An emulsification method for two immiscible solutions under a constant electric field

Abstract

This invention proposes a method for emulsifying two immiscible solutions under a constant electric field, comprising the following steps: S1, adding the solute to be dissolved dropwise into an emulsification device filled with solvent; S2, inputting parameters affecting emulsification into a color model based on the lattice Boltzmann method to simulate the emulsification process, ultimately obtaining the required electric field strength and time for emulsification; the parameters affecting emulsification include the radius of the solute, the density ratio of the solute to the solvent, the dielectric constant, and the conductivity, which can be known through a burette; S3, energizing the emulsification device according to the electric field strength obtained in step S2, and setting a corresponding time, thereby achieving emulsification of the two immiscible solutions. This invention can obtain the optimal electric field strength and time by simulating the emulsification process using a color model based on the lattice Boltzmann method, and strictly control the emulsification process through the emulsification device, thereby achieving the best emulsification effect.

Description

Technical Field

[0001] This invention relates to the field of emulsions and their control, and in particular to a method for emulsifying two immiscible solutions under a constant electric field. Background Technology

[0002] With the advancement and development of microfluidics, microdroplet technology has received widespread attention and application in the fields of chemistry, biomedicine, energy, and environment. For example, in the energy sector, dehydration is a crucial part of the production process in oil extraction. Electric fields are an effective non-contact way for oil droplets suspended in viscous liquids to exhibit complex behaviors, such as movement, deformation, and breakage under the influence of an applied electric field. These behaviors depend on the strength of the electric field and the properties of the liquid.

[0003] In recent years, numerical simulation has become an important research method. Many scholars both domestically and internationally have conducted a series of studies on the dynamic behavior of emulsions under electric fields through experiments and numerical simulations, accumulating rich theoretical, numerical, and experimental research results. Sherwood used the boundary integral method to solve the Laplace and Navier-Stokes equations, obtaining the electric and flow field distributions. Furthermore, he analyzed the influence of electrical parameters on droplet deformation. Meanwhile, Baygents also proposed an electrodynamic model for droplet deformation, incorporating the electric force as a source term into the Navier-Stokes equations. The volumetric fluid model (VOF) was used to analyze the deformation behavior of neutral leaking droplets and charged droplets under uniform and non-uniform electric fields. Peng modified the equation of state of the lattice Boltzmann multiphase flow model to accommodate high liquid-to-gas density ratios and low liquid-phase compressibility. Mousavichoube studied the partial electroaggregation process and showed that DC electric field strength and interfacial tension are the causes of secondary emulsification. However, due to the different methods used in the above studies, their applicability, computational complexity, and degree of agreement with reality vary. For applications requiring high precision and involving small volumes of solution, such as in biopharmaceutical research and development, strict control of the emulsification process is necessary to ensure complete emulsification of the solution. However, existing emulsification methods cannot account for all influencing parameters to achieve optimal emulsification results. Summary of the Invention

[0004] The present invention aims to at least solve the technical problems existing in the prior art, and in particular, innovatively proposes an emulsification method for two immiscible solutions under a constant electric field.

[0005] To achieve the above-mentioned objective of this invention, this invention provides a method for emulsifying two immiscible solutions under a constant electric field, comprising the following steps:

[0006] S1, the solute to be dissolved is dripped into the emulsification device filled with solvent;

[0007] S2, input the parameters affecting emulsification into the color model based on the lattice Boltzmann method to simulate the emulsification process, and finally obtain the electric field strength and time required for emulsification; the parameters affecting emulsification include the radius of the solute, the density ratio of the solute to the solvent, the dielectric constant and the conductivity, which can be known through the burette;

[0008] S3. The emulsification device is energized according to the electric field strength obtained in step S2, and the corresponding time is set to achieve emulsification of two immiscible solutions.

[0009] This invention investigates the morphology simulation of incompatible fluids of varying densities under electric field control. We incorporate the electric field into the Lattice Boltzmann Method (LBM). The focus is on simulating the evolution of two-phase flows using a modified Lattice Boltzmann color gradient model and analyzing the relationship between morphology and electric field parameters. Results show that electric field strength, conductivity, dielectric constant, oil-water density ratio, and droplet radius can regulate stretching, coalescence, and even breakup. Simulation results indicate that a larger dielectric constant leads to smaller deformation, while a larger conductivity is associated with larger deformation. Furthermore, larger droplets are more prone to deformation and breakup, while denser droplets are less likely to break up. The morphologies of droplet stretching and instability at each stage are also presented. These results are consistent with relevant theoretical and experimental findings. This invention provides a basis for studying the electrode dehydration and emulsification mechanisms of emulsions and offers guidance for the design of electric field-fed droplet microreactors.

[0010] Furthermore, the emulsification device includes: a high-voltage electrode plate, a low-voltage electrode plate, a glass bath, and a burette. The low-voltage electrode plate is located at the bottom inner part of the glass bath, and the outer wall of the high-voltage electrode plate is attached to the inner wall of the glass bath and located above the low-voltage electrode plate. The high-voltage electrode plate can move up and down to achieve optimal electric field strength. A burette orifice penetrating the high-voltage electrode plate is provided at the center of the high-voltage electrode plate, and the burette is located directly above the burette orifice; the burette contains the titrant solute.

[0011] The high-voltage plate is connected to the positive terminal of a DC high-voltage power supply, the highest voltage of which is 50KV; the low-voltage plate is connected to the negative terminal of the power supply.

[0012] The high-voltage electrode and the low-voltage electrode are spaced 30mm apart, and both are made of copper.

[0013] Since this invention is designed for cases with a small amount of solution, a voltage of 50KV or less is sufficient to power the high-voltage plate. Copper plates are used because they have better conductivity.

[0014] The burette drips the solute into the solvent through the burette orifice on the high-pressure plate. The burette allows for maximum control of the dripping amount to reduce errors and timely observation of the dissolution of two immiscible solutions. Furthermore, the burette's position above the center of the glass trough ensures that the solute is dripped into the center of the low-pressure plate as much as possible, which is beneficial for liquid emulsification.

[0015] Furthermore, the step of placing the two immiscible solutions into the emulsification device includes the following steps:

[0016] S1-1, During the experiment, the glass tank is filled with the first liquid as a solvent, ensuring that the liquid level of the first liquid is higher than that of the high-voltage plate.

[0017] S1-2, another liquid is injected into the glass bath as a solute through a burette, so that the solute drips into the center of the low-pressure electrode.

[0018] Furthermore, the color model of the lattice Boltzmann method includes:

[0019] The evolution equation is:

[0020] f ki (x+c i ,t+1)=f ki (x,t)+Ω ki (x,t)(1.10)

[0021] f ki (x,t) is the LB distribution function;

[0022] Collision operator Ω ki (x,t) consists of three operators:

[0023]

[0024] It is a single-phase collision operator, representing the particle motion caused by the collision between particles inside a single-phase fluid;

[0025] It is an interface perturbation operator, representing the interaction between particles of different phases in the phase interface region caused by interfacial tension;

[0026] It is a recoloring operator that controls the separation of intersecting particles within the phase interface region, ensuring that particles do not invade each other's phase regions.

[0027] Furthermore, the single-phase collision operator includes:

[0028]

[0029] Where τ represents the relaxation factor;

[0030] f ki (x,t) represents the LB distribution function;

[0031] It is the equilibrium state distribution function:

[0032]

[0033]

[0034]

[0035] It's about α k The function;

[0036] ω i This represents the weight coefficient for the i-th direction;

[0037] ρ k ρ represents the density of the solute or solvent. k For ρ r or ρ b , ρ r ρ b These represent the density of the solute and the density of the solvent, respectively.

[0038] c i Represents the velocity in the i-th direction;

[0039] u represents the total speed;

[0040] ρ represents the total density;

[0041] f ki Represents the distribution function;

[0042]

[0043] Where α k It is a free parameter;

[0044] i represents the i-th direction.

[0045] Furthermore, the interface perturbation operator includes:

[0046] The color gradient of the interface is represented by defining a color gradient F:

[0047]

[0048] Where ρ r ρ b These represent the density of the solute and the density of the solvent, respectively; for example, water is soluble in oil, ρ r ρ b These represent the densities of oil and water, respectively.

[0049] c i Represents the velocity in the i-th direction;

[0050] Therefore, the expression for the perturbation operator is obtained:

[0051]

[0052]

[0053] Where A K It is a free parameter;

[0054] F represents taking the modulus of F;

[0055] F is the value of the expression for the color gradient;

[0056] c i Represents the velocity in the i-th direction;

[0057] B i This represents a parameter in the i-th direction;

[0058] i represents the i-th direction.

[0059] Furthermore, the recoloring operator includes:

[0060]

[0061]

[0062] in Represents the recoloring operator for the solvent;

[0063] Represents the recoloring operator for the solute;

[0064] ρ r Indicates the density of the solvent;

[0065] ρ b Indicates the density of the solute;

[0066] ρ represents the total density;

[0067] Represents the color gradient F and the lattice sound velocity c. i The included angle;

[0068] f i Represents the distribution function;

[0069] This indicates summing over the distribution function.

[0070] Furthermore, it also includes setting the boundary conditions for the electric field:

[0071] Considering that the container is a cuboid or cylinder, a bounce format is used in the X direction and a periodic boundary processing format is used in the Y direction.

[0072] Furthermore, the method also includes: changing the parameters affecting emulsification, then performing emulsification analysis based on a color model using the lattice Boltzmann method; changing the conductivity by adding other solutions under energized conditions; and observing the emulsification of the two immiscible solutions. Since this invention is more suitable for exploratory research, and considering model errors, it is necessary to consider situations where changing the parameters might result in better emulsification.

[0073] In summary, by adopting the above technical solutions, this invention can obtain the optimal electric field strength and time by simulating the emulsification process using a color model based on the lattice Boltzmann method, and strictly control the emulsification process through the emulsification device, thereby achieving the best emulsification effect.

[0074] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0075] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0076] Figure 1 This is a schematic diagram of the overall device of the present invention.

[0077] Figure 2 This is a schematic diagram of the emulsification device according to an embodiment of the present invention. In the figure: 1 is a burette, 2 is a high-voltage electrode plate, and 3 is a low-voltage electrode plate.

[0078] Figure 3 This is a discrete velocity plot of the BGK model.

[0079] Figure 4 This is a schematic diagram illustrating the time evolution of droplet deformation under different voltages. Figure I (a) Time t = 1 × 10 3 , Figure I (b) Time t = 3 × 10 3 , Figure I (c) Time t = 5 × 10 3 , Figure I (a)~ Figure I (c) The voltage V = 150, and the diameter of the solution body d = 25; Figure II (a) Time t = 2 × 10 4 , Figure II (b) Time t = 2.6 × 10 4 , Figure II (c) Time t = 3 × 104 , Figure II (a)~ Figure II (c) The voltage V = 150, and the diameter of the solution body d = 30; Figure III (a) Time t = 1 × 10 3 , Figure III (b) Time t = 3 × 10 3 , Figure III (c) Time t = 5 × 10 3 , Figure III (a)~ Figure III (c) The voltage V = 200, and the diameter of the solution body d = 20;

[0080] Figure 5 This is a schematic diagram illustrating the time evolution of droplet deformation under different dielectric constants, where the viscosity of water η is shown. b =0.1, the viscosity of the oil η r =0.4, the density of water ρ b =1, the density ρ of oil r =0.8, the electrical conductivity of water σ b =0.05, the conductivity σ of the oil r =0.1; Figure I (a) Time t = 3 × 10 3 , Figure I (b) Time t = 1 × 10 4 , Figure I (c) Time t = 2 × 10 4 , Figure I (a)~ Figure I (c) The voltage V = 150; the dielectric constant of water ε r =0.005, the dielectric constant ε of oil b =0.01; the diameter of the solution body d = 30; Figure II (a) Time t = 3 × 10 3 , Figure II (b) Time t = 5 × 10 3 , Figure II (c) Time t = 2 × 10 4 , Figure II (a)~ Figure II (c) The voltage V = 150; the dielectric constant of water ε r =0.006, the dielectric constant ε of oil b =0.01.

[0081] Figure 6 This is a schematic diagram illustrating the time evolution of droplet deformation under different electrical conductivities. Figure 6 (a) The time is t = 2 × 10 3 , Figure 6 (b) The time is t = 4 × 10 3 , Figure 6 (c) The time is t = 1 × 10 4 , Figure 6 (a)~ Figure 6 (c) The voltage V = 150.

[0082] Figure 7 This is a schematic diagram illustrating the evolution of droplet deformation over time at different densities. Figure I (a) Time t = 1 × 10 3 , Figure I (b) Time t = 5 × 10 3 , Figure I (c) Time t = 3.7 × 10 4 , Figure I (a)~ Figure I (c) The voltage V = 150. Figure II (a) Time t = 1 × 10 3 , Figure II (b) Time t = 5 × 10 3 , Figure II (c) Time t = 2.1 × 10 4 , Figure II (a)~ Figure II (c) The voltage V = 150.

[0083] Figure 8 This is a schematic diagram of the time evolution of the deformation of a bilayer droplet. The droplet spacing d = 70, the droplet radius r = 30, the interfacial tension F = 0.03, and the viscosity of water η. b =0.1, the viscosity of the oil η r =0.4, the density of water ρ b =1, the density ρ of oil r =0.8, the dielectric constant of water ε r =0.005, the dielectric constant ε of oil b =0.01, the electrical conductivity of water σ b =0.05, the conductivity σ of the oil r =0.1, Figure I (a) Time t = 1 × 10 3 , Figure I (b) Time t = 5 × 10 3 , Figure I (c) Time t = 1 × 10 4 , Figure I (d) Time t = 2 × 10 4 Figure I (a)~ Figure I (d) Voltage V = 50; Figure II (a) Time t = 1 × 10 3 , Figure II (b) Time t = 2 × 10 3 , Figure II (c) Time t = 4 × 10 3 , Figure II (d) Time t = 3 × 10 5 , Figure II (a)~ Figure II (d) Voltage V = 100; Figure III(a) Time t = 1 × 10 3 Figure III(b) shows a time t = 3 × 10 3 Figure III(c) shows a time t = 7 × 10 3 Figure III(d) shows a time t = 2 × 10 4 The voltage V in Figures III(a) to III(d) is 150.

[0084] Figure 9 This is a schematic diagram of the flow field distribution. Figure 9 (a)t=2×10 3 , Figure 9 (b)t=6×10 3 . Detailed Implementation

[0085] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0086] A schematic diagram of the overall device of the present invention is shown below. Figure 1 As shown, the system includes a camera for observing the liquid state, a computer for simulating the liquid state, an emulsification device, a high-voltage DC regulated power supply, and, to ensure optimal imaging, a sky-blue acrylic glass plate and a frosted glass plate are sequentially placed behind the emulsification device to uniformly illuminate the square tank with reflected light. A cold light source is also included. The camera is positioned in front of the emulsification device to capture the deformation and breakup process of the droplets. Furthermore, the camera can also be placed inside the emulsification device for more comprehensive observation of the solution's dissolution state.

[0087] A schematic diagram of the emulsification device is shown below. Figure 2 As shown, the apparatus includes a high-voltage electrode, a low-voltage electrode, a glass bath, and a burette. The high-voltage electrode (upper electrode) is connected to the positive terminal of a DC high-voltage power supply (adjustable range 0–50 kV), and the low-voltage electrode (lower electrode) is connected to the negative terminal of the power supply and grounded. The distance between the high-voltage and low-voltage electrodes is 30 mm, and both are made of copper.

[0088] In use, the glass tank is filled with the first liquid, ensuring that the water level of the first liquid is higher than that of the high-voltage plate. Then, another liquid is injected into the glass tank through a burette, so that the oil droplet is placed in the center of the lower plate. A uniform electric field is then created by the parallel high-voltage and low-voltage plates.

[0089] 1. The mathematical model used in the method of this invention

[0090] 1.1 Lattice Boltzmann Method for Phase Separation

[0091] LBMs are a highly effective numerical tool for simulating complex multiphase fluid flows. Furthermore, the kinetic theory of LBMs makes it easy to describe the interactions between different phases and automatically track the interfaces between phases. LBMs also offer advantages such as simple boundary treatment and easy program implementation. Therefore, LBMs are particularly suitable for simulating droplet dynamics and multiphase flows, porous media, and chemical reaction flows in many fields.

[0092] In this paper, the LBM color model is used to solve the two-phase flow problem of incompressible fluids. The color model uses different colors to distinguish different fluids, and the interaction between different fluids is achieved by introducing color gradients. However, Guo's model does not guarantee that the two fluid phases are immiscible. The recoloring algorithm proposed by Latva-Kokko and Rothman is used to induce two-phase separation between the droplet and the carrier fluid. It maintains the isotropy of the phase interface and the interface itself, while effectively reducing the pseudo-velocities at the phase interface.

[0093] In oil-water fluids, oil typically exists in the form of droplets in the water. Let water be the carrier fluid, denoted by "b", and the oil droplets be the dispersed phase, denoted by "r"; these two are incompatible. In electrohydrodynamics, fluids are governed by forces such as inertial forces, viscous forces, and electric field forces, which influence the fluid's motion. The calculation process satisfies the following two governing equations.

[0094]

[0095]

[0096] Since the dynamic current on the droplet surface is very small, the effect of magnetic effects can be neglected. The electric field strength is spinless and its relationship with the potential can be expressed as:

[0097]

[0098] The charge accumulation rate at the interface is much higher than the fluid flow rate. The charge control equation can be transformed into a static equation, resulting in the following charge conservation equation for the fluid:

[0099]

[0100] The electric force on the droplet can be represented by the Maxwell stress tensor.

[0101]

[0102] Where ρ, v, p, I, τ, and F are fluid density, fluid velocity, pressure, identity matrix, viscous shear stress tensor, and interfacial tension, respectively. E It refers to physical force or electric field force in this article, σ is conductivity, and ε is dielectric constant.

[0103] 1.2 Mixed Lattice Boltzmann Algorithm for Oil in Water

[0104] The lattice Boltzmann multiphase flow model describes fluid motion through the evolution of the mesoscopic particle distribution function. Based on the relaxation time, it is divided into single-relaxation (LBGK) and multi-relaxation (MRT) models. Based on the number of phases, it is further divided into single-component single-phase and multi-component multiphase models. Based on whether the temperature changes, it is divided into isothermal and non-isothermal models. This paper adopts a multi-relaxation model, which is integrated on a square lattice using two-dimensional nine-level velocities (D2Q9). The distribution function is associated with the lattice vector; the model is shown in [reference needed]. Figure 3 The evolution equation of the electric field is:

[0105] f i (x+c i δ t ,t+δ t )-f i (x,t)=Ω ki (f ki (x,t))(1.6)

[0106]

[0107] As shown in (1.6) and (1.7), the discretization is performed using the LB distribution function, where f i (x,t) is the discrete velocity at time t and position x. δ t τ is the time step, f is the relaxation time, and f is the time step. ki (x,t) is the velocity in equilibrium.

[0108] In this model, the mixed fluid domain is divided into uniform square cells for electrical evolution. We consider the following velocity distribution function of the coupled electric field:

[0109]

[0110] Among them, w i These are weighting coefficients:

[0111]

[0112] 1.3 Color Model for Lattice Boltzmann Method for Phase Separation

[0113] The colored LBM model was first proposed by Gunnstensen. It was later modified by Latva-Kokko and Rothmanequation, who introduced the concept of multiphase flow, using different colors to represent different fluid phases. Each phase has its own distribution function for the evolutionary steps between particles, and the interactions between particles in each phase are also considered.

[0114] In the detailed calculation process, f ki This is used to represent the distribution function for each stage, where 'k' equals 'b' or 'r'. 'r' and 'b' represent the red and blue phases, respectively. The evolution equations are given below.

[0115] f ki (x+c i ,t+1)=f ki (x,t)+Ω ki (x,t)(1.10)

[0116] Collision operator Ω ki (x,t) consists of three operators.

[0117]

[0118] It is a single-phase collision operator, representing the particle motion caused by the collision between particles inside a single-phase fluid. It is an interface perturbation operator, representing the interaction between particles of different phases in the phase interface region caused by interfacial tension. It is a recoloring operator that controls the separation of intersecting particles within the phase interface region, ensuring that particles do not invade each other's phase regions.

[0119] 1.3.1 Collision forces between particles

[0120] The single-phase collision operator represents the relaxation of the distribution function to the local equilibrium state distribution function, and is expressed by the following equation.

[0121]

[0122] Where τ represents the relaxation factor. It is the equilibrium state distribution function.

[0123]

[0124]

[0125]

[0126] It's about α k The function, α k It is a free parameter.

[0127]

[0128] 1.3.2 Interface Perturbation Operator

[0129] In the model, the effect of interfacial tension is implemented by a perturbation operator. We define a color gradient F to represent the color gradient process of the interface. With the help of F, we can give the expression for the perturbation operator.

[0130]

[0131]

[0132]

[0133] 1.3.3 Controlling Phase Interface Equations

[0134] The commonly used recoloring operator returns most of the red particles from the phase interface region to the single-phase region of the red fluid, and the blue particles to the single-phase region of the blue fluid. However, the recoloring process requires relatively cumbersome calculations. Therefore, an improved recoloring operator is proposed, as follows:

[0135]

[0136]

[0137] 1.4 Boundary conditions of the electric field

[0138] The unknown distribution function of the boundary nodes is determined based on simulation conditions and physical properties (periodicity, symmetry), as well as the motion rules between microscopic particles. We use a simpler heuristic scheme that does not require complex formula solutions and mathematical derivations. In the periodic scheme, particles leave the flow field from one boundary and enter the flow field from another boundary in the next time step, and so on, ensuring the conservation of the total mass, momentum, and energy of the system. The bounce scheme is a common method for handling stationary, non-slip walls. This method assumes that particles bounce in the opposite direction after colliding with the wall. Specifically, it prevents particles at each boundary point from participating in the collision, and the boundary distribution function after the collision step is given by the distribution functions of the adjacent grid points that have completed the collision. This scheme is simple to operate, widely used, and is typically used to handle some complex flow phenomena. We use the bounce scheme in the X direction and the periodic boundary treatment scheme in the Y direction. The specific details are as follows.

[0139] X f3=f1 (1.21)

[0140] Y f 2,5,6 (0,j)=f 2,5,6 (N y ,j) (1.22)

[0141] f 4,7,8 (j,N y +1)=f 4,7,8 (j,1) (1.23)

[0142] Where f 2,5,6 (j,0) represents the lower boundary of the position;

[0143] f 2,5,6 (j,N y () indicates the upper boundary;

[0144] f 4,7,8 (j,N y +1 indicates the upper boundary;

[0145] f 4,7,8 (j,1) denotes the lower boundary;

[0146] N y Indicates the left side of the y-axis of the upper boundary point;

[0147] j represents the left side of the upper boundary point x.

[0148] 2. Simulation results and discussion of the method of the present invention

[0149] Under different external conditions and their own physical properties, the effects of each factor on binary phase separation in the presence of an electric field were verified and compared. Initial conditions were fixed at an interface thickness of 0.7 and a tensile coefficient of 0.03. The voltage remained constant throughout the simulation. To demonstrate the factors influencing droplet deformation, quantitative analyses were performed on the dielectric constant, conductivity, density, and voltage.

[0150] 2.1 Influence of External Conditions on Droplet Morphology

[0151] We primarily varied the voltage from 50 to 200 to obtain different morphological changes. The specified values ​​were r = 30, F = 0.03, and η. b =0.1,ρ b =1,ρ r =0.8,ε r =0.005,ε b =0.01,σ b =0.05andσ r =0.1. Figure 4The table below shows the entire simulation process of droplet deformation as the electric field strength increases, from top to bottom. In actual crude oil dehydration operations, the size of the dispersed phase droplets is highly non-uniform. To explore the effect of droplet size on deformation, we selected droplets with different radii for simulation analysis. See Table 1 for details. Figure 4 The average droplet size in the emulsion indicates the degree of emulsification of the droplets. Therefore, the droplet size was set to 15-45, and other conditions were kept unchanged to simulate the droplet deformation of the dispersed phase under different droplet sizes. It can be seen that smaller droplets deform less than larger droplets, and the deformation rate is also slower. The Young-Laplace equation shows that the pressure difference inside and outside the droplet is inversely proportional to the droplet size. As the size increases, the droplet's ability to resist deformation decreases, so the droplet deformation increases. In addition, the initial droplet size greatly affects the electric field strength value that causes droplet instability. Larger initial particle sizes will break under relatively low electric field strength. Through the previous simulation and analysis, it can be inferred that the influence law of droplet deformation is consistent with the influence law of electric field strength. Deformation and breakage under the action of electric field generally have the following modes: (1) When the applied electric field strength is less than the critical electric field strength, the droplet will be stretched along the electric field direction, first becoming a long strip with thick ends and thin middle, and then returning to a long strip with uniform thickness. (2) When the applied electric field strength is greater than the critical electric field strength, the droplet will break up under certain conditions. Similarly, the time of breakup may vary depending on the radius of the droplet. If the radius of the droplet is small, it may break up later, or it may simply be stretched into an elongated shape without breaking. The form of breakup is tensile fracture, which occurs in the weakest part, that is, the middle part where the electric field force is strongest.

[0152] Considering the forces acting on a spherical droplet, a simple explanation can be given for the droplet's deformation and breakage: before the droplet breaks, the interfacial tension is balanced by the force generated by the electric field. The droplet generates polarized charges in the electric field, distributed on its surface. The distribution on the droplet surface is related to the angle between the surface normal vector and the direction of the electric field. When the interfacial normal vector coincides with the direction of the electric field, the charge distribution is most concentrated, the electric force is strongest, and therefore the droplet deforms most in this direction. When the interfacial normal vector is perpendicular to the direction of the electric field, the number of polarized charges on the droplet surface is zero, and the electric force is also zero; the droplet will not extend outward under the influence of surface tension. Therefore, the overall deformation effect of the droplet is a stretching effect along the direction of the electric field. When the stretching force of the electric field is insufficient to break the interfacial tension, the droplet will not break but will only elongate into a flattened ellipse or a long strip. When the stretching force of the electric field is greater than the interfacial tension, the droplet tends to break in the middle. In addition, the elongation and deformation of droplets under the action of electric field force is conducive to the collision between droplets. Since the charge properties are different at different positions of droplets, positive and negative charges will increase the chance of two droplets coalescing due to mutual attraction.

[0153] Table 1: Effect of droplet radius on droplet morphology changes, N = no breakage, Y = breakage.

[0154] 50 N N N N N N N 100 N N N N N N N 150 N N N Y Y Y Y 200 N N Y Y Y Y Y

[0155] 2.2 Influence of intrinsic physical properties on droplet deformation

[0156] 2.21 Effect of volume ratio on droplet deformation

[0157] The dielectric constant affects the magnitude of the electrophoretic force, and therefore influences the deformation and splitting of droplets. Therefore, we investigated the effect of different dielectric constants on droplet deformation, with a voltage of 200 Ω and other conditions remaining constant. Figure 4 As shown, we simulated the deformation and fracturing of different oils in water under the influence of an electric field to better approximate the real-world situation. According to... Figure 5 From Table 2, we can draw some conclusions. (1) As the dielectric constant of the oil increases, the deformation and instability of the oil droplet are delayed in the backward direction. It can be seen that the dielectric constant of the oil droplet and the deformation of the oil droplet are negatively correlated. The higher the dielectric constant of the dispersed phase, the slower the deformation of the oil droplet. (2) Voltage dominates the two factors of low dielectric constant and voltage, while high dielectric constant and voltage can influence each other. This is because polarization charges are generated on the surface of the droplet, and the polarization charges form a polarization electric field. They also show the opposite direction to the original electric field, and the electric field strength will decrease when the two electric fields are superimposed. This results in a smaller electric field force generated at the interface. In general, if a material with a high dielectric constant is placed in an electric field, the electric field strength in the dielectric will decrease considerably. Therefore, the continuous phase with a high dielectric constant will have a significant impact on the deformation of the dispersed phase. The relative dielectric constant of an ideal conductor is infinite, and we can deduce that there exists a dielectric constant ratio that prevents the droplet from becoming unstable and breaking.

[0158] Table 2. Effect of dielectric constant on droplet stability. N indicates no breakage, Y indicates breakage.

[0159] 50 N N N N N 100 N N N N N 150 Y Y N N N 200 Y Y Y Y Y

[0160] 2.22 Effect of electrical conductivity on droplet deformation

[0161] In practical engineering applications, crude oil emulsions extracted from oilfields contain a large amount of inorganic salt ions, the content of which affects the conductivity of the oil-water emulsion, thus significantly impacting the demulsification effect. Higher inorganic salt content results in more freely moving electrons, leading to greater charge polarization on the water droplet surface under the influence of an electric field. The large number of charged ions under the electric field also increases the tensile deformation of the water droplets. Therefore, the conductivity of the water droplets is also a crucial factor affecting oil-water separation. Thus, we maintained an electric field strength of 200. Simultaneously, we investigated the effects of the viscosity, density, dielectric constant, and conductivity of the internal and external media on the degree of deformation of the water droplets. Figure 6 In the middle, the working conditions are d = 30, η b =0.1,η r =0.4,ρ b =1,ρ r =0.8,σ b =0.05,σ r =0.25,ε r =0.005,ε b =0.01 and d=30.

[0162] Under the influence of an electric field, a droplet initially spherical is stretched into a sheet-like shape, thicker at both ends and thinner in the middle. Over time, the droplet develops a uniform thickness because the internal flow creates a uniform force on its surface. As the electric field increases, the surface tension of the droplet becomes less than the electric force. Over a long period, more stress points on the droplet surface are broken. This results in small droplets undergoing continuous oscillations, eventually forming larger droplets. Simultaneously, the larger droplets also fracture under the influence of the electric field, ultimately forming a dynamically balanced fractured structure.

[0163] In short, such as Figure 6 As shown in Table 3, several interesting characteristics of droplet dynamics evolution can be summarized as follows: (1) We found that the higher the conductivity of the oil droplet, the easier it is to deform and break. This also indicates that the distribution of deformation and breakage points is different for different types of oil. This is because crude oil contains different inorganic salt ions and different quantities, resulting in different pH values. Therefore, the magnitude of the force generated by the electric field is also different, and the degree of oil droplet deformation is also different. (2) The higher the voltage, the greater the electric field force, and the greater the possibility of the oil droplet breaking at the stress point. (3) When the voltage is below 100V, the electric field force and the surface tension of the droplet are in equilibrium and cannot overcome the surface tension, causing the droplet to always change shape without breaking. When the voltage is greater than 100V, the electric field force at the stress point on the droplet surface is greater than the surface tension, causing the droplet to break. It can be seen that in industrial production, we can improve the electro-dehydration efficiency by adjusting the pH value and electric field strength to meet industrial needs.

[0164] Table 3. Effect of conductivity on droplet stability. N indicates no breakage, Y indicates breakage.

[0165] 50 N N N N 100 N N N N 150 Y Y Y Y 200 Y Y Y Y

[0166] 2.23 Effect of density on droplet deformation

[0167] The higher the density of a liquid, the smaller the distance between its molecules. This results in stronger intermolecular attraction, which manifests as greater surface tension. This also means a stronger ability to resist external forces caused by deformation. The working condition is (Ⅰ)ρ b =1,ρ r =0.7 and (Ⅱ)ρ b =1,ρ r =0.9, d=30.

[0168] The electric field promotes the stretching deformation of oil droplets, while interfacial tension and the viscous drag of the continuous phase hinder the deformation of water droplets. As the stretching deformation of the oil film along the electric field direction increases, the interfacial tension at both ends of the oil droplet also increases. This is reflected in the initial large stretching deformation of the oil droplet caused by the electric field, where the electric field plays a dominant role. As the droplet deformation increases, the contraction of the oil-water interfacial tension also increases. This generates inertial drag that restrains the droplet deformation, causing the amplitude of the stretching deformation to gradually decrease. This indicates that the electric field still plays a dominant role in the droplet deformation. Finally, as the degree of droplet stretching deformation continues to increase, the oil-water interfacial tension increases to near the level of the electric field. After the electric field and interfacial tension reach a state of mechanical equilibrium, the degree of subsequent droplet stretching deformation will not continue to increase, and will essentially tend towards a fixed deformation level, such as... Figure 7 As shown.

[0169] Table 4. Effect of density on droplet stability. N indicates no breakage, Y indicates breakage.

[0170] 50 N N N N N 100 N N N N N 150 N N Y Y Y 200 Y Y Y Y Y

[0171] 2.3 Simulation results of two oil droplets in water under a uniform electric field

[0172] Two droplets are polarized by an electric field. The electric force on the droplet carrying a polarization charge q can be expressed as F = E × q. Positive charges are transferred to the end of the droplet closer to the negative pole, and negative charges are transferred to the end closer to the positive pole. This causes a dipole force to form between adjacent droplets due to aggregation. The two droplets attract each other under the increasing anisotropic charge force, and then stretch and deform along the direction of the electric field force. Finally, an increase in the electric field strength E will lead to an increase in the electric force on the droplets and a decrease in the aggregation time, such as... Figure 8As shown, when the number of droplets increases and the voltage exceeds 150, the droplets initially aggregate to form a large droplet, then extend and break up into several smaller droplets. Over time, the droplets aggregate in pairs to form a larger droplet, and finally, under the influence of the electric field, the droplet is stretched and broken into even smaller droplets. When the droplet radius is sufficiently small, the surface tension of the droplet is greater than the electric field force, making the droplet stable and undeformed. At this point, a larger electric field force is required to cause it to continue splitting.

[0173] 2.4 Influence of velocity and force field on the morphology of oil in water

[0174] Due to the uniform electric field, the polarization charge is concentrated at the top and bottom of the droplet, resulting in the electric force in the middle of the droplet being much smaller than the combined force of interfacial tension and internal / external pressure. Therefore, the droplet exhibits a shape that is narrow in the middle and wide at both ends, and its deformation increases with the increase of the electric field strength. Figure 9 The distribution of the electric field (b) and the flow field (a) is shown in the figure. Figure 9 In the process, the droplet deforms under the drive of the electric field, overcoming the flow resistance from the middle to the top and bottom ends of the droplet. To quantitatively analyze the relationship between droplet deformation and influencing factors, the degree of droplet deformation is taken as D = (ab)(a+b), where a and b are the major and minor diameters of the deformed elliptical droplet, respectively. (Based on the previous...) Figure 4 and Figure 7 Analysis, Figure 9 This indicates that, under the same conditions, the smaller the droplet diameter or the greater the interfacial tension, the greater the deformation resistance and the smaller the degree of deformation.

[0175] We developed a hybrid numerical method to study the deformation and breakup behavior of droplets under a constant, stable electric field. This method is based on a lattice Boltzmann polymer dynamics model to calculate the two-phase flow. Furthermore, the electric field is calculated using the finite difference method and coupled through a leakage dielectric model. In this paper, we investigated the phase separation behavior of binary mixtures with different densities, conductivities, and dielectric constants under electric fields of varying intensities. By controlling each parameter, we obtained different modes and analyzed the relevant modes under different parameters. We summarized the following characteristics.

[0176] (1) The results show that there is a critical value for the electric field strength controlling the morphology. When the electric field strength is less than the critical value, droplet aggregation can be accelerated. However, when the increase in electric field strength is greater than this value, the droplets cannot aggregate but instead break up.

[0177] (2) In the presence of a uniform electric field, there exists a critical radius that affects the deformation and breakup of a droplet. When the droplet radius is greater than the critical value, the increase in electric field strength will accelerate the deformation and breakup of the droplet. However, when the droplet radius is less than this critical value, as the electric field increases, the droplet will only be stretched and deformed into a slender shape without breaking up.

[0178] (3) According to the simulation results, the dielectric constant has an inhibitory effect on droplet deformation, while the conductivity has a positive effect on droplet deformation and breakage. Dispersed phase droplets with high dielectric constants can maintain their morphological stability in an electric field. However, we can also change and control the degree of droplet deformation by changing the pH value of the droplets in the dispersed phase.

[0179] This work demonstrates the unique advantages and potential of the lattice Boltzmann method in studying multiphase electrohydraulic problems. The lattice Boltzmann method is expected to be extended to other areas of electrohydraulic dynamics and play a greater role as a valuable complement to traditional methods.

[0180] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A method for emulsifying two immiscible solutions under a constant electric field, characterized in that, Includes the following steps: S1, the solute to be dissolved is dripped into the emulsification device filled with solvent; S2, input the parameters affecting emulsification into the color model based on the lattice Boltzmann method to simulate the emulsification process, and finally obtain the electric field strength and time required for emulsification; the parameters affecting emulsification include the radius of the solute, the density ratio of the solute to the solvent, the dielectric constant and the conductivity, which can be known through the burette; S3, energize the emulsification device according to the electric field strength obtained in step S2, and set the corresponding time to achieve emulsification of two immiscible solutions; The emulsification device includes: a high-pressure electrode plate, a low-pressure electrode plate, a glass tank, and a burette. The low-pressure electrode plate is located at the bottom of the glass tank. The outer wall of the high-pressure electrode plate is attached to the inner wall of the glass tank and located above the low-pressure electrode plate. The high-pressure electrode plate can move up and down. A burette orifice penetrating the high-pressure electrode plate is provided at the center of the high-pressure electrode plate. The burette is located directly above the burette orifice. The burette contains the titrant solute. The high-voltage plate is connected to the positive terminal of a DC high-voltage power supply, the highest voltage of which is 50KV; the low-voltage plate is connected to the negative terminal of the power supply. The high-voltage electrode and the low-voltage electrode are spaced 30mm apart, and both are made of copper. The burette drips the solute into the solvent through the burette orifice on the high-pressure plate. The burette allows for maximum control of the dripping amount to reduce errors and timely observation of the dissolution of two immiscible solutions. Furthermore, the burette being positioned above the center of the glass trough ensures that the solute is dripped into the center of the low-pressure plate as much as possible, which is beneficial for liquid emulsification. The color model of the lattice Boltzmann method includes: The evolution equation is: (1.10) The LB distribution function; Collision Operator It consists of three operators: ， It is a single-phase collision operator, representing the particle motion caused by the collision between particles inside a single-phase fluid; It is an interface perturbation operator, representing the interaction between particles of different phases in the phase interface region caused by interfacial tension; It is a recoloring operator that controls the separation of intersecting particles in the phase interface region, ensuring that particles do not invade each other's phase regions; The single-phase collision operator includes: (1.11) in It is a relaxation factor; It is the equilibrium state distribution function: (1.12) (1.13) (1.14) It is about The function; Indicates the first Weight coefficients for each direction; Indicates the density of the solute or solvent. for or , , These represent the density of the solute and the density of the solvent, respectively. Indicates the first Velocity in one direction; Indicates the total speed; Indicates total density; (1.15) in It is a free parameter; Indicates the first One direction; The interface perturbation operator includes: The color gradient process of the interface is represented by defining a color gradient F: ， Therefore, the expression for the perturbation operator is obtained: (1.17) (1.18) in It is a free parameter; Indicates taking The model; The value of the expression for the color gradient; Indicates the first A parameter for each direction.

2. The emulsification method for two immiscible solutions under a constant electric field according to claim 1, characterized in that, S1 includes the following steps: S1-1, During the experiment, the glass tank is filled with the first liquid as a solvent, ensuring that the liquid level of the first liquid is higher than that of the high-voltage plate. S1-2, another liquid is injected into the glass bath as a solute through a burette, so that the solute drips into the center of the low-pressure electrode.

3. The emulsification method for two immiscible solutions under a constant electric field according to claim 1, characterized in that, The recoloring operator includes: (1.19) (1.20) in Represents the recoloring operator for the solute; Represents the recoloring operator for the solvent; Represents color gradient And grid speed of sound The included angle; Represents the distribution function; This indicates summing over the distribution function.

4. The emulsification method for two immiscible solutions under a constant electric field according to claim 1, characterized in that, This also includes setting the boundary conditions for the electric field: Considering that the container is a cuboid or cylinder, a bounce format is used in the X direction and a periodic boundary processing format is used in the Y direction.

5. The emulsification method for two immiscible solutions under a constant electric field according to claim 1, characterized in that, Also includes: The parameters affecting emulsification were changed, and then emulsification analysis was performed based on the color model of the lattice Boltzmann method. Under energized conditions, the conductivity was changed by adding other solutions, and the emulsification of the two immiscible solutions was observed.

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