Connection of fields across the interface in the fluid particle dynamics method for colloidal dispersions

Unlike in conventional hydrodynamics, the viscosity is assumed to smoothly change across a thin interfacial region between two fluid-phases in the fluid particle dynamics (FPD) method, which was proposed to facilitate the numerical study of colloidal dynamics. We study how the pressure and velocity fields are connected in the limit of the thin interfacial region by use of the steady Stokes approximation. We obtain connection formulas to calculate the fields in and around a droplet, far from which the uniform flow or the linear shear flow is imposed. We also show, around a spherical rigid particle in a steady state where the particle center moves uniformly, that the FPD method yields the flow consistent with that of conventional hydrodynamics.