Lattice Boltzmann model for Coulomb-driven flows in dielectric liquids

A Review on Electrohydrodynamic (EHD) Pump

In recent years, functional fluidic and gas electrohydrodynamic (EHD) pumps have received considerable attention due to their remarkable features, such as simple structure, quiet operation, and energy-efficient utilization. EHD pumps can be applied in various industrial applications, including flow transfer, thermal management, and actuator drive. In this paper, the authors reviewed the literature surrounding functional fluidic and gas EHD pumps regarding the following aspects: the initial observation of the EHD effect, mathematical modeling, and the choice of pump structure, electrode configuration, and working medium. Based on the review, we present a summary of the development and latest research on EHD pumps. This paper provides a critical analysis of the current limitations of EHD pumps and identifies potential areas for future research. Additionally, the potential application of artificial intelligence in the field of EHD pumps is discussed in the context of its cross-disciplinary nature. Many reviews on EHD pumps focus on rigid pumps, and the contribution of this review is to summarize and analyze soft EHD pumps that have received less attention, thus reducing the knowledge gap.

Numerical prediction of transient electrohydrodynamic instabilities under an alternating current electric field and unipolar injection

In this paper, a direct numerical simulation (DNS) of dielectric fluid flow subjected to unipolar injection under an alternating current (AC) electric field is carried out. The effect of frequency f of pulsed direct current (PDC) and AC on the transient evolution of electroconvection and their subcritical bifurcations are investigated in details. Electroconvection under PDC or AC tends to exhibit oscillating flow due to the periodic boundary condition of charge density and potential compared to the direct current (DC) case. The results demonstrate that under the PDC field, the linear criterion T _c decreases with increasing frequency, while the nonlinear stability criterion T _f is hardly affected. Under the AC field, a critical frequency f _c  = 0.0316 is found, which separates electroconvection into two typical flow regimes-periodic flow regime (f < f _c ) and inhibited flow regime (f ≥ f _c )-depending on whether free charges can reach the collector electrode before electric field inversion. AC-electrohydrodynamics (EHD) systems promote various flow patterns with relatively lower voltage regimes than DC-EHD systems. These mechanisms of electroconvection under the PDC/AC field offer unique possibilities for fluid flow control in biological EHD-driven flow and portable EHD applications.

Lattice Boltzmann modeling of two-phase electrohydrodynamic flows under unipolar charge injection

In this work, a two-dimensional droplet confined between two parallel electrodes under the combined effects of a nonuniform electric field and unipolar charge injection is numerically investigated using the lattice Boltzmann method (LBM). Under the non-Ohmic regime, the interfacial tension and electric forces at the droplet surface cooperate with the volumetric Coulomb force, leading to complex deformation and motion of the droplet while at the same time inducing a bulk electroconvective flow. After we validate the model by comparing with analytical solutions at the hydrostatic state, we perform a quantitative analysis on the droplet deformation factor D and bulk flow stability criteria T_{c} under different parameters, including the electric capillary number Ca, the electric Rayleigh number T, the permittivity ratio ɛ_{r}, and the mobility ratio K_{r}. It is found that the bulk flow significantly modifies the magnitude of D, which in turn decreases T_{c} of the electroconvective flow. For a droplet repelled by the anode, ɛ_{r}>1, an interesting linear relationship can be observed in the D-Ca curves. However, for a droplet attracted to the anode, ɛ_{r}<1, the system is potentially unstable. After first evolving into a quasisteady state, the droplet successively experiences steady flow, periodic flow, second steady flow, and oscillatory flow with increasing T. Moreover, discontinuities can be observed in the D-T curves due to the transitions of bulk flow.

Electroconvective instability near an ion-selective surface: A mesoscopic lattice Boltzmann study

Direct numerical simulations of electroconvection instability near an ion-selective surface are conducted using a mesoscopic lattice Boltzmann method (LBM). An electrohydrodynamic model of ion transport and fluid flow is presented. We numerically solve the Poisson-Nernst-Planck equations for the electric field and the Navier-Stokes equations for the flow field. The results cover Ohmic, limiting, and overlimiting current regimes, and they are in good agreement with the asymptotic analytical solution for the relationship between current and voltage. The influences of different ion transport mechanisms on the voltage-current relationship are discussed. The results reveal that the electroconvection mechanism is as important as other ion transport mechanisms in electrohydrodynamic flow. By comparing the contribution of different regions in the numerical domain, we find that the flow in the extended space charge layer is dominated by electroconvection. We also study the influences of multiple driving parameters, and the electrohydrodynamic coupling constant plays a dominant role in triggering convective instability. The flow pattern and ion concentration distribution are described in detail. Moreover, the route of flow from steady state to periodic oscillation and then to chaos is discussed.

Electrohydrodynamic Enhancement of Phase Change Material Melting in Circular-Elliptical Annuli

Phase change material (PCM) has received significant attention due to its great potential for thermal energy storage. However, the major undesirable property of PCM is related to its low thermal conductivity. In this work, the electrohydrodynamic (EHD) enhancement of PCM melting in circular-elliptical annuli is investigated numerically by using the lattice Boltzmann method (LBM). The key motivation for our choice of the elliptical shape is due to the fact that the more curved elliptical surface corresponds to stronger charge injection strength, which may lead to stronger flow field, and the consequent increase of heat transfer rate. The influences of several non-dimensional parameters, including electric Rayleigh number T, thermal Rayleigh number (Ra) and the aspect ratio (AR) of the inner ellipse are investigated in detail. Based on the numerical results, it is found that the radial electro-convective flow induced by the external electric field makes a significant contribution to the enhancement of melting heat transfer, and specially, the maximum time saving in some cases is more than 85%. Moreover, we observe that when the Coulomb force is dominant over the buoyancy force, no matter the inner elliptical tube is oriented horizontally or vertically, the total melting times in these two cases are nearly the same, and the melting performance obtained for the circular electrode is usually better than the other cases. However, when the flow regime is dominated by the buoyancy force, the use of a slender vertical-oriented elliptical electrode instead of the circular one is more efficient.

Sparse nonlinear models of chaotic electroconvection

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh-Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

Three-dimensional electroconvective vortices in cross flow

This study focuses on the three-dimensional (3D) electrohydrodynamic flow instability between two parallel electrodes driven by unipolar charge injection with and without cross flow. Lattice Boltzmann method with a two-relaxation time model is used to compute flow patterns. In the absence of cross flow, the base-state solution is hydrostatic, and the electric field is one-dimensional. With strong charge injection and high electrical Rayleigh number, the system exhibits electroconvective vortices. Disturbed by perturbation patterns, such as rolling pattern, square pattern, and hexagon pattern, the flow develops corresponding to the most unstable mode. The growth rate and pattern transitions are studied using dynamic mode decomposition of the transient numerical solutions. The interactions between cross flow and electroconvective vortices lead to suppression and disappearance of structures with velocity components in the direction of cross flow, while the other components are not affected. Surprisingly, the transition from a 3D to a 2D flow pattern enhances the convective charge transport, marked by an increase in the electric Nusselt number. Hysteresis in the 3D to 2D transition is characterized by the nondimensional parameter Y, a ratio of the electrical force term to the viscous term in the momentum equation.

Two Relaxation Time Lattice Boltzmann Method Coupled to Fast Fourier Transform Poisson Solver: Application to Electroconvective Flow

Electroconvective flow between two infinitely long parallel electrodes is investigated via a multiphysics computational model. The model solves for spatiotemporal flow properties using two-relaxation-time Lattice Boltzmann Method for fluid and charge transport coupled to Fast Fourier Transport Poisson solver for the electric potential. The segregated model agrees with the previous analytical and numerical results providing a robust approach for modeling electrohydrodynamic flows.

Efficient lattice Boltzmann method for electrohydrodynamic solid-liquid phase change

Melting in the presence of electrohydrodynamic (EHD) flow driven by the Coulomb force in dielectric phase change material is numerically studied. A model is developed for the EHD flow in the solid-liquid phase change process. The fully coupled equations including mechanical equations, electrical equations, energy equations, and the continuity equations in the solid-liquid interface are solved using a unified lattice Boltzmann model (LBM). Firstly, the numerical model is validated by several cases in the hydrostatic state, and all LBM results are found to be highly consistent with analytical solutions. Besides, our LBM code is able to reproduce the step changes in the distribution of charge density and electric field due to the discontinuous distribution of physical properties at the interface. Then, a systematical investigation is conducted on various nondimensional parameters, including electric Rayleigh number T, Prandtl number Pr, and Stefan number St. Results are presented for the transient evolutions of temperature, fluid flow, charge density fields, and liquid fraction. Four flow stages in the melting process together with three kinds of flow instabilities are observed. It is found that the electric field has significant influence on the melting, especially at high T and Pr and low St. Over the tested cases, a maximum melting time saving of around 50% is found.

Analytical model of electro-hydrodynamic flow in corona discharge

We present an analytical model for electro-hydrodynamic flow that describes the relationship between the corona voltage, electric field, and ion charge density. The interaction between the accelerated ions and the neutral gas molecules is modeled as an external body force in the Navier-Stokes equation. The gas flow characteristics are solved from conservation principles with spectral methods. This multiphysics model is shown to match experimental data for a point-to-ring corona configuration, shedding new insights into mass, charge, and momentum transport phenomena, and can be readily implemented in any numerical simulation.

Lattice Boltzmann solution of the transient Boltzmann transport equation in radiative and neutron transport

Applications of the transient Boltzmann transport equation (BTE) have undergone much investigation, such as radiative heat transfer and neutron transport. This paper provides a lattice Boltzmann model to efficiently resolve the multidimensional transient BTE. For a higher angular resolution, enough transport directions are considered while the transient BTE in each direction is treated as a conservation law equation and solved independently. Both macroscopic equations recovered from a Chapman-Enskog expansion and simulated results of typical benchmark problems show not only the second-order accuracy but also the flexibility and applicability of the proposed lattice Boltzmann model. This approach may contribute a powerful technique for the parallel simulation of large-scale engineering and some alternative perspectives for solving the nonlinear transport problem further.

Lattice Boltzmann model for a steady radiative transfer equation

A complete lattice Boltzmann model (LBM) is proposed for the steady radiative transfer equation (RTE). The RTE can be regarded as a pure convection equation with a source term. To derive the expressions for the equilibrium distribution function and the relaxation time, an artificial isotropic diffusion term is introduced to form a convection-diffusion equation. When the dimensionless relaxation time has a value of 0.5, the lattice Boltzmann equation (LBE) is exactly applicable to the original steady RTE. We also perform a multiscale analysis based on the Chapman-Enskog expansion to recover the macroscopic RTE from the mesoscopic LBE. The D2Q9 model is used to solve the LBE, and the numerical results obtained by the LBM are comparable to the results obtained by other methods or analytical solutions, which demonstrates that the proposed model is highly accurate and stable in simulating multidimensional radiative transfer. In addition, we find that the convergence rate of the LBM depends on the transport properties of RTE: for diffusion-dominated RTE with a large optical thickness, the LBM shows a second-order convergence rate in space, while for convection-dominated RTE with a small optical thickness, a lower convergence rate is observed.