Application of the lattice Boltzmann method to electrohydrodynamics: Deformation and instability of liquid drops in electrostatic fields

Abstract

It is attractive and meaningful to apply the lattice Boltzmann method (LBM) to electrohydrodynamic (EHD) problems. As an important and fundamental problem in EHD, the behavior of freely-suspended liquid drops subjected to electrostatic fields was simulated with a 2-D LBM by means of the permittivity-density relation proposed by the authors and Peng's multiphase LBM which can obtain high liquid-to-vapor density ratio and low liquid-phase compressibility. The phenomena and laws of deformation, especially the instable behavior of the liquid drops were well simulated. And two important critical parameters, i.e. the critical permittivity ratio and the critical electric-field strength were obtained. These results agree with the corresponding theories and experiments. The simulations show the particular advantages and potential of the LBM in studying multiphase electrohydrodynamic problems.

Lattice Boltzmann method for microfluidics: models and applications

“…Energy conversion by means of electrokinetic flows in microchannels have also been simulated (Wang and Kang 2010b). In addition, multiphase LBM models have also been utilized to simulate the electrohydrodynamic deformation of droplets suspending in electric field (Zhang and Kwok 2005a;Huang et al 2007). The simulated droplet deformation and flow field were found in good agreement with other theoretical and experimental studies.…”

Lattice Boltzmann Study of Electrohydrodynamic Drop Deformation With Large Density Ratio

“…12) to study the drop deformation under an external electric field, but in their study the densities of the drop and its surrounding fluid are identical. Huang et al 18 used single-component multiphase LBM to study the drop deformation and burst in gas. In their study, the formula " r ¼ 1 þ ð&Þ þ ð&Þ 6 is proposed to mimic the permittivity property near the interface, where " r is the relative permittivity, and and & are adjustable parameters.…”

“…In their study, the formula " r ¼ 1 þ ð&Þ þ ð&Þ 6 is proposed to mimic the permittivity property near the interface, where " r is the relative permittivity, and and & are adjustable parameters. 18 However, the theoretical base of the above formula is unknown. Besides that, the simulation results seem sensitive to the choice of the adjustable parameters.…”

Simulation of mesoscale interfacial properties using the lattice Boltzmann method

“…Since the mesoscale interparticle potential (MIP) was first proposed and studied by Shan and Chen [5] in 1993, it has achieved significant success for simulating mesoscale multiphase flows and phase transitions [6] such as wetting and jamming at interfaces [7,8]. Recently, Li et al [9,10] simulated electrowetting and Huang et al [11] simulated shape changes motion of a vesicle in a fluid; both using the LB method. Thus, the application of the LB method is further extended in multiphase *Corresponding author (email: longjian@cqu.edu.cn) fields.…”