Migration of a slip-spin solid spherical particle in a micropolar fluid-filled circular cylindrical tube

Abstract

A combined study analytically and numerically for the axially symmetric creeping flow due to a slip-spin solid sphere surface moving in a microstructure fluid of micropolar type along the centreline of a circular cylindrical tube is introduced. This investigation was presented under low Reynolds number conditions. A general solution is obtained by superposing the essential solutions in both spherical and cylindrical coordinates to solve the Eringen micropolar field equations. The condition of the microrotation, along with couple stress, is used at the surface of the solid particle; while the microrotation is used at the inner cylindrical surface. Boundary conditions are imposed initially on the inner cylindrical surface using Fourier transforms and subsequently on the outer surface of the solid particle using a collocation technique. This paper aims to study the wall interaction problem of a translating slip-spin solid spherical particle in a micropolar fluid along the centreline of a circular cylindrical tube. The study also investigates the effect of the addition of slip conditions for velocity and microrotation on the surface of a solid particle. There is good convergence in the numerical findings obtained for the normalised hydrodynamic drag force (the tube-corrected factor) applying on the surface of the solid particle for several values of the micropolarity coefficient, slip-spin coefficients, and the ratio between the radius of the solid particle and tube. Regarding the flow of a solid spherical particle along the centreline of a cylindrical tube, our drag findings compare favourably to the solutions found in the literature. We found that the normalised drag force acting on the solid particle monotonically increases with the increase of the particle-to-tube radius ratio and reaches infinity in the limitless, with the increase of the micropolarity coefficient, and with the increase of the slip-spin coefficients for a steady ratio of particle-to-tube radius.