Method for determining non-newtonian index of polyelectrolyte solution electroosmotic flow

Abstract

This invention provides a method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions, belonging to the fields of complex fluid electrodynamic transport, polyelectrolyte solutions, micro / nanofluids, electroosmotic flow, and computer numerical simulation. The method includes: obtaining the average electroosmotic flow velocity of a polyelectrolyte solution in a micro / nano-scale confined channel under multiple different applied electric field intensities; performing power-law fitting on the multiple different applied electric field intensities and their corresponding average electroosmotic flow velocities to establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field intensity; determining a nonlinear response index based on the power-law response relationship; and calculating the non-Newtonian index of electroosmotic flow based on the nonlinear response index, used to quantitatively characterize the degree to which the electroosmotic flow response of the polyelectrolyte solution in a micro / nano-scale confined channel deviates from classical linear electroosmotic behavior. This invention does not rely on shear rheological paths and can be used for characterizing and predicting the nonlinear behavior of electroosmotic flow under different system and parameter conditions.

Description

Technical Field

[0001] This invention belongs to the technical fields of complex fluid electrodynamic transport, polyelectrolyte solutions, micro / nano fluids, electroosmotic flow and computer numerical simulation, and specifically relates to a method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions. Background Technology

[0002] Electroosmotic transport of polyelectrolyte solutions in confined channels at the micro- and nano-scale is a core mass transfer process in cutting-edge technologies such as micro / nanofluidic chips, nanopore gene sequencing, protein conformation detection, and electric micropumps. How to transform the nonlinear electroosmotic response, which is difficult to describe intuitively under electric field drive, into standardized parameters that can be directly used for engineering evaluation, so that it can be quantified, compared, screened, and designed, is directly related to the optimization of device performance and the accuracy of engineering design in the above-mentioned fields.

[0003] Currently, the technical approach based on shear rheological constitutive models has become the mainstream characterization scheme for the flow response of non-Newtonian fluids. This approach uses equipment such as rotational rheometers or capillary rheometers to measure the shear stress or viscosity of fluids under different shear rates, and then constructs a constitutive relationship model between shear stress and shear rate (such as power-law models, Bingham models, etc.) to determine parameters such as the fluid's flow behavior exponent, yield stress, or viscosity function, which are used to characterize the non-Newtonian nature of the fluid.

[0004] However, shear rheology methods obtain parameters through mechanical shear loading, and their physical meaning is limited to the fluid's response to pure shear. In contrast, the nonlinear response of polyelectrolyte solutions in electroosmotic flow originates from interfacial structural evolution mechanisms such as electric field-induced chain conformational changes, near-wall adsorption and desorption, antiion rearrangement, and double-layer reconstruction. These mechanisms do not appear in shear rheology tests without an electric field, thus failing to characterize the non-Newtonian response of electric field-driven electroosmotic flow. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions.

[0006] To achieve the above objectives, the present invention provides a method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution, comprising: In a micro-nano scale confined channel, the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities was obtained.

[0007] Power-law fitting was performed on multiple different average electroosmotic flow velocities and their corresponding applied electric field strengths to establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field strength. Based on this power-law response relationship, the nonlinear response index of the target polyelectrolyte solution was determined. .

[0008] According to the nonlinear response index The non-Newtonian exponent n of the electroosmotic flow of the target polyelectrolyte solution is calculated. The non-Newtonian exponent n is used to quantitatively characterize the degree to which the electroosmotic flow response of the polyelectrolyte solution deviates from the classical linear electroosmotic flow behavior in a micro-nano scale confined channel.

[0009] Preferably, obtaining the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities specifically includes: for each applied electric field intensity, obtaining the velocity distribution and solvent density distribution of the solvent along the channel direction within the micro / nano-scale confined channel, and calculating the average electroosmotic flow velocity under the applied electric field intensity using a density-weighted average based on the velocity distribution and solvent density distribution.

[0010] Preferably, the average electroosmotic flow velocity under the applied electric field is calculated using a density-weighted average based on the velocity distribution and solvent density distribution, and this is achieved in the following way: in, external electric field strength The average electroosmotic velocity under these conditions; Ω represents the intensity of the j-th applied electric field along the channel direction; r represents the cross-sectional region of the micro / nano-scale confined channel; and r represents the position coordinates within the cross-sectional region. external electric field strength Velocity distribution of the solvent along the channel direction; external electric field strength The solvent density distribution is given below; dA is the area element within the cross-sectional region.

[0011] Preferably, when the micro / nano-scale confined channel is a flat plate channel or a slit channel, the velocity distribution and solvent density distribution are represented as velocity profiles and solvent density profiles along the normal coordinates of the channel wall, respectively, and the average electroosmotic flow velocity is calculated in the following manner: Where z is the normal coordinate of the wall of the micro-nano scale confined channel, and H is the channel height of the micro-nano scale confined channel; external electric field strength The average electroosmotic velocity under these conditions; Let J be the intensity of the applied electric field along the channel direction; external electric field strength The velocity profile of the solvent along the channel direction, where z is the normal coordinate of the channel wall; external electric field strength Solvent density profile below; d Let be a infinitesimal element of length along the normal direction of the channel wall.

[0012] Preferably, the step of performing power-law fitting on multiple different average electroosmotic velocities and their corresponding applied electric field strengths to establish a power-law response relationship between the average electroosmotic velocity and the applied electric field strength specifically includes: substituting the multiple different applied electric field strengths and their corresponding average electroosmotic velocities into the following power-law response relationship: ; in, Let E be the average electroosmotic velocity, and E be the applied electric field strength along the channel direction. These are the characteristic electroosmotic flow response coefficients in the power-law fitting. The nonlinear response exponent is defined as the relationship between the average electroosmotic flow velocity and the applied electric field strength. The characteristic electroosmotic flow response coefficient and nonlinear response exponent are determined by performing a nonlinear least-squares fit on the average electroosmotic flow velocity and the applied electric field strength, or by performing a linear least-squares fit after a logarithmic transformation of the average electroosmotic flow velocity and the applied electric field strength when both are greater than zero. ; According to the nonlinear response index Calculate the non-Newtonian exponent n of the electroosmotic flow in the target polyelectrolyte solution, where, .

[0013] Preferably, the criterion for the non-Newtonian exponent n of the electroosmotic flow is: When the nonlinear response index When the value equals 1, or its deviation from 1 is not greater than a preset threshold, the target polyelectrolyte solution is determined to exhibit a near-linear electroosmotic flow response; when the nonlinear response index... When the non-Newtonian exponent n of the electroosmotic flow is greater than 1 and less than 1, it is determined that the target polyelectrolyte solution exhibits a superlinearly enhanced non-Newtonian electroosmotic flow response in a micro-nano scale confined channel, and the non-Newtonian exponent n of the electroosmotic flow is inversely proportional to the degree of nonlinear enhancement.

[0014] Preferably, the method further includes: if the average electroosmotic flow velocity reverses direction within the study electric field range, determining the reverse electric field strength or reverse electric field interval corresponding to the average electroosmotic flow velocity being zero, and segmenting the data according to the electric field interval where the sign of the average electroosmotic flow velocity remains unchanged; within each segment, performing power-law fitting using the absolute value of the average electroosmotic flow velocity, and recording the flow direction, nonlinear response index, and corresponding electroosmotic flow non-Newton exponent n for each segment; data crossing the flow reversal point are not combined for a single power-law fitting.

[0015] Preferably, the method further includes the step of establishing a prediction function, specifically including: By changing the wall charge density and channel height of the micro / nano-scale confined channel, and by changing at least one of the following parameters of the polyelectrolyte solution: chain charge fraction, salt concentration, monomer concentration, and chain length, the steps of obtaining the average electroosmotic flow velocity, performing power-law fitting to determine the nonlinear response index, and calculating the non-Newtonian index n of the electroosmotic flow are repeated for the changed micro / nano-scale confined channel or polyelectrolyte solution, to obtain a parameter-index dataset consisting of multiple sets of parameters and their corresponding non-Newtonian index n of the electroosmotic flow. Based on the parameter-index dataset, a prediction function is established between the non-Newtonian exponent n of electroosmotic flow and the parameters, which is used to predict the non-Newtonian exponent n of electroosmotic flow under different parameter conditions.

[0016] Preferably, the method further includes a step of inverting the wall charge density, specifically including: Under the conditions of preset polyelectrolyte solution properties and preset channel height, multiple different applied electric field strengths and their corresponding average electroosmotic flow velocities are obtained experimentally. The experimental electroosmotic flow non-Newtonian index n is determined based on the average electroosmotic flow velocity, and the experimental electroosmotic flow non-Newtonian index n is matched with the prediction function to invert the wall charge density of the micro-nano scale confined channel.

[0017] The present invention also provides a system for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution, comprising: The data acquisition module is used to acquire the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities in a micro-nano scale confined channel.

[0018] The relationship establishment module is used to perform power-law fitting on multiple different average electroosmotic flow velocities and corresponding applied electric field intensities, establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field intensity, and determine the nonlinear response index of the target polyelectrolyte solution based on the power-law response relationship.

[0019] The calculation module is used to calculate the electroosmotic non-Newtonian index of the target polyelectrolyte solution based on the nonlinear response index. The electroosmotic non-Newtonian index is used to quantitatively characterize the degree to which the electroosmotic response of the polyelectrolyte solution deviates from the classical linear electroosmotic behavior in a micro-nano scale confined channel.

[0020] The method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions provided by this invention has the following beneficial effects: The average electroosmotic flow velocity of this invention is the interface structure evolution induced by electric field, such as conformational changes of polyelectrolyte chains, near-wall adsorption and desorption, anti-ion rearrangement, and double-layer reconstruction. The final effects of these changes are all reflected in the electroosmotic flow velocity. Therefore, by directly measuring the average electroosmotic flow velocity under different electric field intensities and then refining the parameters through power-law fitting, the data source of the obtained parameters can be consistent with the physical mechanism. Since the parameters come from the actual response process driven by the electric field, rather than from the mechanical shearing process that does not include this mechanism, the inability to characterize the non-Newtonian response of electroosmotic flow driven by the electric field is avoided. Attached Figure Description

[0021] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating a method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to an embodiment of the present invention. Figure 2 This is a schematic diagram of a confined polyelectrolyte solution electroosmosis system according to an embodiment of the present invention; Figure 3 This is a graph showing the fitting results of the average electroosmotic flow velocity and the applied electric field strength in an embodiment of the present invention; wherein, Figure 3 (a) is a graph showing the relationship between the average electroosmotic velocity and the applied electric field strength under normal coordinates. Figure 3 (b) is a power-law fitting plot of the average electroosmotic velocity versus the applied electric field intensity in a double logarithmic coordinate system. Detailed Implementation

[0023] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0024] It should be noted that the micro / nano-scale confined channels described in this invention can be flat plate channels, slit channels, rectangular channels, circular channels, nanopores, or other micro / nano-scale channels capable of forming confined electroosmotic flow. The following embodiments use flat plate or slit-type micro / nano-scale confined channels as examples, which are merely exemplary implementations of this invention and do not constitute a limitation on the applicable channel morphology. For micro / nano-scale confined channels with other cross-sectional morphologies, the average electroosmotic flow velocity can be calculated using the channel cross-section integral form. The subsequent power-law fitting, nonlinear response exponent determination, and non-Newtonian exponent calculation processes for electroosmotic flow are the same as in this embodiment.

[0025] The purpose of this invention is to provide a method for predicting or determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions, in order to solve the problem that existing numerical methods for non-Newtonian fluids are mainly oriented towards shear rheological constitutive models, and are difficult to quantitatively characterize the nonlinear electroosmotic flow response of confined polyelectrolyte solutions under the drive of an applied electric field.

[0026] To achieve the above objectives, this invention aims to accomplish the following: First, to establish a data acquisition process for the electroosmotic flow response of confined polyelectrolyte solutions under multiple electric field intensities, obtaining the average electroosmotic flow velocity corresponding to different applied electric field intensities. Second, to determine the nonlinear response index A, used to characterize the nonlinearity of the electroosmotic flow response, through the power-law relationship between the average electroosmotic flow velocity and the applied electric field intensity. nl Third, set n=A nl -1 Defined as the non-Newtonian index of electroosmotic flow, it is used to quantitatively characterize the degree to which the electroosmotic flow response of polyelectrolyte solutions deviates from the classical linear electroosmotic flow behavior. Fourth, the microstructural characteristics such as near-wall desorption of polyelectrolyte chains, channel center migration, counterion redistribution, net charge density change, and double-layer reconstruction are used as the basis for verifying the rationality and physical source of the non-Newtonian index of electroosmotic flow.

[0027] This invention provides a method for predicting or determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions. Based on the average electroosmotic flow velocity of a confined polyelectrolyte solution under multiple applied electric field strengths, this method establishes a power-law response relationship between the average electroosmotic flow velocity and the electric field strength:

[0028] ; in, Let E be the average electroosmotic velocity, and E be the applied electric field strength along the channel direction. is the characteristic electroosmotic flow response coefficient in power-law fitting, used to characterize the response amplitude of the average electroosmotic flow velocity in a given system to the applied electric field intensity; This is a nonlinear response exponent between the average electroosmotic flow velocity and the applied electric field strength, used to characterize the degree to which the average electroosmotic flow velocity deviates from a linear relationship as the applied electric field strength changes. Further, this invention will... Let n be the non-Newtonian exponent of electroosmotic flow, used to quantitatively characterize the degree to which the electroosmotic flow response of polyelectrolyte solutions deviates from the classical linear electroosmotic behavior. When A nl When A ≈ 1 and n ≈ 1, it indicates that the system is close to a linear electroosmotic flow response; when A nl When n > 1 and n < 1, it indicates that the system exhibits a superlinear enhanced non-Newtonian electroosmotic flow response. The smaller n is, the more significant the average electroosmotic flow velocity becomes with the increase of the applied electric field strength, and the stronger the nonlinearity of the electroosmotic flow of the system.

[0029] The above-mentioned index definition draws on the idea of ​​characterizing the degree of non-Newtonian flow using flow behavior indices in non-Newtonian power-law fluids. For traditional power-law non-Newtonian fluids, their flow behavior indices are usually derived from the constitutive relationship between shear stress and shear rate; however, the electroosmotic non-Newtonian index in this invention is not directly obtained from the shear rate-viscosity curve, but is determined by the electro-transport response relationship between the applied electric field strength and the average electroosmotic flow velocity. Therefore, this index is an equivalent non-Newtonian index established for the electric field-driven electroosmotic transport process, which can reflect the comprehensive influence of interfacial structure evolution such as polyelectrolyte chain conformational changes, chain-wall adsorption and desorption, counterion redistribution, and double-layer reconstruction on the macroscopic electroosmotic flow response.

[0030] The data sources for this method can be dissipative particle dynamics simulations, all-atom molecular dynamics simulations, continuous medium numerical simulations, or micro / nanochannel electroosmotic flow experimental data. All-atom molecular dynamics can provide high-resolution molecular information, but it typically involves large computational loads under polyelectrolyte solutions, micro / nanoscale confined channels, and multi-field parameter scanning conditions. Micro / nanochannel electroosmotic flow experiments can provide direct measurement results, but they involve micro / nanoscale confined channel preparation, wall charge regulation, polyelectrolyte concentration control, applied electric field loading, and weak flow velocity measurement, making the experimental systems complex and usually specific to particular solution and channel conditions. Therefore, as a preferred approach, this invention employs explicit solvent dissipative particle dynamics simulations to obtain velocity field, concentration field, charge density distribution, and polyelectrolyte chain conformation information under multiple electric field intensities, and determines the non-Newtonian exponent of electroosmotic flow based on this information.

[0031] Figure 1 The overall implementation flow of the method of the present invention is shown, including: acquiring system parameters, establishing a confined polyelectrolyte solution electroosmotic flow model, performing multi-electric field intensity sampling, calculating the average electroosmotic flow velocity, establishing the power-law response relationship between the average electroosmotic flow velocity and the applied electric field intensity, outputting the non-Newtonian exponent of electroosmotic flow, and optional steps for structural feature verification and parameter-exponent mapping relationship establishment. Among them, S1 to S6 constitute the basic exponent determination flow of the present invention, and S7 and S8 are optional extension steps used to further verify the physical source of the exponent and establish the prediction relationship under different system parameters.

[0032] Based on this, the present invention provides a method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions. Specifically, it is a method for determining the non-Newtonian index of electroosmotic flow in confined polyelectrolyte solutions based on electroosmotic flow response data under multiple electric field intensities and power-law fitting of the average electroosmotic flow velocity. Figure 1 As shown, it includes the following steps:

[0033] S1. Obtain system parameters Acquire and input the system parameters of the target polyelectrolyte solution and the micro / nano-scale confined channel, including the polyelectrolyte chain length N, chain charge fraction f, and polyelectrolyte monomer concentration. Counterion concentration Salt concentration Ion valence state, solvent parameters, channel height H, wall charge density The set of wall interaction parameters and applied electric field intensity { }

[0034] Where N represents the number of monomers in each polyelectrolyte chain; f represents the proportion of charged monomers in the polyelectrolyte chain to all monomers; This indicates the number density or concentration of polyelectrolyte monomers, with the subscript m representing monomer, i.e., polyelectrolyte monomer; This indicates the counterion number density or concentration; the subscript ct indicates counterion. This indicates the concentration of added salt ions; the subscript 's' represents 'salt'; and 'H' represents the channel height. Represents the wall charge density; { } represents a set consisting of multiple applied electric field intensities; Let j represent the j-th applied electric field intensity, where j is the electric field intensity number.

[0035] This step is used to define the system to be tested or predicted, providing physical properties, boundary conditions, and electric field conditions for subsequent electroosmotic response calculations.

[0036] S2. Establish a confined polyelectrolyte solution electroosmotic flow model. In a preferred embodiment, establish as follows Figure 2 The model illustrates a plate-type or slit-type micro / nano-scale confined channel, with the channel length direction defined as the x-direction, the channel width direction as the y-direction, and the wall normal and channel height directions as the z-direction. The upper and lower walls of the micro / nano-scale confined channel are located at z=0 and z=H, respectively. Coarse-grained models of explicit solvent, polyelectrolyte chains, counterions, and salt ions are established within the channel, with the polyelectrolyte chains preferably described using a bead-spring model. A given surface charge density is set for the upper and lower walls. A uniform external electric field E is applied along the length of the channel, i.e., the x-direction, to drive the polyelectrolyte solution to generate electroosmotic flow.

[0037] Figure 2 An electroosmotic flow system of a polyelectrolyte solution is shown, exemplified by a confined micro / nano-scale channel of either a flat plate or a slit shape. The channel contains polyelectrolyte chains, counterions, solvent, and charged walls; the polyelectrolyte chains are formed by the connection of charged monomers, and the counterions are distributed around the polyelectrolyte chains and inside the channel. The channel length direction is defined as the x-direction, the wall normal direction and the channel height direction as the z-direction, and the channel height is H. An external electric field is applied along the x-direction. As the applied electric field strength increases from E... min Increase to E max The system generates electroosmotic flow along the channel direction. The red curve in the figure illustrates the change in the electroosmotic flow velocity profile under different electric field conditions. Figure 2 The flat or slit-type channel shown is merely an exemplary channel structure of the present invention and does not constitute a limitation on the applicable channel morphology of the present invention. Wherein, x represents the channel length direction coordinate; y represents the channel width direction coordinate; z represents the channel wall normal coordinate; H represents the channel height; and E represents the applied electric field strength along the channel direction. This represents the wall charge density.

[0038] This step is used to reproduce the electric field-driven transport environment of polyelectrolyte solutions in charged micro / nano-scale confined channels.

[0039] S3. Perform multi-electric field intensity sampling Set of applied electric field strengths { Each electric field intensity in} Equilibrium and production sampling were performed separately to obtain corresponding velocity field and structural field data. This data includes, but is not limited to, solvent velocity distribution. Solvent density distribution Polyelectrolyte monomer density distribution Counterion density distribution Salt ion density distribution Net charge density distribution Polyelectrolyte chain conformation information and counterion condensation fraction .

[0040] Where r represents the position coordinates within the confined cross-sectional area of ​​the micro-nano scale channel; This indicates the solvent velocity component along the channel direction, i.e., the x-direction; the subscript x indicates the channel length direction; the subscript sol indicates solvent; the subscript m indicates monomer; and the subscript ct indicates counterion. This represents the number density of the i-th type of ion, where i is the ion type number. When the system contains both cations and anions, i can be either + or −. This represents the net charge density, with the subscript 'e' indicating electric charge. This indicates the fraction of counterion condensation; the subscript "con" indicates condensation. Let represent the intensity of the j-th applied electric field.

[0041] When the confined channel is a flat plate channel or a slit channel, the above distribution can be simplified as a cross-sectional form along the normal coordinate z of the wall, including the solvent velocity profile. Solvent density profile Polyelectrolyte monomer density profile Counterion density profile Salt ion density profile and net charge density profile .

[0042] This step is used to obtain the average electroosmotic velocity data required for the index calculation, as well as the microstructure data required for verifying the reasonableness of the index.

[0043] S4. Calculate the average electroosmotic velocity. For each applied electric field strength The average electroosmotic flow velocity is calculated based on the velocity distribution and solvent density distribution. For micro / nano-scale confined channels with general cross-sectional shapes, the average electroosmotic flow velocity can be calculated using the following density-weighted averaging method:

[0044] in, external electric field strength The average electroosmotic velocity under these conditions; Ω represents the intensity of the j-th applied electric field along the channel direction; r represents the cross-sectional region of the micro / nano-scale confined channel; and r represents the position coordinates within the cross-sectional region. external electric field strength Velocity distribution of the solvent along the channel direction; external electric field strength The solvent density distribution is shown below; dA is the area element within the cross-sectional region; the subscript sol represents the solvent; the subscript x represents the velocity component in the channel length direction.

[0045] When the micro / nano-scale confined channel is a flat plate channel or a slit channel, the average electroosmotic velocity can be further written as: Where z is the normal coordinate of the channel wall; H is the channel height of the micro-nano scale confined channel; external electric field strength Velocity profile of the solvent along the channel direction; external electric field strength The solvent density profile is shown below; dz is the length element along the normal direction of the channel wall.

[0046] When the solvent density of the system is approximately uniform, the cross-sectional average of the velocity distribution can also be used as the average electroosmotic velocity. If flow reversal occurs under certain parameter conditions, the direction information of the average electroosmotic velocity is recorded, and the absolute value or velocity amplitude |v̄( Perform power-law exponent fitting.

[0047] If the average electroosmotic velocity reverses direction within the studied electric field range, the reverse electric field strength or reverse electric field interval corresponding to the zero average electroosmotic velocity is determined, and the average electroosmotic velocity data is segmented according to the electric field interval where the sign of the average electroosmotic velocity remains unchanged. Within each segment, a power-law fit is performed using the absolute value of the average electroosmotic velocity, and the flow direction, nonlinear response index, and corresponding electroosmotic non-Newtonian exponent n are recorded for each segment. Data crossing the flow reversal point must not be combined for a single power-law fit.

[0048] This step is used to convert the local velocity distribution into an average response that represents the overall electroosmotic transport intensity.

[0049] S5. Establish the power-law response relationship The average electroosmotic velocity data obtained under different applied electric field intensities were fitted as follows: Among them, A char A is the characteristic electroosmotic flow response coefficient. nl A is a nonlinear response exponent. Preferably, A is determined using a nonlinear least squares fitting method. char and A nl And output the goodness-of-fit R. 2 The residual distribution and the range of parameter errors.

[0050] like Figure 3 As shown, by performing a power-law fitting on the average electroosmotic velocity under different applied electric field intensities, the nonlinear response exponent A can be obtained. nl This data is further used to calculate the non-Newtonian exponent of electroosmotic flow, to demonstrate the variation of the average electroosmotic flow velocity under different applied electric field strengths, and to determine the nonlinear response exponent through the power-law response relationship. The non-Newtonian exponent of electroosmotic flow, n, is used. Square data points represent the average electroosmotic flow velocity of the simple 1:1 symmetric electrolyte control system, while circular data points represent the average electroosmotic flow velocity of the polyelectrolyte solution system. Solid or dashed lines represent the corresponding fitting results, and error bars represent the statistical error of the average electroosmotic flow velocity. The left figure shows the fitting results of the average electroosmotic flow velocity and the applied electric field strength in ordinary coordinates, and the right figure shows the fitting results of the corresponding data in double logarithmic coordinates. The average electroosmotic flow velocity of the simple 1:1 symmetric electrolyte system is approximately linearly related to the applied electric field strength, while the polyelectrolyte solution system exhibits a significant superlinear power-law response. This indicates that the method of this invention can distinguish between the near-linear electroosmotic flow response of the simple electrolyte system and the non-Newtonian electroosmotic flow response of the polyelectrolyte solution system.

[0051] This step is used to convert discrete multi-field electroosmotic response data into comparable nonlinear response exponents.

[0052] S6, Output electroosmotic flow non-Newtonian index According to the nonlinear response index A nl Calculate the non-Newtonian index of electroosmotic flow: . When A nl When A ≈ 1 and n ≈ 1, the system is considered to have a near-classical linear electroosmotic flow response; when A nl >1. When n<1, the system exhibits a superlinear enhanced non-Newtonian electroosmotic flow response; the smaller n is, the faster the average electroosmotic flow velocity increases with the applied electric field strength, and the stronger the nonlinearity of the electroosmotic flow of the system.

[0053] This step is used to form a final prediction or determination result and to provide quantitative criteria for the non-Newtonian behavior of electroosmotic flow.

[0054] S7. Perform structural feature verification. Structural features such as the near-wall enrichment peak intensity of polyelectrolyte chains, the migration amount of polyelectrolyte chains towards the channel center, the counterion aggregation fraction, the net charge integral in the central region, the double-layer reconstruction factor, and the velocity profile morphology factor under multiple electric field conditions were extracted, and the trends of these structural features with the applied electric field strength were analyzed. If, with the increase of the electric field, the system exhibits near-wall desorption of polyelectrolyte chains, migration towards the channel center, counterion redistribution, a decrease in the net charge density in the central region hindering the mainstream direction, and a transformation of the velocity profile from a centrally concave type to a centrally enhanced type, these can be used as verification evidence for the rationality of the non-Newtonian exponent n of electroosmotic flow.

[0055] This step is used to establish the correspondence between the index results and the microstructure reconstruction mechanism.

[0056] S8. Establish parameter-exponential mapping relationship For different wall charge densities σ s Chain charge fraction f, salt concentration ρ sMicro-nano scale confined channel height H, polyelectrolyte monomer concentration ρ m Repeat steps S1-S7 with parameters such as chain length N to obtain the parameter-exponential dataset, and establish a prediction function of the following form: Where F represents the mapping function established by the parameter-exponential dataset; The wall charge density is represented by f; the chain charge fraction of the polyelectrolyte chain is represented by f. Indicates salt concentration; H represents channel height; The value represents the polyelectrolyte monomer concentration; N represents the polyelectrolyte chain length; the ellipsis indicates that other parameters affecting the electroosmotic flow response, such as ion valence state, wall interaction parameters, solvent parameters, temperature, or channel cross-sectional morphology, may also be included.

[0057] In a further preferred embodiment, the parameter-exponential mapping function can also be used to invert the charge density of the wall surface of micro / nano-scale confined channels. Specifically, given that the chain length, chain charge fraction, salt concentration, monomer concentration, ion valence state, and channel height of the target polyelectrolyte solution are known, the average electroosmotic flow velocity under different applied electric field intensities can be experimentally measured, and the non-Newtonian exponent n of the experimental electroosmotic flow can be obtained according to the power-law response relationship. exp Subsequently, the non-Newtonian exponent n of the experimental electroosmotic flow was determined. exp The wall charge density is determined by matching the pre-established parameter-exponential mapping function with a table lookup, interpolation, fitting, or optimization inversion method. or effective wall charge density σ s,eff .

[0058] For example, when the polyelectrolyte solution parameters and channel height H are known, the mapping function (prediction function) can be written as: By comparing the calculated n with the experimentally measured n exp By matching them, the σ that satisfies the conditions can be determined. s,eff When multiple possible solutions exist, the inversion results can be further constrained by combining independently measured flow velocity amplitudes, wall material properties, salt concentration response, or other auxiliary experimental data.

[0059] This step is used to enable rapid screening, comparison, and parameter design of the non-Newtonian index of electroosmotic flow under different polyelectrolyte solutions and different channel conditions.

[0060] In the above steps, S1-S6 constitute the basic technical solution of the present invention, and S7-S8 are preferred technical solutions. Specifically, S7 is used to verify the physical origin of the non-Newtonian exponent of electroosmotic flow, and S8 is used to extend the predictive capability of this method under different system and parameter conditions. Those skilled in the art can also replace the dissipative particle dynamics simulation data with all-atom molecular dynamics simulation data or micro / nano channel experimental velocimetry data based on actual data sources, but multi-field strength averaged electroosmotic flow velocity data, power-law response fitting, and n=A should still be used. nl -1 The process for determining the index.

[0061] Therefore, this invention solves the technical problem of "how to quantitatively determine the non-Newtonian index of polyelectrolyte solutions in electric field-driven electroosmotic flow transport". Compared with common numerical simulation methods for non-Newtonian fluids, this invention focuses on the conformational changes of polyelectrolyte chains, chain-wall desorption, counterion redistribution, and double-layer reconstruction induced by an applied electric field, as well as the resulting nonlinear response of the average electroosmotic flow velocity; its core is not the viscosity change in ordinary shear flow, but the nonlinear transport law of electroosmotic flow of polyelectrolyte solutions under electric field driving.

[0062] This invention also provides simulation verification, the process of which is as follows: To demonstrate that the method of this invention can solve the above-mentioned technical problems, this invention provides the following simulation and verification content. Among them, the average electroosmotic flow velocity-electric field intensity relationship, power-law fitting results, and control system results are the core verification content in the embodiments of this invention; steady-state verification, structural verification, repeatability verification, and applicability verification can be used as preferred verification methods or auxiliary explanatory content, and are not considered as necessary limitations for the implementation of the method of this invention.

[0063] (1) Core fit verification.

[0064] Linear and power-law fitting were performed on the average electroosmotic velocity data obtained under different applied electric field intensities, and the fitting results of the two methods were compared. The characteristic coefficient A was obtained through power-law fitting. char and nonlinear response index A nl Further based on Calculate the non-Newtonian exponent n of electroosmotic flow. This verification is used to demonstrate that the present invention can convert electroosmotic flow response data under multiple electric field strengths into an outputtable and comparable non-Newtonian exponent of electroosmotic flow.

[0065] (2) Core comparison verification.

[0066] Under conditions of the same channel height, the same wall charge density, and similar ionic strength, a simple 1:1 symmetrical electrolyte system was established as a control system. If the average electroosmotic flow velocity of the simple electrolyte system is approximately linearly correlated with the applied electric field strength, while the polyelectrolyte solution system exhibits a significant superlinear power-law response, it indicates that the non-Newtonian index of electroosmotic flow defined in this invention can distinguish between the near-linear electroosmotic flow response of the simple electrolyte system and the non-Newtonian electroosmotic flow response of the polyelectrolyte solution.

[0067] (3) Optimal steady-state verification.

[0068] As a preferred verification method, each applied electric field intensity can be fully balanced before production sampling; and the average electroosmotic flow velocity can be checked to see if it reaches a steady state over time, and whether the velocity and density profiles no longer exhibit systematic drift. This verification is used to improve the reliability of the statistical results of the average electroosmotic flow velocity.

[0069] (4) Optimal structure verification.

[0070] As a preferred verification method, the monomer density, counterion density, net charge density, and velocity profile of the polyelectrolyte under different electric field strengths can be further extracted to analyze near-wall desorption of polyelectrolyte chains, channel center migration, counterion redistribution, double-layer reconstruction, and changes in velocity profile morphology. This verification is used to explain the microscopic physical source of the non-Newtonian exponential variation in electroosmotic flow, but it is not a necessary step in the exponential calculation process of this invention.

[0071] (5) Prefer repeatability verification.

[0072] As a preferred verification method, key electric field intensity points can be independently and repeatedly simulated, or the same production sampling trajectory can be segmented and statistically analyzed to estimate the average electroosmotic flow velocity and A. nl The error range of n. This verification is used to demonstrate that the exponent obtained by the method of the present invention has statistical reliability.

[0073] (6) Explanation of the preferred scope of application.

[0074] As a preferred description, the parameters used in the method of this invention, such as the range of applied electric field strength, wall charge density, polyelectrolyte chain length, chain charge fraction, polyelectrolyte concentration, salt concentration, and channel height, can be recorded. It should be explained that the obtained non-Newtonian exponent for electroosmotic flow is mainly applicable to steady-state electroosmotic transport processes within the corresponding parameter range. This description is intended to avoid directly extrapolating the exponent to unverified regions of extremely strong electric fields, unsteady transport, or strong non-equilibrium structural abrupt changes.

[0075] Example 1: Determination and Verification of the Non-Newtonian Index of Electroosmotic Flow in a Reference Confined Polyelectrolyte Solution In one specific embodiment, a confined nanoslit channel model is established, with a channel height H = 10σ, where σ = 0.65 nm, and σ is a unit of length in dissipative particle dynamics simulation. The upper and lower walls of the micro / nano-scale confined channel are uniformly positively charged, with a surface charge density of... Where e is the unit charge, This represents the charge per unit area of ​​the wall surface. The channel contains explicit dissipative particle dynamics solvent, polyelectrolyte chains, and monovalent counterions, with a solvent number density of... The polyelectrolyte chain length N=16, chain charge fraction f=1.0, and polyelectrolyte monomer concentration... And add an appropriate number of monovalent counterions to satisfy the total electroneutrality of the system.

[0076] In this embodiment, the polyelectrolyte chain is described using a finitely stretchable nonlinear elastic bead-spring model, with adjacent polyelectrolyte monomers connected by finitely stretchable nonlinear elastic bonds. The polyelectrolyte chain is described using an average charge method, with each polyelectrolyte monomer carrying a charge of −fe; since the chain charge fraction f = 1.0 in this embodiment, each polyelectrolyte monomer carries a negative elementary charge −e. The counterion carries a positive elementary charge +e. The number of counterions is determined based on the fixed charges on the upper and lower walls and the total charge carried by the polyelectrolyte monomers, ensuring that the entire simulation system, including the fixed charges on the walls, the charges of the polyelectrolyte monomers, and the counterion charges, satisfies the electroneutrality condition. The explicit solvent is described using dissipative particle dynamics, with each solvent particle corresponding to approximately three water molecules. The characteristic size of the solvent particles, polyelectrolyte monomers, and counterions is taken as σ. At a temperature T = 300 K, the solvent particles interact through conservative forces, dissipative forces, and random forces. The parameter for the conservative force between solvent particles is set to a. ij =78k B The friction coefficient for dissipation, T / σ, is set to γ ​​= 4.5τk. B Tσ −2 , where k B T is the Boltzmann constant, τ = σ(m / k) B T) 1 / 2 The time unit is used for simulation, and m is the particle mass.

[0077] Dissipative and stochastic forces satisfy fluctuation-dissipation relations to maintain temperature stability in the simulated system. The cutoff distance for the aforementioned dissipative particle dynamics is set as σ. Polyelectrolyte monomers and counterions, as solute particles, exchange momentum with the explicit dissipative particle dynamics solvent through dissipative and stochastic forces to characterize the kinetic coupling and hydrodynamic interactions between solute particles and solvent. The coefficient of friction between solute and solvent particles is set as γ. s=5γ, with the interaction cutoff distance set to σ. The friction coefficient between solute particles is set to γ, and the interaction cutoff distance is also set to σ. To prevent non-physical overlap between polyelectrolyte monomers and ions, a purely repulsive Weeks–Chandler–Andersen potential is further applied between the solute particles, with a potential energy parameter of k. B T. Long-range electrostatic interactions between polyelectrolyte monomers, counterions, and charged walls were calculated using a particle-particle-particle-grid algorithm, with a relative computational accuracy set to 10. −4 The dielectric environment of the solution was achieved by setting the dielectric constant to 80. Slab was used to correct the electrostatic force calculation in the z-direction with a parameter of 3.0. The upper and lower walls of the simulated channel were located at z=0 and z=H, respectively. The minimum approach distance of the solute particles to the walls was set to 0.5σ, and approximately no-slip boundary conditions were applied to the upper and lower walls. Periodic boundary conditions were set in the x and y directions parallel to the walls, while a constrained boundary condition was applied in the z-direction normal to the walls.

[0078] A uniform external electric field E is applied along the length direction (x-direction) of the confined channel at the micro / nano scale to drive electroosmotic flow in the polyelectrolyte solution. In this embodiment, the applied electric field strength is set to 0.10~0.50 in reduced units, and multiple different electric field strengths within this range are selected for simulation. According to the length, energy, and charge mapping relationship used in this embodiment, the physical electric field strength corresponding to the above-mentioned reduced electric field range is approximately 0.037~0.183 V / nm. For each applied electric field strength, the simulation system first performs a 1.0×10⁻⁶ V / nm test. 6 Equilibrium calculations were performed at each time step to bring the polyelectrolyte chain conformation, ion distribution, and flow field to a stable state; subsequently, 6.0 × 10⁻⁶ time steps were performed. 6 The production calculations are performed at each time step to statistically determine the velocity field, solvent density field, polyelectrolyte monomer density field, counterion density field, and net charge density field. The integration time step for the equations of motion is set to Δt = 0.005τ.

[0079] The average electroosmotic flow velocity was calculated using a density-weighted method based on the solvent velocity profile and solvent density profile. in, external electric field strength The average electroosmotic velocity at that point, The local solvent velocity is along the channel direction. denoted as solvent number density, z as the wall normal coordinate, and H as the channel height.

[0080] The average electroosmotic velocity obtained under different applied electric field intensities was fitted with a power law to the electric field intensity: Among them, A char A is the characteristic coefficient. nl This represents the nonlinear response exponent. In this embodiment, the fitting result for the polyelectrolyte solution is:

[0081] Goodness of fit R 2 It is approximately 0.99. Therefore, the nonlinear response exponent A nl =1.710. According to The non-Newtonian exponent of electroosmotic flow was obtained as n=0.585.

[0082] like Figure 3 As shown, the results indicate that, under the channel size, wall charge density, and polyelectrolyte solution conditions of this embodiment, the average electroosmotic flow velocity exhibits a significant superlinear increase with the applied electric field strength, indicating that the polyelectrolyte solution has a non-Newtonian enhanced electroosmotic flow response.

[0083] To verify that this method can distinguish the electroosmotic flow response between polyelectrolyte solutions and simple electrolyte systems, a simple 1:1 symmetrical electrolyte control system was further established under the same channel height, wall charge density, and electric field range. In this control system, the concentration of small ions corresponds to the concentrations of charged monomers and counterions in the polyelectrolyte system. The results show that the average electroosmotic flow velocity of the simple 1:1 symmetrical electrolyte system approximately linearly satisfies the applied electric field strength.

[0084] ; Its power-law exponent is close to 1, indicating that the electroosmotic mobility of this simple electrolyte system is approximately constant. In contrast, the A of the polyelectrolyte solution system... nl =1.710, which is significantly greater than 1. This comparison result indicates that the n<1 obtained in this embodiment is not caused by the electric field strength setting itself, but mainly comes from the unique interfacial structural responses of polyelectrolytes, such as polyelectrolyte chain conformational changes, chain-wall desorption, counterion redistribution, and double-layer reconstruction.

[0085] As further verification, structural and velocity field information under different applied electric field intensities can be extracted. With increasing applied electric field, the enrichment peak of polyelectrolyte monomers in the near-wall region gradually decreases, and the monomer distribution expands towards the channel center; the counterion distribution rearranges as the polyelectrolyte chains migrate; the positive net charge region in the channel center, which originally hindered the mainstream direction, gradually weakens; and the velocity profile gradually changes from a central depression or M-shaped distribution under low field to a central enhancement distribution under high field. These structural and velocity field changes can serve as supplementary verification evidence that the non-Newtonian exponent n of electroosmotic flow has a microscopic physical origin.

[0086] Therefore, this embodiment demonstrates the feasibility and technical effectiveness of the method of the present invention through the core process of multi-electric field velocity sampling, average electroosmotic flow velocity calculation, power-law fitting, exponential output, and simple electrolyte comparison; and can further illustrate the correspondence between the non-Newtonian exponent of electroosmotic flow and the electric field-induced interface structure reconstruction through structural field analysis.

[0087] In summary, this invention abandons the traditional rheological constitutive path of non-Newtonian fluids that relies on shear rate-viscosity curves. Instead, it starts from the electro-transport response driven by an electric field. By collecting average electroosmotic flow velocity data under multiple applied electric field intensities, a power-law relationship between velocity and electric field intensity is established, and a non-Newtonian exponent for electroosmotic flow is defined accordingly. This method effectively solves the problem that classical electroosmotic flow theory, which assumes a linear response, cannot describe the superlinear enhancement effect caused by polyelectrolyte chain conformational changes, chain-wall desorption, counterion redistribution, and double-layer reconstruction. It also overcomes the limitations of relying solely on complex micro-nano experiments for point-by-point measurements, which is inefficient and difficult to scan parameters.

[0088] This invention relates to electroosmotic transport scenarios of polyelectrolyte solutions in confined channels at the micro / nano scale, including but not limited to engineering applications such as nanopore gene sequencing, protein conformation detection, and electric micropumps. Taking nanopore gene sequencing as an example, the DNA molecule to be tested passes through the nanopore under the drive of an electric field, and its passage speed is significantly affected by the electroosmotic flow: if the electroosmotic flow rate is too fast, the number of signal sampling points is insufficient, and the base recognition error rate increases; if the speed is too slow or fluctuates, the sequencing throughput decreases and the signal baseline drifts. Similarly, in the design of electric micropumps, the relationship between the electroosmotic flow rate of the polyelectrolyte solution and the applied voltage directly determines the pump's output characteristics and control linearity.

[0089] Electroosmotic flow is a crucial mass transfer mechanism in fields such as micro / nanofluidic chips, biomolecule transport, nanopore detection, and electrodynamic control. According to classical electroosmotic flow theory, for simple dilute electrolyte solutions, under conditions of low surface potential and an electric double layer thickness much smaller than the channel characteristic size, the average electroosmotic flow velocity is approximately proportional to the applied electric field strength, and the electroosmotic flow mobility can be considered a constant. This linear response law has been widely applied in the design and operation of various micro / nanofluidic devices.

[0090] However, polyelectrolyte solutions differ significantly from simple small-ion electrolytes in their physicochemical properties. Polyelectrolyte solutions contain long-chain polymers, each carrying numerous ionizable charged groups, along with a large number of counterions and salt ions. Within micro / nano-scale confined channels, various coupling effects—including conformational changes in polyelectrolyte chains, adsorption and desorption between chains and the wall, aggregation and release of counterions around the chains, reconstruction of the electrical double layer at the solid-liquid interface, and redistribution of local viscous resistance—make electroosmotic flow behavior extremely complex. Studies have shown that in partially confined polyelectrolyte solution systems, the average electroosmotic flow velocity may deviate from the classical linear law with respect to the applied electric field strength, exhibiting a superlinear growth trend; the stronger the applied electric field, the faster the velocity increases. This nonlinear response does not originate from shear thinning in conventional fluid dynamics, but is controlled by the rearrangement of the polyelectrolyte-rich layer structure near the solid-liquid interface induced by the electric field. Essentially, it belongs to a non-Newtonian electrodynamic transport behavior driven by the electric field and regulated by the evolution of the interfacial structure.

[0091] To address the aforementioned nonlinear electroosmotic behavior, existing microscopic or mesoscopic numerical simulation methods (such as dissipative particle dynamics and all-atom molecular dynamics) can perform relatively detailed calculations of polyelectrolyte solution systems, obtaining physical field information such as velocity field, concentration field, and charge density distribution. However, these simulation results are usually presented in raw data form, making it difficult to summarize the electroosmotic flow response data under multiple electric field conditions into a comparable, outputtable, and applicable characterization parameter for cross-system evaluation. Furthermore, electroosmotic flow experiments with confined polyelectrolyte solutions involve multiple complex steps, including the fabrication of micro / nanoscale confined channels, precise control of wall charge, polyelectrolyte concentration control, application of external electric fields, and measurement of weak flow velocities. These processes require sophisticated equipment, are difficult to operate, and have long experimental cycles, making it difficult to rapidly obtain systematic multi-electric field response data over a wide parameter range. Meanwhile, existing non-Newtonian fluid characterization methods based on shear rheological constitutive models have a theoretical framework centered on the constitutive relationship between shear stress and shear rate, and the characterization parameters are derived from mechanical rheological experiments, making them difficult to apply to electroosmotic transport processes driven by electric fields. Furthermore, classical electroosmotic flow theory itself only covers the linear response range and cannot quantitatively describe the aforementioned nonlinear behavior in polyelectrolyte solutions.

[0092] In summary, existing technologies lack a method that can quantitatively characterize the nonlinear electroosmotic flow behavior of confined polyelectrolyte solutions based on electric field response data, without relying on traditional shear rheological paths. The method provided by this invention aims to solve the aforementioned problems.

[0093] In summary, existing non-Newtonian fluid characterization methods are mostly based on shear rate-viscosity curves, which are difficult to apply to the analysis of electroosmotic flow response driven by electric fields. Classical electroosmotic flow theory is only applicable to linear response scenarios of simple electrolyte solutions and cannot describe the superlinear electroosmotic flow behavior in polyelectrolyte solutions caused by coupling mechanisms such as chain conformational changes, chain-wall desorption, counterion redistribution, and double-layer reconstruction. At the same time, electroosmotic flow experiments in confined polyelectrolyte solutions involve complex steps such as the fabrication of micro / nano-scale confined channels, wall charge regulation, concentration control, and weak flow velocity measurement, making it difficult to efficiently obtain systematic multi-electric field response data. Although existing numerical simulations can obtain rich information such as velocity field, concentration field, and charge density distribution, they lack a method to convert average electroosmotic flow velocity data under multiple electric field intensities into unified characterization parameters, and the obtained parameters lack verification of microstructural mechanisms, resulting in insufficient credibility and interpretability of the characterization results. Furthermore, electroosmotic flow experiments with confined polyelectrolyte solutions involve multiple complex steps, including the fabrication of micro / nano-scale confined channels, precise control of wall charge, polyelectrolyte concentration control, application of an external electric field, and measurement of weak flow velocities. These processes are demanding in terms of equipment, operational difficulty, and experimental duration, making it challenging to rapidly acquire systematic multi-electric field response data over a wide parameter range. Therefore, current technologies lack a nonlinear quantitative characterization method for the electroosmotic flow of polyelectrolyte solutions that is based on electric field response data, independent of traditional shear rheological paths, and possesses microscopic verification evidence.

[0094] To address the aforementioned problems, this invention provides a method for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions. This method obtains the average electroosmotic flow velocity of the polyelectrolyte solution in a micro / nano-scale confined channel under multiple different applied electric field intensities; based on the multiple different applied electric field intensities and their corresponding average electroosmotic flow velocities, a power-law response relationship is established between the average electroosmotic flow velocity and the applied electric field intensity; a nonlinear response index is determined based on the power-law response relationship; and the non-Newtonian index of electroosmotic flow is calculated based on the nonlinear response index, used to quantitatively characterize the degree to which the electroosmotic flow response of the polyelectrolyte solution in a micro / nano-scale confined channel deviates from the classical linear electroosmotic flow behavior.

[0095] Compared to existing technologies, this invention offers the following advantages: First, it does not rely on traditional shear rheological paths, but directly starts from the response relationship between the applied electric field strength and the average electroosmotic flow velocity, avoiding the fundamental defect that shear constitutive models are unsuitable for electric field-driven scenarios. Second, by using the nonlinear response exponent in the power-law response relationship, allowing the exponent to deviate from 1, it can quantitatively characterize the superlinear electroosmotic flow behavior in polyelectrolyte solutions caused by coupling mechanisms such as chain conformational changes, chain-wall desorption, counterion redistribution, and double-layer reconstruction. Third, the data sources are flexible, and data can be obtained through various methods such as numerical simulation or experiments, avoiding the inefficiency of relying solely on complex experiments while ensuring the versatility of the method. Fourth, it provides a complete data extraction process, transforming the originally scattered multi-field velocity data into a unified index that can be output, compared, and used for cross-system evaluation across different systems. Fifth, the microstructural features such as near-wall desorption of polyelectrolyte chains, channel center migration, counterion redistribution, net charge density reconstruction, and velocity profile morphology changes are extracted simultaneously as verification basis, so that the characterization parameters have clear physical sources and interpretability. Furthermore, prediction functions can be established based on the obtained parameter-index sample library for rapid screening and parameter design of the nonlinear behavior of electroosmotic flow in new systems.

[0096] Based on the same inventive concept, the present invention also provides a system for determining the non-Newtonian index of electroosmotic flow in polyelectrolyte solutions, comprising: The data acquisition module is used to acquire the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities in a micro-nano scale confined channel.

[0097] The relationship establishment module is used to perform power-law fitting on multiple different average electroosmotic flow velocities and corresponding applied electric field intensities, establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field intensity, and determine the nonlinear response index of the target polyelectrolyte solution based on the power-law response relationship.

[0098] The calculation module is used to calculate the electroosmotic non-Newtonian index of the target polyelectrolyte solution based on the nonlinear response index. The electroosmotic non-Newtonian index is used to quantitatively characterize the degree to which the electroosmotic response of the polyelectrolyte solution deviates from the classical linear electroosmotic behavior in a micro-nano scale confined channel.

[0099] Specific limitations on the calculation system for determining the non-Newtonian index of polyelectrolyte solution electroosmotic flow can be found in the limitations section above, and will not be repeated here. Each module in the system for determining the non-Newtonian index of polyelectrolyte solution electroosmotic flow can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0100] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification. Furthermore, the above embodiments only illustrate several implementation methods of this application, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution, characterized in that, Includes the following steps: In a micro-nano scale confined channel, the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities was obtained; Power-law fitting was performed on multiple different average electroosmotic flow velocities and their corresponding applied electric field strengths to establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field strength. Based on this power-law response relationship, the nonlinear response index of the target polyelectrolyte solution was determined. ; According to the nonlinear response index The electroosmotic non-Newtonian index n of the target polyelectrolyte solution is calculated. The electroosmotic non-Newtonian index n is used to quantitatively characterize the degree to which the electroosmotic response of the polyelectrolyte solution deviates from the classical linear electroosmotic behavior in micro-nano scale confined channels.

2. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 1, characterized in that, The process of obtaining the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities specifically includes: for each applied electric field intensity, obtaining the velocity distribution and solvent density distribution of the solvent along the channel direction within the micro-nano scale confined channel, and calculating the average electroosmotic flow velocity under the applied electric field intensity using a density-weighted average based on the velocity distribution and solvent density distribution.

3. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 2, characterized in that, Based on the velocity distribution and solvent density distribution, the average electroosmotic velocity under an applied electric field is calculated using a density-weighted average, which is achieved in the following way: in, external electric field strength The average electroosmotic velocity under these conditions; Ω represents the intensity of the j-th applied electric field along the channel direction; r represents the cross-sectional region of the micro / nano-scale confined channel; and r represents the position coordinates within the cross-sectional region. external electric field strength Velocity distribution of the solvent along the channel direction; external electric field strength The solvent density distribution is given below; dA is the area element within the cross-sectional region.

4. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 2, characterized in that, When the micro / nano-scale confined channel is a flat plate channel or a slit channel, the velocity distribution and solvent density distribution are represented as velocity profiles and solvent density profiles along the normal coordinates of the channel wall, respectively. The average electroosmotic velocity is calculated in the following way: Where z is the normal coordinate of the wall of the micro-nano scale confined channel, and H is the channel height of the micro-nano scale confined channel; external electric field strength The average electroosmotic velocity under these conditions; Let J be the intensity of the applied electric field along the channel direction; external electric field strength The velocity profile of the solvent along the channel direction, where z is the normal coordinate of the channel wall; external electric field strength Solvent density profile below; d Let be a infinitesimal element of length along the normal direction of the channel wall.

5. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 1, characterized in that, The step of performing power-law fitting on multiple different average electroosmotic velocities and their corresponding applied electric field strengths to establish a power-law response relationship between the average electroosmotic velocity and the applied electric field strength specifically includes: substituting the multiple different applied electric field strengths and their corresponding average electroosmotic velocities into the following power-law response relationship: ； in, Let E be the average electroosmotic velocity, and E be the applied electric field strength along the channel direction. These are the characteristic electroosmotic flow response coefficients in the power-law fitting. The nonlinear response exponent is defined as the relationship between the average electroosmotic flow velocity and the applied electric field strength. The characteristic electroosmotic flow response coefficient and nonlinear response exponent are determined by performing a nonlinear least-squares fit on the average electroosmotic flow velocity and the applied electric field strength, or by performing a linear least-squares fit after a logarithmic transformation of the average electroosmotic flow velocity and the applied electric field strength when both are greater than zero. ; According to the nonlinear response index Calculate the non-Newtonian exponent n of the electroosmotic flow in the target polyelectrolyte solution, where, .

6. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 1, characterized in that, The criterion for the non-Newtonian exponent n of the electroosmotic flow is: When the nonlinear response index When the value equals 1, or its deviation from 1 is not greater than a preset threshold, the target polyelectrolyte solution is determined to exhibit a near-linear electroosmotic flow response; when the nonlinear response index... When the non-Newtonian exponent n of the electroosmotic flow is greater than 1 and less than 1, it is determined that the target polyelectrolyte solution exhibits a superlinearly enhanced non-Newtonian electroosmotic flow response in a micro-nano scale confined channel, and the non-Newtonian exponent n of the electroosmotic flow is inversely proportional to the degree of nonlinear enhancement.

7. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 1, characterized in that, Also includes: If the average electroosmotic velocity reverses direction within the studied electric field range, the reverse electric field strength or reverse electric field interval corresponding to the zero average electroosmotic velocity is determined, and the data is segmented according to the electric field interval where the sign of the average electroosmotic velocity remains unchanged. Within each segment, a power-law fit is performed using the absolute value of the average electroosmotic velocity, and the flow direction, nonlinear response index, and corresponding electroosmotic non-Newtonian exponent n of each segment are recorded. Data crossing the flow reversal point are not combined for a single power-law fit.

8. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 1, characterized in that, It also includes the step of establishing the prediction function, specifically including: By changing the wall charge density and channel height of the micro / nano-scale confined channel, and by changing at least one of the following parameters of the polyelectrolyte solution: chain charge fraction, salt concentration, monomer concentration, and chain length, the steps of obtaining the average electroosmotic flow velocity, performing power-law fitting to determine the nonlinear response index, and calculating the non-Newtonian index n of the electroosmotic flow are repeated for the changed micro / nano-scale confined channel or polyelectrolyte solution, to obtain a parameter-index dataset consisting of multiple sets of parameters and their corresponding non-Newtonian index n of the electroosmotic flow. Based on the parameter-index dataset, a prediction function is established between the non-Newtonian exponent n of electroosmotic flow and the parameter, which is used to predict the non-Newtonian exponent n of electroosmotic flow under different parameter conditions.

9. The method for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution according to claim 8, characterized in that, It also includes the step of inverting the wall charge density, specifically including: Under the conditions of preset polyelectrolyte solution properties and preset channel height, multiple different applied electric field strengths and their corresponding average electroosmotic flow velocities are obtained experimentally. The experimental electroosmotic flow non-Newtonian index n is determined based on the average electroosmotic flow velocity, and the experimental electroosmotic flow non-Newtonian index n is matched with the prediction function to invert the wall charge density of the micro-nano scale confined channel.

10. A system for determining the non-Newtonian index of electroosmotic flow in a polyelectrolyte solution, characterized in that, include: The data acquisition module is used to acquire the average electroosmotic flow velocity of the target polyelectrolyte solution under multiple different applied electric field intensities in a micro-nano scale confined channel. The relationship establishment module is used to perform power-law fitting on multiple different average electroosmotic flow velocities and corresponding applied electric field intensities, establish a power-law response relationship between the average electroosmotic flow velocity and the applied electric field intensity, and determine the nonlinear response index of the target polyelectrolyte solution based on the power-law response relationship. The calculation module is used to calculate the electroosmotic non-Newtonian index of the target polyelectrolyte solution based on the nonlinear response index. The electroosmotic non-Newtonian index is used to quantitatively characterize the degree to which the electroosmotic response of the polyelectrolyte solution deviates from the classical linear electroosmotic behavior in a micro-nano scale confined channel.

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