Direct simulation of falling droplet in a closed channel

The direct simulation of a droplet falling in a different background liquid is presented. The complete Navier-Stokes problem is solved using a projection method coupled with a level set method. A detailed analysis is given to show that reinitialization procedure of level set method [M. Sussman, P. Smereka, S. Osher, Level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics 114 (1) (1994) 146-159] cannot preserve the volume of a droplet. A variable time step method is presented to improve conservation. We study the effect of a wall on the droplet motion by settling a single circular droplet through a quiescent fluid at different lateral positions between parallel walls. The effect of inertial force on the deformation and oscillatory motion of a droplet is investigated by changing the Reynolds numbers. The deformation mechanism is studied for different Weber numbers. In addition, the interaction effect between droplets is studied by settling two and three droplets in the parallel channel. The Karman vortex distribution is shown to explain the oscillatory mechanism of droplet motion.