Axisymmetric slow motion of a non-deformable spherical droplet or slip particle toward an orifice in a plane wall

Abstract

This paper reports the axisymmetric motion of a viscous droplet or solid spherical particle with a slip-flow surface that moves perpendicular toward an orifice in a plane wall. The motion is studied in the quasi-steady limit under a low Reynolds number. To maintain the spherical shape of the droplet, we assumed that the interfacial tension is very large. The radius of the droplet/particle may be either smaller or larger than the radius of the orifice. A general solution is established from fundamental solutions in both spherical and cylindrical coordinate systems. A semi-analytical approach based on dual integral equations and a collocation scheme is used. Numerical results show that the normalized drag coefficient acting on the droplet/particle is obtained with good convergence for different values of slip parameter, viscosity ratio, and spacing parameters. The findings demonstrate that the collocation results of the drag coefficient are consistent with the limiting cases available in the literature.