Prolate Spheroidal Coordinate: An Approximation To Modeling Of Ellipsoidal Drops In Rotating Disc Contractor Column

Abstract

In many situations the shape of the drops contained in a liquid or porous media is not perfectly spherical. Accurate modeling of the process extraction in Rotating Disc Contractor (RDC) column is only possible with accurate description of the geometry of the drop. In this research, the diffusion equation given in prolate spheroidal coordinate system is used for a two-dimensional case. An analytical solution of the unsteady diffusion equation describing mass transfer for prolate spheroidal drops, considering a constant diffusion coefficient is presented. The resulting equations are analytically solved by using the separation method. The solution describes that the concentration of the drop decreases with the increases of drop shapes. This model can be used to study the mass transfer process of liquid-liquid extraction in RDC Column for spheroidal drop.