects at corners 33 and 34. The width of the flat surface 32 is... Figure 6 The distance between the faces 32 of adjacent supports is denoted as "a", and the distance between them is denoted as "b". The gap width between two opposite edges 34 is given by the Pythagorean theorem as √2b. 2 .like Figure 4 As shown, the side edges of the array are formed by supports 31 with triangular cross-sections. Each support 30 is positioned such that the diagonal of the square cross-section spanning between the corner edges 33 is aligned with the overall flow direction, i.e., this diagonal is parallel to the imaginary line from inlet 26 to outlet 28. The flat surface 32 of each support is inclined towards this overall flow direction. Figure 6 As shown in the enlarged view, the working fluid flows through the gap between the opposing edges 34 of adjacent supports 30, but is subsequently forced to rotate by another support. Therefore, the array of supports 30 obstructs the straight flow of the working fluid, resulting in… Figure 6 The flow lines shown by the dashed line bend repeatedly.

[0042] The heat exchange device 12, which is immersed in water to be heated, has a cubic housing 40, which is the interface through which heat energy leaves the working fluid. Fins 42 extending from the housing 40 facilitate the conduction of heat from the housing 40 to the surrounding water.

[0043] The interior of device 12 is similar to that of device 10. Housing 40 defines a chamber for the flow of working fluid. A rod extending from one side through the internal chamber to the other side has a square cross-section and provides an array 30 of struts that impede flow, as described with respect to device 10.

[0044] Figure 7Another possible cross-section of the strut 30 is shown. Surface 44 has a convex curvature and intersects with concave surface 45 at edge 46. Fluid flows through the gap between edges 46, as shown by dashed lines, and is forced to change direction by the arrangement of the struts.

[0045] The working fluid circulating through heat transfer devices 10 and 12 is an aqueous solution of the first type of polymer and the second type of polymer described above. The working fluid also contains a small concentration of biocide to prevent the biodegradation of these polymers.

[0046] The circulating pump 16 propels the working fluid, causing the fluid entering the device at inlet 26 of device 10 to be in a laminar flow state. The flow entering device 12 is also laminar. This flow rate causes the working fluid to be in an elastic turbulent state as it flows through the strut array within devices 10 and 12. In device 10, this has the effect of transferring heat energy from the outer casing surface 20 to the working fluid at a rate faster than that transferred by conduction under laminar flow conditions without elastic turbulence. Similarly, in device 12, elastic turbulence increases the rate of heat transfer from the working fluid to the outer casing 40 of device 12, and from the outer casing to the fins 42 and the water surrounding device 12.

[0047] The flow velocity (volume per unit time) in the pipe 14 connecting devices 10 and 12 to pump 11 is the same as the flow velocity through devices 10 and 12. This pipe 14 is designed to be large enough that the flow velocity inside is low, so that the fluid flowing through the pipe is subjected to low shear in addition to being in a laminar flow state. Therefore, the creep time of the fluid is short to avoid an increase in pressure drop along this pipe 14 due to elastic instability within the fluid.

[0048] Figures 8 to 13 A system demonstrating elastic turbulence is illustrated, in which a fluid is pumped through an electrochemical half-cell. Flow electrochemical cells are used in a variety of devices. One such device is the flow battery, which typically comprises two half-cells separated by a membrane. The membrane separates the fluids in the two half-cells but allows ions to pass from one half-cell to the other. During charging and discharging, in each half-cell, a fluid containing one or more substances undergoing an electrochemical reaction is pumped from an associated storage container through the half-cell, and after passing through the half-cell, it is either discharged to the other storage container or recycled back to the container from which it originated. A key characteristic of flow batteries is that the energy storage capacity is determined not by the size of the electrochemical cell, but by the amount of fluid contained in the storage container.

[0049] Figure 8 and Figure 9 A flow cell with a central membrane 50 is shown, which separates the two half-cells, and... Figure 8The thickness is exaggerated. To the left of membrane 50 is shown a half-cell formed by a porous carbon electrode 52a, which is kept in contact with membrane 50 by a rigid plate 54a made of a conductive material (such as graphite or metal). To the right of membrane 50 is another half-cell formed by a porous electrode 52b, which is kept in contact with membrane 50 by a conductive rigid plate 54b. Porous electrodes 52a and 52b can be identical. Plates 54a and 54b can also be identical to each other. Each electrode 52 is made of carbonized fibrous material, thus containing many carbon wires stacked together and having a high surface area. Membrane 50, electrodes 52, and plates are surrounded by a housing (not shown). Electrical connection to electrodes 52 is provided by a conductive plate 54, which is itself connected to a cable 56.

[0050] like Figure 9 As shown, electrode 52b is surrounded by frame 57 having a fluid inlet and a fluid outlet. In this view, plate 54b is located behind electrode 52b and frame 57. As shown, plate 54b extends slightly beyond frame 57, and frame is sealed to plate 54b. Electrode 52a is surrounded by a similar frame.

[0051] The inlet 58 and outlet 59 of frame 57 are connected to an electrolyte fluid storage tank 66b via conduit 64. During charging and discharging, the electrolyte fluid circulates through electrode 52b via pumps 67b and 68b. Similarly, the frame surrounding porous electrode 52a is connected to an electrolyte fluid storage tank 66a via conduit, and the electrolyte fluid circulates through electrode 52a via pumps 67a and 68a. The conduit 64 is preferably constructed without sharp bends or other features that could cause pressure drops. Fluid pumped to inlet 58 enters porous electrode 52b through its end 60 and flows through electrode 52b to its opposite end 61, from where it continues to outlet 59, and then forward through conduit 64 to pump 68b and storage tank 66b. Flow from tank 66a passes through porous electrode 52a in a similar manner.

[0052] According to the present invention, the electrolyte fluid flowing through each half-cell comprises an aqueous solution of the aforementioned first-type polymer and the aforementioned second-type polymer. The working fluid also contains a small concentration of a biocide to prevent the biodegradation of such polymers. The pumping power ensures that the flow reaching the end 60 of the porous electrode is laminar. As the flow enters the electrode, the carbonized fiber mesh forming the porous electrode causes the flow streamlines to change direction multiple times, thereby generating elastic turbulence. This elastic turbulence mixes the electrolyte as it flows, transports electrochemically active substances to the carbon surface in contact with the porous electrode, and transports reaction products away from the carbon surface. Compared to a half-cell with the same structure but without the first-type polymer in the electrolyte fluid, the increased chemical transport due to elastic turbulence will increase the maximum current in the half-cell.

[0053] Pressure sensors 69 are mounted near the ends 60 and 61 of the porous electrode. These allow for the measurement of the pressure drop between the electrode inlet and outlet. This pressure drop measurement can be used to detect the onset of elastic turbulence by pumping fluid at a gradually increasing flow rate until the pressure drop suddenly increases at the onset of elastic turbulence.

[0054] Numerous compounds capable of undergoing electrochemical redox reactions have been proposed for use in flow batteries, which remains a research area. Many of these compounds have been reported to be usable under mild conditions at neutral or near-neutral pH. For example, the fluid at the positive electrode could be an aqueous solution of iodine and iodides, which can reversibly generate triiodide ions in the following reaction: The fluid at the negative electrode may be an aqueous solution of 2,6-dihydroanthraquinone, which can be electrochemically reduced to the corresponding hydroquinone. Furthermore, 2,6-anthraquinone derivatives obtained by reacting at the hydroxyl group have been proposed in several articles, including Kerr et al. in ACS Energy Letters, Vol. 8, pp. 600-607 (2023), and Jin et al. in ACS Energy Letters, Vol. 4, pp. 1342-1348 (2019).

[0055] Other species that could be used as electrochemically active materials include other quinones, ferrocene, and bipyridine compounds. The latter is also known as viologen. DeBruler et al. described an experimental flow battery in ACS Energy Letters, Vol. 3, pp. 663-668 (2018), in which one half-cell contains 1,1'-bis[2-sulfopropyl]-4,4'-bipyridinium, and the other half-cell contains iodine and iodides as described above. The separation membrane is a cation exchange membrane. Lv et al. described another experimental flow battery in ACS Energy Letters, Vol. 7, pp. 2428-2434 (2022), which uses an anion exchange separation membrane, with one half-cell containing substituted viologen and the other half-cell containing substituted ferrocene.

[0056] Figure 10 and Figure 11 The flow battery is shown, and its structure is similar to... Figure 8 and Figure 9This is different from other flow batteries. This battery also has two half-cells separated by a membrane 50. Each half-cell has a thin, porous electrode near the membrane 50 and a flow guide directly adjacent to this electrode and held in place by the flow battery housing 75. The flow guide is an array 30 of square cross-section pillars integral with a planar base 74. As shown, the pillars are arranged in a regular array. For each half-cell, this structure defines a chamber for fluid flow between the housing and the electrode, and the pillars 30 of the flow guide act as obstructions within the chamber, inducing elastic turbulence.

[0057] Electrolyte fluid from tanks 66a and 66b is pumped through the half-cell via pumps 67a and 67b, and then returned to the same tank via pumps 68a and 68b. Figure 8 and Figure 9 Similar to the system shown, the electrolyte fluid contains the first and second types of long-chain linear polymers described above. The first type of polymer causes elastic turbulence as the fluid flows through the guide, as referenced above. Figures 4 to 6 As the electrolyte fluid passes through the flow guide, this elastic turbulence causes a pressure drop, which in turn forces the fluid to flow into the thin porous electrode. These porous electrodes can have a fibrous structure, allowing the flow within the fibrous structure to change direction, thus enabling the elastic turbulence to continue within the fibrous structure. Furthermore, even if these electrodes do not force the fluid within them to change direction, the elastic turbulence induced within the flow guide will persist for a distance within the thin porous electrode.

[0058] exist Figure 10 In the arrangement shown, the current conductors can be made of graphite or other conductive materials to conduct electricity from or to the thin electrodes. However, if the thin electrodes have sufficient conductivity, they can be connected to cable 56 as shown, and the current conductors can be made of electrically insulating materials. They can be manufactured using additive manufacturing processes such as 3D printing.

[0059] Figure 12 It shows Figure 10 Five electrochemical cells are arranged side-by-side in what is called a cell stack. The cells are shown connected in series via cable 56, but parallel connection is also possible. Tank 66a and pump 67a are connected together to pump electrolyte fluid into the left half of each cell. Similarly, tank 66b and pump 67b are connected together to pump another electrolyte fluid through the right half of each cell in the cell stack. Figure 12 (In the image, the pipeline is shown schematically as a single line.) Figure 13 Another embodiment of this disclosure is shown, namely a fuel cell using methanol as fuel. It has a membrane 50 separating two half-cells within a housing 81. Figure 13As shown, on the right side, a thin porous electrode 82 is adjacent to the membrane 50. As described above, a flow guide 73 is located immediately adjacent to this porous electrode 82. Electrode 82 contains a catalyst for the electrochemical reaction of methanol. The electrical connection for power generation is indicated at 56.

[0060] The electrolyte fluid is an aqueous methanol solution containing a mixture of the first and second type polymers described above. It is drawn from the mixing tank 86 by pump 87 and pumped into the half-cell through pipe 84, thereby reaching the flow guide 73. Within the flow guide, the flow around the support induces elastic turbulence, such as… Figures 4 to 6 As shown, this increases the delivery of methanol to the thin catalytic electrode 82. The electrolyte fluid, depleted of methanol concentration, flows out from the electrode 82 and the guide member 73, and returns to the mixing tank 86 via pump 88. Additional methanol is drawn from the fuel tank 90 and delivered to the mixing tank 86 via pump 91 to maintain a stable methanol concentration in the mixing tank, thereby maintaining a stable methanol concentration in the fluid entering the guide member 73.

[0061] In the left half-cell, atmospheric oxygen combines with hydrogen ions passing through membrane 50. A thin, porous electrode 92 near membrane 50 contains a catalyst for this electrochemical reaction. A fan 93 blows air into a plate 94, which has a channel system 95, providing a uniform airflow to the catalytic electrode 92. The oxygen-depleted, humid air exits as exhaust gas.

[0062] exist Figures 8 to 12 In all the electrochemical half-cell systems shown, the first type of polymer has a high average molecular weight, allowing the electrolyte fluid to exhibit elastic turbulence as it flows through the half-cell, but the dimensions of the pipes 64 and 84 leading into and out of the half-cell cause the flow within the pipes to be in a low-shear state. The second type of polymer reduces the elastic instability as it flows through this pipe, thus avoiding the need for excessive pumping power wasted to overcome such elastic instability.

[0063] In the above implementation scheme, by observing the pressure drop between the inlet and outlet of the heat transfer device or half-cell, the flow velocity required to generate elastic turbulence through the heat transfer device or half-cell can be experimentally determined. Figure 14 use Figure 10 The structure of one of the half-cells illustrates this process. There is no membrane or thin electrode. Instead, plate 100 is mounted on the support 30 of flow guide 73. Pressure sensors 104 and 105 are installed in the inlet and outlet regions of the fluid path through flow guide 73. Inlet 106 is connected to pump 103, which pumps fluid from tank 102. This fluid can be the same as the electrolyte fluid flowing through the half-cell in a flow battery. Outlet 108 is connected to graduated container 109 for measuring the volume of liquid pumped through the half-cell at selected time intervals, thereby determining the flow rate.

[0064] When liquid from the tank is pumped through the half-cell, a pressure drop will occur between the inlet pressure sensor 104 and the outlet pressure sensor 105. At very low flow rates, the flow will be laminar, without any elastic turbulence. By gradually increasing the pump speed to increase the flow rate and plotting the pressure drop versus flow rate, the minimum flow rate required to induce elastic turbulence in the half-cell can be found. This plot will show the change in slope as the initial flow rate of elastic turbulence is reached.

[0065] The following are similar to Figure 14 The description of the experimental operation of the device shown illustrates this point. The experimental results are as follows: Figure 14 and Figure 15 As shown. Initial calibration determined the relationship between pump speed and flow rate. Tank 102 was filled with water. The pump was used to push water through the half-cell at a gradually increasing flow rate. Pump speed and flow rate measured downstream of the half-cell were recorded, as shown. Figure 15 As shown (triangle point). This calibration procedure was then repeated in the container with an aqueous solution containing 0.1% by weight of Flopaam 3630 polyacrylamide. This yielded the same result shown in the diagram. Figure 15 Nonlinear curves (circular points) in the graph.

[0066] Figure 16 The graph shows the relationship between measured pressure drop and flow velocity as the velocity gradually increases. For water, the curve is approximately linear (as expected, since water is a Newtonian fluid), but for the polyacrylamide solution, the slope of the curve changes very sharply at point E, indicating that the flow velocity at that point is the minimum required to induce elastic turbulence using the polyacrylamide solution and equipment.

[0067] Such measurements enable the estimation of flow through, for example Figures 4 to 6 The pillar array 30 shown or as Figures 10 to 13 The flow Reynolds number in the guide member 73 shown. This can be used to determine the flow Reynolds number through a chamber containing an obstruction. Re The formula for forcing the streamlines to bend is: in ρ It is the density of the fluid, measured in kilograms per cubic meter. U It is the flow rate, measured in meters per second. L It is the width of the gap between obstacles in the chamber, and η It is the viscosity of the fluid, measured in Pascals per second.

[0068] If flow rate is measured in volume per unit time, the above formula becomes: inQ It is the flow rate, measured in cubic meters per second, and A It is the cross-sectional area, transverse to the overall direction of flow, through which the flow passes.

[0069] In the example of the support array 30, the width "a" of the plane 32 of the support is 4 mm, and the height of the support is 7 mm. The spacing "b" between the planes 32 of adjacent supports is 2 mm, and therefore the gap between adjacent edges 34 is √8 = 2.83 mm. A row of supports transverse to the entire flow direction contains 12 supports, with 11 gaps between the edges 34, so the cross-section available for flow is: 11 x 7 x 2.83mm 2 = 11 x 7.10 -3 x 2.83.10 -3 m 2 .

[0070] The measured flow rate was 75 ml / sec. -1 = 7.5 x 10 -5 m 3 sec -1 The fluid density is 1000 kg / m³; the viscosity is 0.008 Pa·sec. Substituting these figures into the above formula: That is, Re = 12.17.

[0071] It is conceivable that embodiments of this disclosure may employ flow velocities and geometries that generate elastic turbulence, thereby resulting in Reynolds numbers in the range of 1 to 1000, possibly in the range of 1 to 250 or 1 to 500.

[0072] The various embodiments of this disclosure described above are intended to aid in understanding this disclosure, but do not in any way limit the scope of this disclosure as defined by the appended claims. It should be understood that any feature or possibility described in combination may be used individually, if doing so is feasible. Furthermore, features or possibilities mentioned in the appended claims or described in any embodiment may be used in any other embodiment, as long as doing so is feasible, and particularly where two or more of the appended claims are dependent on the same preceding claim, the reader should understand that this disclosure includes any two or more or all of those dependent claims with each other and with any possible combination of those dependent claims and the preceding claim.

Claims

1. A fluid composition capable of exhibiting elastic turbulence during flow, said fluid composition being a solution of two or more polymers, said solution comprising: At least one dissolved first polymer, which is a linear polymer with a weight-average molecular weight of at least 10 megadaltons; At least one dissolved second polymer, which is a linear polymer with a weight-average molecular weight in the range of 0.25 to 5 megadaltons; and The amount of the first polymer is in the range of 0.05 to 5% by weight of the solution and is sufficient to enable the solution containing the first polymer but not the second polymer to exhibit elastic turbulence, and the amount of the second polymer is greater than the amount of the first polymer but does not exceed 10% by weight of the solution.

2. The fluid composition of claim 1, wherein the first polymer comprises at least one linear chain, the at least one linear chain containing at least 20,000 monomer units linked by single chemical bonds.

3. The fluid composition of claim 1, wherein the second polymer comprises at least one linear chain, the at least one linear chain containing at least 2000 monomer units linked by a single chemical bond.

4. The fluid composition of claim 1, wherein the first polymer comprises at least one linear chain with a length and composition corresponding to at least 5,000 Kuhn monomers and a Kuhn length not exceeding 100 angstroms.

5. The fluid composition of claim 1, wherein the second polymer comprises at least one polymer chain with a length and composition corresponding to at least 100 Kuhn monomers and a Kuhn length not exceeding 100 angstroms.

6. The fluid composition of claim 1, wherein the first polymer comprises at least one linear polymer chain with a chain length of at least 50,000 monomer units and a Kuhn length of no more than 100 angstroms, and the second polymer comprises at least one linear polymer chain with a chain length of at least 5,000 monomer units and a Kuhn length of no more than 100 angstroms.

7. The fluid composition of claim 1, wherein the first polymer is polyacrylamide or partially hydrated polyacrylamide with a weight-average molecular weight of at least 15 megadaltons.

8. The fluid composition of claim 1, wherein the concentration of the first polymer does not exceed 1 wt%.

9. The fluid composition of claim 1, wherein the second polymer is polyacrylamide or partially hydrated polyacrylamide with a weight-average molecular weight of 1 to 5 megadaltons.

10. The fluid composition of claim 1, wherein the concentration of the second polymer is greater than 1% by weight and is at least twice the concentration of the first polymer.

11. The fluid composition of claim 1, wherein the concentration of the second polymer is at least three times the concentration of the first polymer.

12. A system comprising a fluid containment structure defining a fluid flow path, the fluid containment structure including... A chamber with inlets and outlets, as well as internal barriers, to force the streamlines of fluid flow to change direction, and A conduit leading to the inlet of the chamber and the outlet of the chamber; wherein the system further includes at least one pump for propelling fluid through the conduit and the chamber, and wherein the structure contains the fluid composition according to claim 1.

13. The system of claim 12, wherein the fluid flow path is a loop.

14. The system of claim 12, wherein the chamber is part of a heat transfer device, wherein the wall of the chamber in contact with the fluid flowing through the chamber is an interface through which heat is conducted to or from the fluid flowing through the chamber.

15. The system of claim 12, wherein the chamber is part of an electrochemical half-cell, and the fluid contains at least one chemical substance capable of undergoing an electrochemical reaction at the electrodes of the electrochemical cell.

16. A method of operating the system of claim 12, comprising: The fluid is pumped through the pipe and the chamber at a certain flow rate, such that the fluid is in laminar flow without elastic turbulence in the pipe leading to the chamber, and in elastic turbulence in the chamber.

17. The method of claim 16, wherein the Reynolds number of the flow through the conduit leading to the chamber is in the range of 1 to 250.

18. The method of claim 16, wherein the Reynolds number of the flow in the elastic turbulent state within the chamber is in the range of 1 to 500.

19. A method for introducing or removing heat from a flowing fluid, comprising: The fluid is pumped through a heat transfer device, which includes a chamber for fluid flow and wherein the chamber wall in contact with the flowing fluid is an interface through which heat energy is transferred to or from the flowing fluid, wherein the chamber includes a series of spaced barriers that force the streamlines of the flowing fluid to repeatedly change direction so as to flow through the gaps between the barriers. The fluid is the composition according to claim 1; and The flow velocity of the fluid in the chamber causes the fluid to be in an elastic turbulent state.

20. A method of operating a flowing electrochemical half-cell, the electrochemical half-cell having an electrode in contact with a flow path of a fluid, the fluid containing components capable of undergoing an electrochemical reaction at the electrode, wherein: The fluid is the composition according to claim 1. The flow path in contact with the electrode causes a change in flow direction, and The method includes pumping the fluid along the flow path, wherein the fluid is in an elastic turbulent state while in contact with the electrode.

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