Lattice Boltzmann simulation of deformation and breakup of a droplet under gravity force using interparticle potential model

In this paper interparticle potential model of the lattice Boltzmann method (LBM) is used to simulate the deformation and breakup of a falling droplet under the gravity force. First, this model is applied to ensure that the surface tension effect is properly implemented in this model. Two tests have been considered. First, it has been checked an initial square drop in a 2D domain can freely deform to a circular drop and secondly the coalescence of two static drops that merge to become a single circular drop is simulated. In order to further verify the model, Laplace law for static drops is performed. In the next step, wall effects on the droplet shape and its average velocity have been studied. It is seen that the average velocity of droplet at different times is independent of wall effects when the ratio of the width of the channel to droplet diameter (W/D) is more than 6. In the final section of the paper, deformation and breakup of a falling droplet for some range of Eotvos and Ohnesorge numbers are investigated. It is seen that at very low Eotvos numbers, where the surface tension force is dominant, the droplet deforms slowly and reaches a steady state without breakup. At higher Eotvos numbers gravitational force overcome the surface tension force and the droplet deforms more. For breakup modes at the small Ohnesorge number, if Eotvos number be increased to an intermediate value, the droplet deforms more than from a state of low Eotvos number value and eventually forms a backward-facing bag. Finally, for high Eotvos numbers, fragments of droplet are sheared from the edges and the shear breakup mechanism is seen. On the other hand, the stabilizing effect of the Ohnesorge number, (the ratio of viscous stresses and surface tension) is shown. At higher Ohnesorge number, the simulations show that the main effect of increasing Ohnesorge number is to move the boundary between the different breakup modes to higher Eotvos number.