Dynamics of Two Charged Particles in a Creeping Flow

Hassan Hk Stepanyants Ya

doi:10.4172/2090-0902.1000145

Abstract

We study the interaction of two charged solid particles in a viscous fluid. It is assumed that the particles move either side-by-side or one after another along the same vertical line under the influence of the buoyancy/gravity force, Coulomb electrostatic force or its modification, and viscous drag force. The drag force consists of two components: the quasi-stationary Stokes drag force and Boussinesq–Basset drag force resulting from the unsteady motion. Solutions of the governing equations are analysed analytically and numerically for the cases of perfect fluid and viscous fluid; the comparison of these two cases is presented.

Highlights

Despite the fact that the study of particle dynamics in a viscous fluid has a long history, many important problems still remain unsolved [1]
One of the intriguing problems that has not been solved so far is the dynamics of two inter- acting charged particles in viscous fluid
We have considered the dynamics of two unlike and like charged particles in viscous fluid in the creeping flow approximation

Summary

Introduction

Despite the fact that the study of particle dynamics in a viscous fluid has a long history, many important problems still remain unsolved [1]. This pertains to the collective behaviour of big particle ensembles, but even to interactions of two particles in a complex environment of shear flows or in the presence of solid obstacles, walls or free surfaces. Much research efforts have been undertaken over the years to elucidate the particle dynamics in various situations Importance of such investigations is backed by many practical applications of mixtures of fluids and suspensions; examples being particle motions in the cooling systems of nuclear reactors and particle-liquid mixtures used for pharmaceutical purposes. We study two configurations of particles: i) when they move side-by-side perpendicular to the line connecting their centers and ii) when they move vertically one after another along the same line

Equations of Motion and Problem Formulation

Particle dynamics in an in viscid fluid

Particle dynamics in viscous fluid

Two Particles Moving One After Another

Discussion and Conclusion