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

Abstract

The invention discloses a non-Newtonian fluid high-precision ion concentration measurement system and method based on a liquid flexoelectric effect, and the measurement device comprises a halfpace-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 upper and lower inner surfaces of the container, and a charge amplifier connected with the electrodes. The signal processing module is connected with the charge amplifier, a torque motor is used for rotating 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 direction and the radial direction to generate flexoelectric effect electric polarization; ions in the solution gather on the electrode to form a double-electric-layer effect to partially shield flexoelectric polarization. Polarized charges on the electrodes pass through the charge amplifier and are converted into voltage signals, the voltage signals are transmitted to the signal processing module, and the ion concentration of the solution can be obtained after material parameters of the solution and container structure parameters are combined. In addition, the method can also be used for measuring the concentration of various ions contained in the non-Newtonian fluid under specific conditions.

Description

Technical Field

[0001] The present invention relates to the field of electromechanical coupling technology in materials science, and in particular to a high-precision ion concentration measurement system and method for non-Newtonian fluids based on the liquid flexoelectric effect. Background Art

[0002] The flexoelectric effect is a phenomenon in which the electric polarization is generated by the strain gradient or the material deformation is generated by the electric field gradient. It is a mechanoelectric coupling property that is widely present in dielectric materials. Since it exists in all dielectric materials, the flexoelectric effect is seen as a promising alternative to the piezoelectric effect. The study of the flexoelectric effect is still in the theoretical stage, but the potential applications of the flexoelectric effect have always been a research hotspot in this field. Due to the coupling of the flexoelectric effect and the double electric layer in liquids, how to explain its mechanism and apply it to fields such as ion detection is a research difficulty. Summary of the invention

[0003] In order to fill the gaps in relevant theories and application fields, the purpose of the present invention is to provide a high-precision ion concentration measurement system and method for non-Newtonian fluids based on the liquid flexoelectric effect. The strain gradient and electric polarization in the liquid are generated by designing a measuring device, and then the coupled flexoelectric effect and double layer effect are measured, so as to reversely solve and apply it to the field of ion concentration measurement.

[0004] In order to achieve the above objectives, the present invention adopts the following technical solutions.

[0005] A high-precision ion concentration measurement system for non-Newtonian fluid based on liquid flexoelectric effect comprises a terraced container 1 made of an insulating material, a cylindrical rotor 2 located on the central axis of the terraced container 1, a torque motor 3 connected to the upper end of the cylindrical rotor 2, a first electrode 4-1 fixed on the upper inner surface of the terraced container 1, a second electrode 4-2 fixed on the lower inner surface of the terraced 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 end of the charge amplifier 5; the torque motor 3 applies torque to the non-Newtonian fluid inside the terraced container 1 through the cylindrical rotor 2, the non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate electric polarization, and polarized charges with opposite signs and the same magnitude are induced on the first electrode 4-1 and the second electrode 4-2; at the same time, trace ions in the liquid gather on the surfaces of the first electrode 4-1 and the second electrode 4-2 to generate a double electric layer effect, which partially shields the polarized charges. The higher the ion concentration, the stronger the shielding degree and the weaker the residual flexoelectric effect.

[0006] The terraced container 1 and the cylindrical rotor 2 are made of high-impedance insulator 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 can meet the micro-charge measurement requirements of flexoelectric liquid dielectrics.

[0009] The measurement method of the non-Newtonian fluid high-precision ion concentration measurement system based on the liquid flexoelectric effect adopts a torque motor 3 to apply torque to the non-Newtonian fluid inside the terraced container 1 through a cylindrical rotor 2. The non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate polarization, and polarized charges with opposite signs and the same 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 gather on the surfaces of the first electrode 4-1 and the second electrode 4-2 to generate a double layer effect, which will be near the electrodes. An additional local electric field is formed, and this local electric field is coupled with the flexoelectric polarization and is affected by the flexoelectric polarization electric field; the double layer effect occupies the charge attachment points near the electrode and partially shields the polarization charge; the amount of charge shielded by the double layer is obtained by comparing the flexoelectric polarization charge of the standard ion-free non-Newtonian fluid with the polarization charge of the non-Newtonian fluid containing ions, and then the material parameters of the non-Newtonian fluid and the structural parameters of the terraced container are combined to solve the flexoelectric effect equation and the double layer equation jointly to obtain the ion concentration of the non-Newtonian fluid.

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

[0011] The cylindrical rotor 2 causes the corresponding shear flow of the non-Newtonian fluid in the axial torsion. The cylindrical coordinate system (r, θ, z) is established with the center of the bottom circle of the terraced container 1 as the origin. The flow velocity distribution of the non-Newtonian fluid is:

[0012]

[0013] Where v is the velocity of the shear flow at a certain point (r, θ, z), r is the radial length at this point, and z is the axial height; R 1 , R 2 , R 3 are the radius of the cylindrical rotor, the bottom radius and the top radius of the terraced container 1 respectively; H is the axial distance between the first electrode and the second electrode; ω 0 is the angular velocity of the cylindrical rotor, f is the rotation frequency, and t is the time; the calculation formula for the shear flow 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 gradient of velocity in the θ direction, the equation can be simplified. The strain formula is obtained by solving equations (1) and (2) together:

[0016]

[0017] Among them, γ θr is the circumferential-radial shear strain, γ θz is the circumferential-axial shear strain;

[0018] The flexoelectric effect of the material is expressed as:

[0019]

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

[0021]

[0022] Where V is the volume of the container, μ θrrz is the liquid flexoelectric coefficient; Formula (5) describes the flexoelectric polarization intensity when there are no ions involved. When there are ions in the non-Newtonian fluid, a double electric layer effect will be generated on the surface of the first electrode 4-1 and the second electrode 4-2, which is described by the Poisson-Boltzmann equation:

[0023]

[0024] where ε 0 and ε r are the vacuum and material dielectric constants, ψ is the electric potential, ρ e is the volume charge density; Substituting Gauss's law into equation (6), the relationship between the electrode surface charge density and the potential is:

[0025]

[0026] Where σ d is the surface charge density, N A , k b , e and T are Avogadro constant, Boltzmann constant, electron charge and temperature respectively; z i and c i is the valence and concentration of the i-th ion in the non-Newtonian fluid; combining equation (5) and equation (7) to obtain the final polarization intensity equation:

[0027]

[0028] The electric polarization of the non-Newtonian fluid is obtained by applying torque displacement to the cylindrical rotor 2, and the data of the signal processing module 6 and the charge amplifier 5 are used to obtain the polarization intensity. Substituting it into formula 8 can reversely solve 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 the present invention is the first to measure concentration mechanically, and can accurately measure the ion concentration of non-Newtonian fluids without chemical reaction.

[0031] 2. The method of the present invention is more sensitive to low concentrations but insensitive to high concentrations. This feature is significantly different from and superior to the prior art, forming a complementary advantage.

[0032] 3. The concentration of multiple ions can be accurately measured through prior calibration and limited mechanical loading design. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the measurement system of the present invention.

[0034] Figure 2 It is a microscopic schematic diagram of the electrode surface of the measuring device of the present invention under different ion concentrations. DETAILED DESCRIPTION

[0035] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0036] like Figure 1 As shown, the non-Newtonian fluid high-precision ion concentration measurement system based on the liquid flexoelectric effect of the present invention comprises a terraced container 1 made of an insulating material, a cylindrical rotor 2 located on the central axis inside the terraced container 1, a torque motor 3 connected to the upper end of the cylindrical rotor 2, a first electrode 4-1 fixed on the upper inner surface of the terraced container 1, a second electrode 4-2 fixed on the lower inner surface of the terraced 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 end of the charge amplifier 5; the torque motor 3 applies torque to the non-Newtonian fluid inside the terraced container 1 through the cylindrical rotor 2, and the non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate polarization, and polarized charges with opposite signs and the same magnitude are induced on the first electrode 4-1 and the second electrode 4-2; at the same time, trace ions in the liquid gather on the surfaces of the first electrode 4-1 and the second electrode 4-2 to generate a double electric layer effect, which partially shields the polarized charges. The higher the ion concentration, the stronger the shielding degree and the weaker the residual flexoelectric effect.

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

[0038] As a preferred embodiment of the present invention, the first electrode 4-1 and the second electrode 4-2 are made of highly conductive metal having a surface oxide dielectric with limited and uniform thickness and stable chemical properties. While preventing the system from undergoing chemical reactions to produce unexpected external electrical signals, it can also have good conduction characteristics for charge information of a smaller order of magnitude to achieve accurate measurement.

[0039] The measurement accuracy of the charge amplifier 5 can meet the micro-charge measurement requirements of flexoelectric liquid dielectrics.

[0040] The measurement method of the non-Newtonian fluid high-precision ion concentration measurement system based on the liquid flexoelectric effect of the present invention adopts a torque motor 3 to apply torque to the non-Newtonian fluid inside the terraced container 1 through a cylindrical rotor 2, and the non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate electric polarization, and polarized charges with opposite signs and the same magnitude are induced on the first electrode 4-1 and the second electrode 4-2; at the same time, Figure 2 As shown, trace ions in the non-Newtonian fluid gather on the surfaces of the first electrode 4-1 and the second electrode 4-2 to produce a double layer effect. The double layer effect will form an additional local electric field near the electrodes, and this local electric field is coupled with the flexural electric polarization and is affected by the flexural electric polarization electric field; the double layer effect occupies the charge attachment points near the electrodes and partially shields the polarized charges; the flexural electric polarization charge of the standard ion-free non-Newtonian fluid and the polarization charge of the non-Newtonian fluid containing ions are compared to obtain the amount of charge shielded by the double layer, and then combined with the material parameters of the non-Newtonian fluid and the structural parameters of the terraced container, the flexoelectric effect equation and the double layer equation are solved jointly to obtain the ion concentration of the non-Newtonian fluid.

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

[0042] The cylindrical rotor 2 causes the corresponding shear flow of the non-Newtonian fluid in the axial torsion. The cylindrical coordinate system (r, θ, z) is established with the center of the bottom circle of the terraced container 1 as the origin. The flow velocity distribution of the non-Newtonian fluid is:

[0043]

[0044] Where v is the velocity of the shear flow at a certain point (r, θ, z), r is the radial length at this point, and z is the axial height; R 1 , R 2 , R 3are the radius of the cylindrical rotor, the bottom radius and the top radius of the terraced container 1 respectively; H is the axial distance between the first electrode and the second electrode; ω 0 is the angular velocity of the cylindrical rotor, f is the rotation frequency, and t is the time; the calculation formula for the shear flow 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 gradient of velocity in the θ direction, the equation can be simplified. The strain formula is obtained by solving equations (1) and (2) together:

[0047]

[0048] Among them, γ θr is the circumferential-radial shear strain, γ θz is the circumferential-axial shear strain;

[0049] The flexoelectric effect of the material is expressed as:

[0050]

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

[0052]

[0053] Where V is the volume of the container, μ θrrz is the liquid flexoelectric coefficient; Formula (5) describes the flexoelectric polarization intensity when there are no ions involved. When there are ions in the non-Newtonian fluid, a double electric layer effect will be generated on the surface of the first electrode 4-1 and the second electrode 4-2, which is described by the Poisson-Boltzmann equation:

[0054]

[0055] where ε 0 and ε r are the vacuum and material dielectric constants, ψ is the electric potential, ρ e is the volume charge density; Substituting Gauss's law into equation (6), the relationship between the electrode surface charge density and the potential is:

[0056]

[0057] Where σd is the surface charge density, N A , k b , e and T are Avogadro constant, Boltzmann constant, electron charge and temperature respectively; z i and c i is the valence and concentration of the i-th ion in the non-Newtonian fluid; combining equation (5) and equation (7) to obtain the final polarization intensity equation:

[0058]

[0059] The electric polarization of the non-Newtonian fluid is obtained by applying torque displacement to the cylindrical rotor 2, and the data of the signal processing module 6 and the charge amplifier 5 are used to obtain the polarization intensity. Substituting it into formula 8 can reversely solve 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 the figure (A), the density of ions adsorbed on the ion-electrode interface is very small, and the degree of shielding of the shear flexoelectric effect is very small. Therefore, the electrical signal measured on the electrode is basically consistent with the real flexoelectric effect. As the liquid concentration gradually increases ( Figure 2 In the middle (B), the ion adsorption density gradually increases, the shielding degree gradually increases, and the measured residual electrical signal gradually decreases; and as the ion concentration further increases ( Figure 2 In C), the shielding electric field generated by the ion concentration adsorbed on the ion-electrode interface has completely offset the polarization generated by the flexoelectric effect, so the output electrical signal is static noise. Since the residual electric polarization degree is closely related to the ion concentration, the residual electric polarization degree can be used to measure the ion concentration.

Claims

1. A high-precision ion concentration measurement system for non-Newtonian fluids based on the liquid flexoelectric effect, characterized by: The invention comprises a stepped container (1) made of an insulating material, a cylindrical rotor (2) located on the central axis of the stepped 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 stepped container (1), a second electrode (4-2) fixed to the lower inner surface of the stepped 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 end of the charge amplifier (5); the torque The motor (3) applies torque to the non-Newtonian fluid inside the terraced container (1) through the cylindrical rotor (2), and the non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate electric polarization, and polarized charges with opposite signs and the same magnitude are induced on the first electrode (4-1) and the second electrode (4-2); at the same time, trace ions in the liquid gather 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 polarized charges. The higher the ion concentration, the stronger the shielding degree and the weaker the residual flexoelectric effect.

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

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

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

5. The measurement method of the non-Newtonian fluid high-precision ion concentration measurement system based on the liquid flexoelectric effect according to any one of claims 1 to 4, characterized in that: A torque motor (3) is used to apply torque to a non-Newtonian fluid inside a terraced container (1) through a cylindrical rotor (2), so that the non-Newtonian fluid generates shear flow strain gradients in the axial and radial directions to generate electric polarization, and polarized charges with opposite signs and the same 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 gather on the surfaces of the first electrode (4-1) and the second electrode (4-2) to generate a double electric layer effect, which forms an additional local electric field near the electrodes, and this local electric field is coupled with the flexural electric polarization and is affected by the flexural electric polarization electric field; the double electric layer effect occupies the charge attachment points near the electrodes and partially shields the polarized charges; by comparing the flexural electric polarization charge of a standard non-Newtonian fluid without ions with the polarization charge of a non-Newtonian fluid containing ions, the charge amount shielded by the double electric layer is obtained, and then the flexural electric effect equation and the double electric layer equation are solved jointly in combination with the material parameters of the non-Newtonian fluid and the structural parameters of the terraced container to obtain the ion concentration of the non-Newtonian fluid.

6. The measuring method according to claim 5, characterized in that: The method for solving the ion concentration of non-Newtonian fluid is as follows: The cylindrical rotor (2) causes a corresponding shear flow of the non-Newtonian fluid in the axial torsion. A cylindrical coordinate system (r, θ, z) is established with the center of the bottom circle of the terraced container (1) as the origin. The flow velocity distribution of the non-Newtonian fluid is: Where v is the velocity of the shear flow at a certain point (r, θ, z), r is the radial length at this point, and z is the axial height; R1, R2, and R3 are the radius of the cylindrical rotor, the bottom radius, and the top radius of the terraced container (1), respectively; H is the axial distance between the first electrode and the second electrode; ω0 is the angular velocity of the cylindrical rotor, f is the rotation frequency, and t is time; the calculation formula for the shear flow strain in the liquid is: Where τ is the shear stress and γ is the shear strain. Both τ and γ are in tensor form. Since there is no gradient of velocity in the θ direction, the equation can be simplified. The strain formula is obtained by solving equations (1) and (2) together: Among them, γ θr is the circumferential-radial shear strain, γ θz is the circumferential-axial shear strain; The flexoelectric effect of the material is expressed as: Where P l , μ ijkl , γ ij and u k are the polarization degree, flexoelectric coefficient, strain and gradient direction respectively; the polarization degree is described as the ratio of charge to charge distribution area; combining equations (3) and (4) to obtain the average electric polarization intensity P: Where V is the volume of the container, μ θrrz is the liquid flexoelectric coefficient; Equation (5) describes the flexoelectric 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 surface of the first electrode (4-1) and the second electrode (4-2), which is described by the Poisson-Boltzmann equation: where ε0 and ε r are the vacuum and material dielectric constants, ψ is the electric potential, ρ e is the volume charge density; Substituting Gauss's law into equation (6), the relationship between the electrode surface charge density and the potential is: Where σ d is the surface charge density, N A , k b , e and T are Avogadro constant, Boltzmann constant, electron charge and temperature respectively; z i and c i is the valence state and concentration of the i-th ion in the non-Newtonian fluid; combining equation (5) and equation (7), the polarization intensity equation is derived: The electric polarization of the non-Newtonian fluid is obtained by applying torque displacement to the cylindrical rotor (2), and the polarization intensity is obtained by substituting the data of the signal processing module (6) and the charge amplifier (5). The ion concentration c of the non-Newtonian fluid can be reversely solved by substituting it into formula (8): i .

Images