Breakup and deformation of a falling droplet under high voltage electric field

In this paper the lattice Boltzmann method (LBM) is employed to simulate deformation and breakup of a falling drop under gravity and electric field. First the two-phase LBM is applied to verify the Laplace law for static drops. Then relaxation of a square droplet is conducted. Furthermore a comparison is made with Taylor theoretical results for different electrical capillary number, permittivity and conductivity ratio. It is seen that with permittivity ratio larger than conductivity, droplet takes an oblate and for lower ratio takes prolate shape. It is seen that for relatively low Eotvos number where the surface tension is a dominant factor and for high Ohnesorge number where the viscosity plays an important role shear breakup occurs. On the other hand it is also found that by increasing the Eotvos number and decreasing Ohnesorge number drop distorts more and back breakup happens in addition to shear breakup.