Slow viscous flow past cylindrical particles with thin liquid layer: Cell model

In order to investigate the hydrodynamic interaction between an interface and a cylindrical particle, it is essential to compute the drag and other physical properties exerted on the cylinder in the vicinity of the interface. The present study examines the analytical solution of slow viscous flow past a swarm of cylindrical particles, where each particle consists of a solid core covered by a liquid shell coated with thin monomolecular layer of surfactant using cell model technique. We have assumed that each particle is enclosed by a hypothetical cell. The boundary conditions of Happel, Kuwabara, Kvashnin and Mehta-Morse models are considered on hypothetical cell. The effects of Surfactants are accommodated by considering the Scriven boundary conditions at the shell involving Surface Shear viscosity and Surface Dilatational viscosity. The variation of drag force and hydrodynamic permeability with various parameters is graphically presented. The result reveals in all cases the strong influence of surface viscosity on the motion of cylindrical particle, following cell model technique. It is seen that the presence of surfactant layer increases drag force on the contrary decreases hydrodynamic permeability. In the limiting cases, the analytical solutions describing the drag force reduces to known results of Happel, Kuwabara, Kvashin and Mehta-Morse.