Abstract: The pseudo-potential model of the lattice Boltzmann method (LBM) coupled with the discrete electric field governing equations was used to simulate the dielectric-medium droplet breakup process under electric field. By introducing deformation rate as a measurement of droplet's deformation, the whole evolution process of the droplet from deformation to breakup was presented. The influences of applied electric field strength and dielectric permittivity ratio of component inside to outside the droplet on the dynamic behavior of droplet breakup were investigated. Applied electric field promoted the deformation of droplet with deformation rate oscillating with time. There existed a critical electric capillary number (i.e. critical electric field strength) or a critical dielectric permittivity ratio, above which deformation rate oscillation amplitude was magnified continuously until breakup happened and below which the oscillation amplitude of deformation rate decayed continuously until deformation rate stabilized to a final steady value. Based on the simulation results, a modification of the present definition of electric capillary number was presented. With the modified electric capillary number, the influences of both electric field strength and dielectric permittivity ratio on droplet deformation and breakup could be analyzed integrally using a single parameter.

Key words: lattice Boltzmann method, droplet, breakup, electric field, numerical simulation, mass transfer, microfluidics

摘要： 采用格子Boltzmann方法（LBM）伪势模型，耦合流场和电场控制方程，研究了电场作用下油水共存体系中水滴分裂的动力学行为及特性，借助形变率衡量液滴的形变大小，展现了液滴从形变至分裂的动态演变过程，分析了外加电场大小和液滴内外介电常数比对液滴分裂行为的影响。结果表明：外加电场能促使液滴发生振荡形变，且存在临界电毛细数和临界介电常数比决定液滴是否发生分裂：高于临界值，液滴形变率振荡幅度随时间不断增长，最终发生分裂；低于临界值，则液滴形变率振荡幅度不断衰减，并最终趋于一稳定值。在此基础上，综合考虑电场强度与介电常数比的影响，提出了基于现有电毛细数的修正电毛细数唯一地表征电场作用下液滴分裂与否。

关键词: 格子Boltzmann方法, 液滴, 分裂, 电场, 数值模拟, 传质, 微流体学