Mathematical Model for Biological Vesicle in Osmophoretic Migration

Abstract

Osmophoresis indicates the motion of biological cells or small capsules in concentration gradients. This study presents a mathematical model that combined analytical- numerical study for the osmophoretic migration of a spherical biological vesicle perpendicular to two parallel plates. The imposed concentration gradient is constant and perpendicular to two parallel plates. The biological vesicle, which is a body of fluid enveloped by a continuous semipermeable membrane, may hold arbitrary solute and is assumed to maintain its spherical shape. The existence of the plane walls result in two basic effects on the biological vesicle velocity: first, the walls increase viscous retardation of the moving biological vesicle; secondly, the local concentration gradient on the biological vesicle surface is enhanced by the walls, therefore speeding up the biological vesicle. In order to solve the concentration and hydrodynamic governing equations, general solutions are constructed from the fundamental solutions in both the circular cylindrical and spherical coordinate systems. The boundary conditions are enforced first at the plane wall by the Hankel transforms and then on the biological vesicle surface by means of a boundary collocation method. For special cases of osmophoretic migration of a spherical biological vesicle normal a single plane wall, the collocation result of numerical simulations agree well with the solutions obtained by using spherical bipolar coordinates. In general, the existence of the walls always give rise to an enhancement in the osmophoretic migration.