Numerical simulation method and device for Quincke rotating liquid drop self-driving process

Abstract

The invention discloses a numerical simulation method and device for a Quincke rotating liquid drop self-driving process, and the method comprises the steps: building a geometric model, carrying out the grid division, and carrying out the grid encryption at a phase interface through employing a self-adaptive grid technology; the method comprises the following steps: adding electric field force induced by charges into a Navier-Stokes equation for controlling fluid flow in the form of volume force to obtain a control equation; solving the control equation by using an interlaced time discretization method; and carrying out numerical simulation on the Quincke rotating liquid drop arranged on the wall surface of the solid. By adopting the technical scheme of the invention, the problem that the current simplified electrohydrodynamic numerical model cannot comprehensively reveal the Quincke rotation behavior of the liquid drop is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of electrohydrodynamic numerical modeling, and in particular relates to a numerical simulation method for a Quincke rotating droplet self-driving process. Background Art

[0002] The precise manipulation of droplets is a multidisciplinary research field, which is of great significance to the development of disciplines such as materials science, chemistry and engineering thermal management. Especially in micro-scale industries such as microfluidic machinery, chips, and drug delivery, how to make droplets spontaneously move in a directional manner is the current technical barrier. Although great progress has been made in recent years, there are still many challenges, such as low speed, short distance, and complex operating platform. Recently, a new droplet dynamic behavior has been discovered: Quincke rotation, that is, under the action of a uniform electrostatic field, when the conductivity of the droplet is lower than the conductivity of the surrounding fluid, the droplet will spontaneously produce asymmetric and unstable rotational motion. A rotating object placed on a solid wall can produce a directional horizontal displacement. Based on this phenomenon, Quincke rotation has been applied to the transport and directional manipulation of solid particles. However, research on droplets has not yet been carried out. Therefore, coupling the droplet Quincke rotation with the wall effect is expected to develop a new droplet self-driving method.

[0003] In order to verify the rationality of this method and reveal the mechanism of droplet self-propelled, numerical simulation is an efficient method. The existing electrohydrodynamic models are all based on the leakage dielectric theory established by Taylor and Melcher in 1969. But it has an important assumption: the interfacial charge accumulation is completed instantly, and the charge only exists at the interface between the two phases. Therefore, the sufficient condition for the generation of droplet Quincke rotation-the charge convection induced by fluid flow can only exist in the model in the form of interface conditions, which brings great challenges to the establishment of numerical models. At present, only the boundary integral method (Boundary Integral Method) based on the linear Green Function can be used to solve the leakage dielectric numerical model considering the charge convection effect, but this method can only obtain the linear stable solution of the droplet Quincke rotation, which is also the reason why the current research on the droplet Quincke rotation cannot be further carried out. Therefore, it is necessary to establish a multiphase electrohydrodynamic model that accurately predicts the droplet Quincke rotation. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a numerical simulation method and device for the self-driving process of Quincke rotating droplets, so as to solve the problem that the current simplified electrohydrodynamic numerical model cannot fully reveal the Quincke rotating behavior of droplets.

[0005] To achieve the above object, the present invention adopts the following technical solution:

[0006] The present invention provides a numerical simulation method for a Quincke rotating droplet self-driving process, comprising:

[0007] Step S1, establishing a geometric model and performing mesh division, and using adaptive mesh technology to perform mesh encryption at the phase interface;

[0008] Step S2, obtaining a control equation by adding the electric field force induced by the charge in the form of volume force to the Navier-Stokes equation controlling the fluid flow;

[0009] Step S3, solving the control equation using staggered time discretization method;

[0010] Step S4, performing numerical simulation on a Quincke rotating droplet placed on a solid wall.

[0011] Preferably, in step S1, the phase interface mesh is encrypted using an adaptive mesh technology based on volume fraction gradient.

[0012] Preferably, in step S2, the electric field force induced by the charge is added to the Navier-Stokes equations controlling the flow of the fluid in the form of volume force to obtain the control equation:

[0013]

[0014] in, is the surface tension, For the electric field force.

[0015] Preferably, the control equation is solved by using the staggered time discretization method, as follows:

[0016]

[0017]

[0018] in, *Indicates the amount obtained in the previous iteration.

[0019] The present invention also provides a numerical simulation device for the self-driving process of Quincke rotating droplets, comprising:

[0020] The first processing module is used to establish a geometric model and perform mesh division, and use adaptive mesh technology to perform mesh encryption at the phase interface;

[0021] a second processing module for obtaining a control equation by adding the electric field force induced by the charge in the form of volume force to the Navier-Stokes equations controlling the flow of the fluid;

[0022] A third processing module is used to solve the control equation using an interleaved time discretization method;

[0023] The fourth processing module is used to perform numerical simulation on a Quincke rotating droplet placed on a solid wall.

[0024] Preferably, the first processing module uses an adaptive grid technology based on volume fraction gradient to encrypt the phase interface grid.

[0025] Preferably, the second processing module adds the electric field force induced by the charge in the form of volume force to the Navier-Stokes equations controlling the flow of the fluid to obtain the control equation:

[0026]

[0027] in, is the surface tension, For the electric field force.

[0028] Preferably, the third processing module uses an interleaved time discretization method to solve the control equation, as follows:

[0029]

[0030]

[0031] in, *Indicates the amount obtained in the previous iteration.

[0032] The present invention solves the charge conservation equation including the charge convection effect and couples the VOF method to establish a numerical model capable of solving the Quincke rotation dynamics of droplets. The model breaks the limitations of the leaky dielectric model and can accurately predict all electrohydrodynamic behaviors. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0034] Figure 1 Flow chart of the numerical simulation method for the self-driving process of Quincke's rotating droplet;

[0035] Figure 2(a) shows the geometric model and boundary conditions;

[0036] Figure 2(b) shows the grid system generated based on adaptive grid technology;

[0037] Figure 3 Schematic diagram for rationalization and verification of numerical models;

[0038] Figure 4(a) shows the situation when R=0.01,S=0.5,E 0 =2.5kv / cm, the trajectory of the Quincke droplet;

[0039] Figure 4(b) shows the droplet self-driving performance under different electric field strengths (|U * ave |), where R is the conductivity ratio of the droplet to the surrounding fluid; S is the dielectric constant ratio of the droplet to the surrounding fluid; E 0 is the electric field strength; |U * | ave is the absolute average translational velocity. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] Embodiment 1:

[0043] like Figure 1 As shown, an embodiment of the present invention provides a numerical simulation method for a Quincke rotating droplet self-driving process, comprising:

[0044] Step S1: Establish a three-dimensional cube geometric model

[0045] Figure 2(a) shows the parameters involved (e.g., the bottom wall contact angle; the calculation area is defined as 60a×30a to avoid the influence of the area boundary on the numerical results) and the boundary conditions: the electromotive force on the left boundary (-V) and the right boundary (V) is kept constant (V = V r =-V l ), thus forming a uniform electric field; the electric potential of the upper and lower boundaries is Vx / 30a; for the calculation of the flow field, the lower boundary condition is that the boundary has no slip, and the other boundary conditions are Note: To activate Quincke rotation of droplets, the two-phase flow system must satisfy In order to accurately predict the interface evolution, the adaptive mesh technology is used to refine the interface. An adaptive grid technique with c (c is the volume fraction) is used to refine the interface grid. Note that c originates from the VOF method used in this model, which realizes interface tracking by solving the volume fraction equation.

[0046]

[0047] Among them, c = 0 represents the surrounding fluid; c = 1 represents the droplet fluid; 0 < c < 1 represents the interface. It is explained as the interface region, and its grid size is L×2 -lmax (L is the side length of the region, and lmax is the refinement degree of the interface grid). When It indicates that it is a single-phase region and its grid size is L×2 -lmin (lmin is the refinement degree of the single-phase region grid). Figure 2(b) shows the grid system generated based on the adaptive grid technique.

[0048] Step S2: Construct the mathematical control equations

[0049] The existing electrohydrodynamics numerical models ignore the charge convection effect, which is a sufficient condition for generating Quincke rotation. Therefore, to establish a complete electrohydrodynamics numerical model, the charge conservation equation containing charge convection needs to be considered.

[0050]

[0051] Among them, q v is the free charge, σ is the conductivity, is the electric field strength.

[0052] The Gauss's theorem in electrostatics is used to solve the electric field.

[0053]

[0054] Among them, ε is the permittivity; V represents the electric potential.

[0055] Under the action of the electric field, the dynamic behavior of the droplet mainly originates from the coupling of the electric field and the flow field. The realization of this coupling effect is by adding the electric field force induced by the charge to the Navier-Stokes equation that controls the fluid flow in the form of a body force.

[0056]

[0057] Among them, is the surface tension, is the electric field force.

[0058] These three equations include all the physical effects involved, so they can accurately predict the electrohydrodynamic behavior of the droplet.

[0059] Step S3: Numerical solution of control equations

[0060] In order to obtain a high-precision numerical solution, the staggered time discretization method is used to solve the control equation. The detailed discretization scheme is as follows:

[0061]

[0062] Where c represents the volume fraction; subscript n, Indicates time; represents the gradient operation; ε represents the dielectric constant; Indicates speed; q v represents the free charge density; represents the electric field strength; Δt represents the time step; ρ represents the conductivity; V represents the electric potential; * indicates the quantity obtained in the previous iteration process; μ indicates the dynamic viscosity; γ indicates the surface tension coefficient; k indicates the interface slope; δ s represents the Diktonic function; represents the unit normal vector; represents the electric field force; ρ represents the density.

[0063] Step S4: numerically simulate the dynamic behavior prediction of the Quincke spinning droplet placed on the solid wall

[0064] Firstly, the model is used to calculate the tilt angle of the suspended droplet under different electric field depths and compared with Feng's theoretical results. Figure 3 It shows that the two results are in good agreement, which means that the numerical model can accurately predict the Quincke rotation of droplets. Next, the droplet motion trajectory of the two-phase flow system R = 0.01, S = 0.5 under an electric field strength of 2.5kv / cm was numerically detected. Figure 4(a) shows the motion trajectory of the droplet. This result demonstrates that the rotating droplets placed on the wall can be self-driven. In addition, this model is used to further study the regulatory effect of electric field strength on droplet self-drive. Figure 4(b) shows the droplet self-drive under different electric field strengths (|U * ave |The absolute average horizontal movement speed of the droplets, used to indicate the self-propulsion performance) Performance changes: Increasing the electric field strength can speed up the droplet self-propulsion.

[0065] Embodiment 2:

[0066] The embodiment of the present invention provides a numerical simulation device for a Quincke rotating droplet self-driving process, comprising:

[0067] The first processing module is used to establish a geometric model and perform mesh division, and use adaptive mesh technology to perform mesh encryption at the phase interface;

[0068] a second processing module for obtaining a control equation by adding the electric field force induced by the charge in the form of volume force to the Navier-Stokes equations controlling the flow of the fluid;

[0069] A third processing module is used to solve the control equation using an interleaved time discretization method;

[0070] The fourth processing module is used to perform numerical simulation on a Quincke rotating droplet placed on a solid wall.

[0071] As an implementation of the embodiment of the present invention, the first processing module uses an adaptive grid technology based on volume fraction gradient to encrypt the phase interface grid.

[0072] As an implementation of the embodiment of the present invention, the second processing module adds the electric field force induced by the charge in the form of volume force to the Navier-Stokes equations controlling the flow of the fluid to obtain the control equation:

[0073]

[0074] in, is the surface tension, For the electric field force.

[0075] As an implementation method of the embodiment of the present invention, the third processing module uses an interleaved time discretization method to solve the control equation, which is as follows:

[0076]

[0077] in, *Indicates the amount obtained in the previous iteration.

[0078] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A numerical simulation method for the self-driving process of Quincke rotating droplets, characterized in that: include: Step S1, establishing a geometric model and performing mesh division, and using adaptive mesh technology to perform mesh encryption at the phase interface; Step S2, obtaining a control equation by adding the electric field force induced by the charge in the form of volume force to the Navier-Stokes equation controlling the fluid flow; Step S3, solving the control equation using staggered time discretization method; Step S4, performing numerical simulation on a Quincke rotating droplet placed on a solid wall.

2. The numerical simulation method of the Quincke rotating droplet self-driving process according to claim 1, characterized in that: In step S1, the phase interface mesh is encrypted using an adaptive meshing technique based on volume fraction gradient.

3. The numerical simulation method of the Quincke rotating droplet self-driving process according to claim 2, characterized in that: In step S2, the electric field force induced by the charge is added to the Navier-Stokes equations controlling the fluid flow in the form of volume force to obtain the control equation: in, is the surface tension, For the electric field force.

4. The numerical simulation method of the Quincke rotating droplet self-driving process according to claim 3, characterized in that: The staggered time discretization method is used to solve the control equations as follows: in, *Indicates the amount obtained in the previous iteration.

5. A numerical simulation device for the self-driving process of Quincke rotating droplets, characterized in that: include: The first processing module is used to establish a geometric model and perform mesh division, and use adaptive mesh technology to perform mesh encryption at the phase interface; a second processing module for obtaining a control equation by adding the electric field force induced by the charge in the form of volume force to the Navier-Stokes equations controlling the flow of the fluid; A third processing module is used to solve the control equation using an interleaved time discretization method; The fourth processing module is used to perform numerical simulation on a Quincke rotating droplet placed on a solid wall.

6. The numerical simulation device for the self-driving process of Quincke rotating droplets according to claim 5, characterized in that: The first processing module uses an adaptive grid technology based on volume fraction gradient to encrypt the phase interface grid.

7. The numerical simulation device for the self-driving process of Quincke rotating droplets according to claim 6, characterized in that: The second processing module adds the electric field force induced by the charge to the Navier-Stokes equations that control the fluid flow in the form of volume force to obtain the governing equation: in, is the surface tension, For the electric field force.

8. The numerical simulation device for the Quincke rotating droplet self-driving process according to claim 7, characterized in that: The third processing module uses the staggered time discretization method to solve the control equations, as follows: in, *Indicates the amount obtained in the previous iteration.

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