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.