Non-newtonian fluid high-precision ion concentration measurement system and method based on liquid flexoelectric effect

Abstract

The application discloses a high-precision ion concentration measuring system and method of non-Newtonian fluid based on liquid flexoelectric effect, which comprises a ladder-shaped container, a cylindrical rotor located at the central axis in the container, a torque motor connected with the cylindrical rotor, metal electrodes fixed on the inner surfaces of the upper and lower parts of the container, a charge amplifier connected with the electrodes, and a signal processing module connected with the charge amplifier. The torque motor is used to rotate the cylindrical rotor to generate gradient velocity and strain on the liquid in the container, and the liquid generates shear strain gradient in the axial and radial directions to generate flexoelectric effect polarization. Ions in the solution gather on the electrodes to form double-layer effect and partially shield the flexoelectric polarization. The polarization charge on the electrodes is converted into a voltage signal by the charge amplifier and transmitted into the signal processing module. After the material parameters of the solution and the structure parameters of the container are combined, the ion concentration of the solution can be obtained. In addition, the method can also be used for measuring the concentration of multiple ions in the non-Newtonian fluid under specific conditions.

Description

Technical Field

[0001] This invention relates to the field of electromechanical coupling technology in materials science, specifically to a high-precision ion concentration measurement system and method based on the flexoelectric effect of liquids and non-Newtonian fluids. Background Technology

[0002] Flexural electricity is a phenomenon caused by polarization due to strain gradients or deformation due to electric field gradients in materials. It is a mechanoelectric coupling property widely present in dielectric materials. Because it exists in all dielectric materials, flexural electricity is considered a promising alternative to the piezoelectric effect. Research on flexural electricity is currently still in the theoretical stage, but its potential applications remain a hot research topic in this field. Due to the coupling between flexural electricity and the electric double layer in liquids, explaining its mechanism and applying it to fields such as ion detection is a research challenge. Summary of the Invention

[0003] To fill the gaps in related theoretical and application fields, the present invention aims to provide a high-precision ion concentration measurement system and method for non-Newtonian fluids based on the flexoelectric effect of liquids. The system generates strain gradients and polarization in the liquid through the design of the measurement device, and then measures the coupled flexoelectric effect and electric double layer effect, thereby solving the problem in reverse and applying it to the field of ion concentration measurement.

[0004] To achieve the above objectives, the present invention adopts the following technical solution.

[0005] A high-precision ion concentration measurement system for non-Newtonian fluids based on the flexoelectric effect of liquids includes a trapezoidal container 1 made of insulating material, a cylindrical rotor 2 located on the central axis inside the trapezoidal container 1, a torque motor 3 connected to the upper end of the cylindrical rotor 2, a first electrode 4-1 fixed to the inner surface of the upper part of the trapezoidal container 1, a second electrode 4-2 fixed to the inner surface of the lower part of the trapezoidal container 1, a charge amplifier 5 connected to the first electrode 4-1 and the second electrode 4-2, and a signal processing module 6 connected to the output of the charge amplifier 5. The torque motor 3 applies torque to the non-Newtonian fluid inside the trapezoidal container 1 through the cylindrical rotor 2. The non-Newtonian fluid generates shear flow strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitudes are induced on the first electrode 4-1 and the second electrode 4-2. At the same time, trace ions in the liquid accumulate on the surfaces of the first electrode 4-1 and the second electrode 4-2, generating a double-layer effect, which partially shields the polarization charges. The higher the ion concentration, the stronger the shielding and the weaker the remaining flexoelectric effect.

[0006] The trapezoidal container 1 and the cylindrical rotor 2 are made of high-impedance insulating materials to ensure that there is no direct charge transfer between the first electrode 4-1 and the second electrode 4-2.

[0007] The first electrode 4-1 and the second electrode 4-2 are made of highly conductive metal.

[0008] The measurement accuracy of the charge amplifier 5 is sufficient to meet the micro-charge measurement requirements of the flexural liquid dielectric.

[0009] The measurement method of the high-precision ion concentration measurement system for non-Newtonian fluids based on the liquid flexure electrical effect employs a torque motor 3 to apply torque to the non-Newtonian fluid inside the trapezoidal container 1 via a cylindrical rotor 2. The non-Newtonian fluid generates shear strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitudes are induced on the first electrode 4-1 and the second electrode 4-2. Simultaneously, trace ions in the non-Newtonian fluid accumulate on the surfaces of the first electrode 4-1 and the second electrode 4-2, generating a double-layer effect. This double-layer effect will affect the electrodes... An additional local electric field is formed, and this local electric field is coupled with the flexure polarization and is affected by the flexure polarization electric field. The double layer effect occupies the charge attachment sites near the electrode and partially shields the polarization charge. By comparing the flexure polarization charge of a standard non-ion non-Newtonian fluid with the polarization charge of a non-Newtonian fluid containing ions, the amount of charge shielded by the double layer can be obtained. Then, by combining the material parameters of the non-Newtonian fluid and the structural parameters of the truncated container, the flexure effect equation and the double layer equation can be solved simultaneously to obtain the ion concentration of the non-Newtonian fluid.

[0010] The method for determining the ion concentration of non-Newtonian fluids is as follows:

[0011] The cylindrical rotor 2 induces a corresponding shear flow of non-Newtonian fluid during axial torsion. A cylindrical coordinate system (r, θ, z) is established with the bottom center of the trapezoidal container 1 as the origin. The velocity distribution of the non-Newtonian fluid is as follows:

[0012]

[0013] Where v is the velocity of the shear flow at a certain point (r, θ, z), r is the radial length at that point, and z is the axial height; R1, R2, and R3 are the radii of the cylindrical rotor, the bottom radius of the trapezoidal container 1, and the top radius, respectively; H is the axial distance between the first and second electrodes; ω0 is the rotational angular velocity of the cylindrical rotor, f is the rotational frequency, and t is time; the formula for calculating the shear strain in the liquid is:

[0014]

[0015] Where τ is the shear stress and γ is the shear strain; both τ and γ are in tensor form; since there is no velocity gradient in the θ direction, the equation can be simplified. Solving equations (1) and (2) simultaneously yields the strain formula:

[0016]

[0017] Where, γ θr For circumferential-radial shear strain, γ θz For circumferential-axial shear strain;

[0018] The flexural electrical effect of a material is expressed as:

[0019]

[0020] Where P l μ ijkl γ ij and u k These are the polarization degree, flexural coefficient, strain, and gradient direction, respectively; while the polarization degree is described as the ratio of charge to the area of ​​charge distribution; combining equations (3) and (4) yields the average polarization intensity.

[0021]

[0022] Where V is the volume of the container, μ θrrz Let be the flexural conductivity coefficient of the liquid; Equation (5) describes the flexural polarization intensity without ions. When there are ions in the non-Newtonian fluid, a double-layer effect will be generated on the surfaces of the first electrode 4-1 and the second electrode 4-2, which can be described by the Poisson-Boltzmann equation:

[0023]

[0024] Where ε0 and ε r These are the dielectric constants of vacuum and the material, respectively; ψ is the electric potential; ρ is the dielectric constant of the material. e Let the volume charge density be ; substituting Gauss's law into equation (6), we obtain the relationship between the electrode surface charge density and the electric potential as follows:

[0025]

[0026] In the formula σ d N is the surface charge density. A k b e and T are Avogadro's constant, Boltzmann's constant, electron charge, and temperature, respectively; z i and c i Let represent the valence state and concentration of the i-th ion in the non-Newtonian fluid; combining equations (5) and (7), the final polarization intensity equation is obtained:

[0027]

[0028] The polarization of the non-Newtonian fluid is obtained by applying a torque displacement to the cylindrical rotor 2. The polarization intensity is obtained from the data of the signal processing module 6 and the charge amplifier 5. Substituting these values ​​into formula 8 allows for the reverse solution of the ion concentration c of the non-Newtonian fluid.i .

[0029] Compared with the prior art, the present invention has the following advantages:

[0030] 1. The method of this invention is the first of its kind in mechanical concentration measurement, which can accurately measure the ion concentration of non-Newtonian fluids without the need for a chemical reaction.

[0031] 2. The method of the present invention is more sensitive to low concentration ranges but less sensitive to high concentrations. This feature is significantly different from and has advantages over existing technologies, forming a complementary advantage.

[0032] 3. The concentration of various ions can be accurately measured through prior calibration and a limited number of mechanical loading designs. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the measurement system of the present invention.

[0034] Figure 2 This is a microscopic schematic diagram of the electrode surface of the measuring device of the present invention under different ion concentrations. Detailed Implementation

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0036] like Figure 1 As shown, the present invention discloses a high-precision ion concentration measurement system for non-Newtonian fluids based on the flexoelectric effect of liquids. The system includes a trapezoidal container 1 made of an insulating material, a cylindrical rotor 2 located on the central axis inside the trapezoidal container 1, a torque motor 3 connected to the upper end of the cylindrical rotor 2, a first electrode 4-1 fixed to the inner surface of the upper part of the trapezoidal container 1, a second electrode 4-2 fixed to the inner surface of the lower part of the trapezoidal container 1, a charge amplifier 5 connected to the first electrode 4-1 and the second electrode 4-2, and a signal processing module 6 connected to the output of the charge amplifier 5. The torque motor 3 applies torque to the non-Newtonian fluid inside the trapezoidal container 1 through the cylindrical rotor 2. The non-Newtonian fluid generates shear strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitudes are induced on the first electrode 4-1 and the second electrode 4-2. Simultaneously, trace ions in the liquid accumulate on the surfaces of the first electrode 4-1 and the second electrode 4-2, generating a double-layer effect that partially shields the polarization charges. The higher the ion concentration, the stronger the shielding and the weaker the remaining flexoelectric effect.

[0037] The trapezoidal container 1 and the cylindrical rotor 2 are made of high-impedance insulating materials to ensure that there is no direct charge transfer between the first electrode 4-1 and the second electrode 4-2.

[0038] In a preferred embodiment of the present invention, the first electrode 4-1 and the second electrode 4-2 are made of a highly conductive metal with a surface oxide dielectric having a limited and uniform thickness and stable chemical properties. This prevents the system from generating the expected external electrical signal through a chemical reaction, while also providing good conductivity for a small order of magnitude of charge information, thereby enabling accurate measurement.

[0039] The measurement accuracy of the charge amplifier 5 is sufficient to meet the micro-charge measurement requirements of the flexural liquid dielectric.

[0040] The measurement method of the high-precision ion concentration measurement system for non-Newtonian fluids based on the flexural electrical effect of liquids described in this invention employs a torque motor 3 to apply torque to the non-Newtonian fluid inside a trapezoidal container 1 via a cylindrical rotor 2. The non-Newtonian fluid generates shear strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitudes are induced on the first electrode 4-1 and the second electrode 4-2. Simultaneously... Figure 2 As shown, trace ions in a non-Newtonian fluid accumulate on the surfaces of the first electrode 4-1 and the second electrode 4-2, generating a double-layer effect. This double-layer effect creates an additional local electric field near the electrodes, and this local electric field is coupled with the flexural polarization and is affected by the flexural polarization electric field. The double-layer effect occupies charge attachment sites near the electrodes and partially shields the polarization charge. By comparing the flexural polarization charge of a standard ion-free non-Newtonian fluid with the polarization charge of a non-Newtonian fluid containing ions, the amount of charge shielded by the double-layer can be obtained. Combined with the material parameters of the non-Newtonian fluid and the structural parameters of the truncated trapezoidal container, the flexural effect equation and the double-layer equation can be solved simultaneously to obtain the ion concentration of the non-Newtonian fluid.

[0041] The method for determining the ion concentration of non-Newtonian fluids is as follows:

[0042] The cylindrical rotor 2 induces a corresponding shear flow of non-Newtonian fluid during axial torsion. A cylindrical coordinate system (r, θ, z) is established with the bottom center of the trapezoidal container 1 as the origin. The velocity distribution of the non-Newtonian fluid is as follows:

[0043]

[0044] Where v is the velocity of the shear flow at a certain point (r, θ, z), r is the radial length at that point, and z is the axial height; R1, R2, and R3 are the radii of the cylindrical rotor, the bottom radius of the trapezoidal container 1, and the top radius, respectively; H is the axial distance between the first and second electrodes; ω0 is the rotational angular velocity of the cylindrical rotor, f is the rotational frequency, and t is time; the formula for calculating the shear strain in the liquid is:

[0045]

[0046] Where τ is the shear stress and γ is the shear strain; both τ and γ are in tensor form; since there is no velocity gradient in the θ direction, the equation can be simplified. Solving equations (1) and (2) simultaneously yields the strain formula:

[0047]

[0048] Where, γ θr For circumferential-radial shear strain, γ θz For circumferential-axial shear strain;

[0049] The flexural electrical effect of a material is expressed as:

[0050]

[0051] Where P l μ ijkl γ ij and u k These are the polarization degree, flexural coefficient, strain, and gradient direction, respectively; while the polarization degree is described as the ratio of charge to the area of ​​charge distribution; combining equations (3) and (4) yields the average polarization intensity.

[0052]

[0053] Where V is the volume of the container, μ θrrz Let be the flexural conductivity coefficient of the liquid; Equation (5) describes the flexural polarization intensity without ions. When there are ions in the non-Newtonian fluid, a double-layer effect will be generated on the surfaces of the first electrode 4-1 and the second electrode 4-2, which can be described by the Poisson-Boltzmann equation:

[0054]

[0055] Where ε0 and ε r These are the dielectric constants of vacuum and the material, respectively; ψ is the electric potential; ρ is the dielectric constant of the material. e Let the volume charge density be ; substituting Gauss's law into equation (6), we obtain the relationship between the electrode surface charge density and the electric potential as follows:

[0056]

[0057] In the formula σ d N is the surface charge density. A k b e and T are Avogadro's constant, Boltzmann's constant, electron charge, and temperature, respectively; z i and c i Let represent the valence state and concentration of the i-th ion in the non-Newtonian fluid; combining equations (5) and (7), the final polarization intensity equation is obtained:

[0058]

[0059] The polarization of the non-Newtonian fluid is obtained by applying a torque displacement to the cylindrical rotor 2. The polarization intensity is obtained from the data of the signal processing module 6 and the charge amplifier 5. Substituting these values ​​into formula 8 allows for the reverse solution of the ion concentration c of the non-Newtonian fluid. i .

[0060] like Figure 2 As shown, when the concentration in the liquid is very small ( Figure 2 In section A), the ion density adsorbed at the ion-electric interface is very small, resulting in minimal shielding of the shear-flexure electrical effect. Therefore, the electrical signal measured at the electrode is essentially consistent with the actual flexure electrical effect. As the liquid concentration gradually increases ( Figure 2 As the ion adsorption density gradually increases (as shown in section B), the shielding effect gradually increases, and the measured residual electrical signal gradually decreases; however, as the ion concentration further increases (…), the residual electrical signal decreases. Figure 2 In the case of C), the shielding electric field generated by the concentration of ions adsorbed at the ion-electric interface completely cancels out the polarization caused by the flexural effect, thus the output electrical signal is static noise. Since the degree of residual polarization is closely related to the ion concentration, the degree of residual polarization can be used to measure the ion concentration.

Claims

1. A measurement method for a high-precision ion concentration measurement system based on the flexoelectric effect of liquids and non-Newtonian fluids, characterized in that: The system includes a trapezoidal container (1) made of insulating material, a cylindrical rotor (2) located on the central axis inside the trapezoidal container (1), a torque motor (3) connected to the upper end of the cylindrical rotor (2), a first electrode (4-1) fixed to the upper inner surface of the trapezoidal container (1), a second electrode (4-2) fixed to the lower inner surface of the trapezoidal container (1), a charge amplifier (5) connected to the first electrode (4-1) and the second electrode (4-2), and a signal processing module (6) connected to the output terminal of the charge amplifier (5); The torque motor (3) applies torque to the non-Newtonian fluid inside the trapezoidal container (1) through the cylindrical rotor (2). The non-Newtonian fluid generates shear flow strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitude are induced on the first electrode (4-1) and the second electrode (4-2). At the same time, trace ions in the liquid accumulate on the surfaces of the first electrode (4-1) and the second electrode (4-2) to generate a double layer effect, which partially shields the polarization charges. The higher the ion concentration, the stronger the shielding degree and the weaker the remaining flexural effect. The measurement method is as follows: a torque motor (3) is used to apply torque to the non-Newtonian fluid inside the trapezoidal container (1) through a cylindrical rotor (2). The non-Newtonian fluid generates shear flow strain gradients along the axial and radial directions, resulting in polarization. Polarization charges of opposite signs and equal magnitude are induced on the first electrode (4-1) and the second electrode (4-2). At the same time, trace ions in the non-Newtonian fluid accumulate on the surfaces of the first electrode (4-1) and the second electrode (4-2) to generate a double layer effect. The double layer effect will form an additional local electric field near the electrode, and this local electric field is coupled with the flexural polarization and is affected by the flexural polarization electric field. The double layer effect occupies the charge attachment sites near the electrode and partially shields the polarization charge. By comparing the flexural polarization charge of the standard non-ion non-Newtonian fluid and the polarization charge of the non-Newtonian fluid containing ions, the charge amount shielded by the double layer is obtained. Then, by combining the material parameters of the non-Newtonian fluid and the structural parameters of the trapezoidal container, the flexural effect equation and the double layer equation can be solved simultaneously to obtain the ion concentration of the non-Newtonian fluid. The method for determining the ion concentration of non-Newtonian fluids is as follows: The cylindrical rotor (2) induces a corresponding shear flow of non-Newtonian fluid during axial torsion. A cylindrical coordinate system is established with the bottom center of the trapezoidal container (1) as the origin. r,θ,z The velocity distribution of a non-Newtonian fluid is as follows: (1) in v For shear flow at a certain point ( r,θ,z ) speed, r This is the radial length at this location. z This refers to the axial height. R 1. R 2. R 3 are the radius of the cylindrical rotor, the bottom radius of the trapezoidal container (1), and the top radius, respectively; H The axial distance between the first and second electrodes; ω 0 represents the rotational angular velocity of the cylindrical rotor. f For rotation frequency, t For time; the formula for calculating shear strain in a liquid is: （2） in τ It is shear stress. γ It is shear strain; here τ and γ All are in tensor form; due to the velocity in θ Since there is no gradient in the direction, the equation can be simplified. Solving equations (1) and (2) simultaneously yields the strain formula: （3） in, γ θr For circumferential-radial shear strain, γ θz For circumferential-axial shear strain; The flexural electrical effect of a material is expressed as: （4） in P l , μ ijkl , γ ij and u k These are the polarization degree, flexural coefficient, strain, and gradient direction, respectively; while the polarization degree is described as the ratio of charge to the area of ​​charge distribution; combining equations (3) and (4) yields the average polarization intensity. : （5） in V For container volume, μ θrrz Let be the flexural conductivity coefficient of the liquid; Equation (5) describes the flexural polarization intensity when there are no ions involved. When there are ions in the non-Newtonian fluid, a double layer effect will be generated on the surfaces of the first electrode (4-1) and the second electrode (4-2), which can be described by the Poisson-Boltzmann equation: （6） in ε 0 and ε r These are the dielectric constants of vacuum and the material, respectively. ψ For electric potential, ρ e Let the volume charge density be ; substituting Gauss's law into equation (6), we obtain the relationship between the electrode surface charge density and the electric potential as follows: （7） In the formula σ d Surface charge density, N A , k b , e and T These are Avogadro's constant, Boltzmann's constant, electron charge, and temperature, respectively. z i and c i Let represent the valence state and concentration of the i-th ion in the non-Newtonian fluid; combining equations (5) and (7), the polarization intensity equation is derived: （8） The polarization of the non-Newtonian fluid is obtained by applying a torque displacement to the cylindrical rotor (2), and the polarization intensity is obtained from the data of the signal processing module (6) and the charge amplifier (5). Substituting this into formula (8) allows the inverse solution to obtain the ion concentration of the non-Newtonian fluid. .

2. The measurement method of the high-precision ion concentration measurement system based on the flexoelectric effect of liquid non-Newtonian fluid according to claim 1, characterized in that: The trapezoidal container (1) and cylindrical rotor (2) are made of high-impedance insulating material to ensure that there is no direct charge transfer between the first electrode (4-1) and the second electrode (4-2).

3. The measurement method of the high-precision ion concentration measurement system based on the flexoelectric effect of liquid non-Newtonian fluids according to claim 1, characterized in that: The first electrode (4-1) and the second electrode (4-2) are made of highly conductive metal.

4. The measurement method of the high-precision ion concentration measurement system based on the flexoelectric effect of liquid non-Newtonian fluid according to claim 1, characterized in that: The measurement accuracy of the charge amplifier (5) can meet the micro-charge measurement requirements of the flexural liquid dielectric.

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