Thermophoresis of a particle in a concentric cavity with thermal stress slip

Abstract

The thermophoretic motion of a spherical particle situated at the center of a spherical cavity filled with a gaseous medium under a prescribed temperature gradient is studied analytically. The Knudsen number is small for the gas motion in the slip-flow regime, and the temperature jump, thermal creep, frictional slip, and particularly, thermal stress slip are allowed on the solid surfaces. After solving the equations of heat conduction and fluid motion, an explicit formula for the migration velocity of the confined particle is obtained for different temperature conditions of the cavity with arbitrary values of the particle-to-cavity radius ratio and other parameters. Contributions from the thermoosmotic flow along the cavity wall and from the wall-corrected thermophoretic force to the particle velocity are equivalently important and can be linearly superimposed. With either or both of these contributions, the particle velocity in general is a decreasing function of the particle-to-cavity radius ratio and vanishes in the limit. The effects of the thermal stress slip at the solid surfaces to the migration velocity of the confined particle can be significant and interesting, dependent on the thermal and interfacial properties of the particle and surrounding gas. The wall effect on the thermophoretic migration of the particle in a cavity is qualitatively different from that on the motion of the particle in a circular tube.

Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

“…The transformed system of ordinary differential equations of Equations (22)- (24) with the boundary conditions of Equation (25) were solved by using the built-in numerical solver BVP4C. Here, BVP4C stands for the boundary value problem fourth order.…”

“…The numerical solutions of the proposed model by FDM were obtained on the entire surface of the flow geometry. On the other hand, solutions by the built-in numerical solver BVP4C were obtained only at the leading edge of the surface of the proposed geometry for a similar form of the equations given in Equations (22)- (24) with the boundary conditions of Equation (25). Therefore, the results computed by the finite difference method were validated by the built-in numerical solver BVP4C at the leading edge.…”

“…The gas considered by them had a non-uniform temperature filled in the region of the free molecule. The thermophoresis transportation of spherical particles suspended in gas within a spherical-shaped cavity along with its material properties were examined by Li and Keh [24] analytically. The characteristics of the shear stress and heat transfer rate around the surface of a sphere are discussed in [25].…”

Impact of Maxwell velocity slip and Smoluchowski temperature slip on CNTs with modified Fourier theory: Reiner-Philippoff model

“…The results of the thermal and velocity boundary conditions on thermally radiative ferrofluid motions over a flat plate are studied by Sejunit and Khaleque [ 41 ]. Li and Keh [ 42 ] discussed analytically the thermophoretic displacement of the spherical particles at the core of a gaseous material in the specified temperature gradient. Sarabandi and Moghadam [ 43 ] analyzed the steady-state laminar flow of non-Newtonian fluid in a circular microchannel embedded with slip velocity condition.…”