Author(s)

M. Mikhaylenko & A. Povitsky

Abstract

A method of allocation of Stokeslets and collocation points for the Boundary Singularity Method (BSM) is proposed to solve Stokes flows about single droplets and merging droplets settling on the surface of fibers in filtration process using moderate number of singularities. In the recent studies of optimal location of singularities for Stokes flows about spherical rigid particles, the location of Stokeslets was determined as a fraction of particle radius. The current study represents further extension to the Stokeslet allocation schemes that was developed in order to evaluate Stokes flowfield about single droplets and the \“peanut-shape” clusters of merging droplets settling at relatively long cylindrical fibers. Three test problems are solved to demonstrate capability of the BSM and proposed schemes of allocation of singularities. The first problem is a cross-flow about cylindrical fiber with a spherical droplet settling at its equatorial plane. This flow is modeled for a range of ratios of droplet to fiber radii. The second problem is a cross-flow about droplet on a fiber at the range of angles between flow and fiber corresponding to position of droplet on fiber ranging from attached to equatorial point of fiber to the back of fiber. The third problem is the BSM computation of Stokes force exerted on a pair of merging droplets, one of which is sliding toward another along the fiber. Keywords: boundary singularity method, Stokes equations, microfluids, Stokeslet, allocation of Stokeslets, droplet, fiber.

Keywords

boundary singularity method, Stokes equations, microfluids, Stokeslet, allocation of Stokeslets, droplet, fiber