The mechanism of surface charge convection (SCC) reveals inherently nonlinear coupling between the electrostatic problem and the hydrodynamic flow in the Melcher–Taylor electrohydrodynamic (EHD) model. Considering that most previous numerical models are based on decoupled leaky dielectric equations, the quantitative effect of SCC on two-phase EHD under different parameters remains unclear. In the present study, we propose a new numerical scheme to solve the two-phase EHD problems in the framework of the lattice Boltzmann method. The fully coupled equations including the Navier–Stokes equations, the Nernst–Planck equations, and the Poisson equation are solved using three well-designed lattice Boltzmann equations. The problem of droplet deformation under a uniform electric field is studied. By neglecting SCC at a small electric Reynolds number Re_E ≪ 1, our model successfully reproduces previous theoretical and numerical results. When considering the SCC mechanism at finite values of Re_E, the intensity of the EHD flow is reduced. Consequently, oblate droplets are predicted to be less deformed, while prolate droplets are enhanced. In addition, the SCC effect increases as the values of both Re_E and the electric capillary number, Ca, increase. In addition, a sharp variation in surface charge density is observed near the equator of the droplet due to SCC.

Electro-thermo-hydrodynamic (ETHD) flows induced by simultaneous Coulomb and buoyancy forces in a dielectric medium are studied. Previous results limited to two dimensions are extended to three dimensions. The fully coupled governing equations, including the Navier–Stokes equations, the electrohydrodynamic equations, and the energy equation, are solved using a unified lattice Boltzmann model. Various flow patterns, determined by the balance between the buoyancy-driven mechanism and the Coulomb-driven mechanism, can be observed for different combinations of the governing parameters (the electric Rayleigh number T and the Rayleigh number Ra). It is found that the electrical effect on enhancement of heat transfer becomes significant at a relatively low value of Ra. Besides, an approximately linear relationship is found between the Nusselt number Nu and T. Finally, ETHD flows for different directions of charge injection are investigated, and the results reveal that the heat transfer performance of the system is improved when the injection direction is the same as the direction of the temperature gradient.

The transition process from laminar to chaotic flow in electro-thermal convection of a dielectric liquid is numerically investigated using a unified lattice Boltzmann method. The liquid is confined in a closed square cavity, and free charges are introduced into the system through a strong unipolar injection mechanism. Three cases with different Rayleigh numbers are considered. With the increase of electric Rayleigh number, various complicated dynamical behaviors are observed and three diverse transition routes to chaos are identified, namely, the quasi-periodic sequence involving four incommensurable frequencies, the intermittency sequence, and the alternating periodic-chaotic sequence. Numerical results are illustrated using time histories, Fourier frequency spectra, and phase portraits. The chaotic behavior is quantitatively analyzed through the calculation of fractal dimension and Lyapunov exponent. Typical flow patterns for both steady-state regime and periodic regime are also presented and discussed.

In this study, the strong unipolar charge injection induced by a uniform electric field was found to have a suppressing effect on Rayleigh-Bénard secondary instability, regardless of the charge injection direction. The liquid was modeled as a perfect dielectric, and the charge injection was assumed to be autonomous and homogeneous. Direct numerical simulations were performed using a newly developed unified lattice Boltzmann model for electrothermohydrodynamics (ETHD). The electric field was applied only when the flow is in a stable oscillation state of the secondary instability. Two different cases representing charge injection from above and below were considered. The results show that periodic temperature fluctuations can be fully suppressed by a sufficiently strong electric field and that the charge injection direction has a significant impact on the flow patterns. For even stronger electric field strength, the system turns into periodic oscillatory flow again and the fundamental frequency is two orders of magnitude higher than the original ones. Besides, the effects of charge injection direction on the flow intensity and heat transfer rate of ETHD are also investigated.

In this paper, a two-dimensional numerical study on the nonlinear behaviors of electrohydrodynamic flows of Oldroyd-B viscoelastic dielectric liquid subjected to unipolar injection is performed via the finite volume method. The entire set of coupled equations, which includes the Navier–Stokes equations, simplified Maxwell’s equations, and conformation transport equations, is solved for the first time. The effects of elasticity on the nonlinear evolution of electroconvection and instability patterns are mainly investigated. Various physical models including free and rigid boundary cases are simulated entirely, and detailed analyses of stability parameters are performed. Convection and fluid motion instability are investigated and explained in detail, with a focus on the onset of motion transitions from a purely conducted state to losing its stability. It is found that the coupling of the electric field with the elasticity field gives rise to new instability and completely new mechanisms. In addition to instabilities such as subcritical bifurcation in electroconvection of Newtonian fluids, supercritical bifurcation and Hopf bifurcation are also possible as the first instability in electroconvection of viscoelastic fluids under free boundary conditions. Under rigid boundary conditions, the system with a large Weissenberg number can also lose its stability via earlier Hopf bifurcation. The stability threshold is not affected by the elastic effect if the Weissenberg number is small enough but decreases when the first instability of the system becomes Hopf bifurcation. Moreover, elasticity promotes the transition from a steady state flow to unsteady convection after the onset of convection. These phenomena are closely related to the elastic parameters.

In this paper, we perform a two-dimensional numerical investigation into the electro–thermoconvection with a melting boundary in horizontal concentric annuli filled with a dielectric phase change material. The whole set of coupled equations is solved by lattice Boltzmann method: Navier–Stokes equations, electrohydrodynamics (EHD) equations, and the energy equation. It is found that there exist three regimes during melting with EHD, namely, diffusive regime, thermal convection regime, and electroconvection regime, and the augmentation of melting heat transfer is due to the radial electroconvective flow induced by Coulomb force in the third regime. Moreover, the continuous melting of solid leads to the dynamical transition between the different flow patterns of electro–thermo-convection, as well as the interesting evolutions of temperature and charge density distribution. In different regimes of melting, the liquid fraction f_l and Nusselt number Nu follow different power laws. In detail, before the onset of radial flow motion, f_l scales as Fo^1/2 whereas Nu scales as f_l^−4/5 (Fo represents the Fourier number), and in the electroconvection dominated regime, we have f_l ∼ Fo and Nu ∼ f_l⁰.