Simulation of falling droplet by the lattice Boltzmann method

In this paper the lattice Boltzmann method (LBM) is employed to simulate deformation and breakup of a falling drop under gravity. First the two-phase LBM is applied to verify the Laplace law for static drops. In order to further verify the model, relaxation of a square droplet with two different viscosities is conducted. Then deformation and breakup of a falling drop for some range of Eotvos and Ohnesorge numbers are investigated. It is seen that at relatively low Eotvos numbers, where the surface tension force is dominant, the drop deforms slowly and reaches a steady state without breakup. At higher Eotvos numbers gravitational force prevail over the surface tension force and the drop distorts more. Breakup of the drop can be seen for a large enough Eotvos value. On the other hand the stabilizing effect of the Ohnesorge number, which is the ratio of viscous stresses and surface tension, is shown. It is found that at higher Ohnesorge values, the viscous forces are dominant and the drop tends to maintain its original shape.