Thermophoresis of an aerosol sphere perpendicular to two plane walls

Abstract

in Wiley InterScience (www.interscience.wiley.com). The problem of the thermophoretic motion of a spherical particle in a gaseous medium situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The imposed temperature gradient is uniform and perpendicular to the plane walls. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface.The presence of the confining walls causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is altered by the walls, thereby speeding up or slowing down the particle; second, the walls enhance the viscous retardation of the moving particle. A boundary collocation method is used to solve the thermal and hydrodynamic governing equations of the system. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded gaseous medium are presented for various cases. The collocation results agree well with the available approximate analytical solutions obtained by using a method of reflections. The presence of the walls can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle as well as the relative particle-wall separation distances. The boundary effect on thermophoresis of a particle normal to two plane walls is found to be quite significant and generally stronger than that parallel to the confining walls. © 2006 American Institute of Chemical Engineers AIChE J, 52: 1690AIChE J, 52: -1704AIChE J, 52: , 2006 Keywords: thermophoresis, aerosol sphere, continuum regime, fluid mechanics, boundary effect, plane walls IntroductionA particle, when suspended in a gas possessing a temperature gradient, acquires a velocity relative to the gas in the direction of decreasing temperature. This phenomenon, known as thermophoresis, was first observed by Tyndall in 1870 when it was discovered that a dust-free space surrounded a hot body. 1 The thermophoretic effect can be explained in part by appealing to the kinetic theory of gases. 2 The higher energy molecules in the hot regions of the gas impinge on the particle with greater momenta than molecules coming from the cold regions, thus resulting in the migration of the particle in the direction of decreasing temperature. Being a mechanism for the capture of aerosol particles on cool surfaces, thermophoresis is of considerable importance in many practical applications, such as sampling of aerosol particles, 3 cleaning of air, 4 scale formation on surfaces of heat exchangers, 5 modified chemical vapor deposition, 6 manufacturing of microelectronics, 7 nuclear reactor safety, 8 and removal of soot aerosol particles for combustion exhaust gas systems. 9,10 On the basis of the assumptions of small Knudsen number (l/a, where a is the...

Boundary effects on thermophoresis of aerosol cylinders

“…(35) that, as l-0, the wall correction to the thermophoretic velocity of the cylinder is O(l 2 ), which is different from that obtained for a thermophoretic sphere (Keh and Chang, 2006), in which the leading wall correction is O(l 3 ) and l for this case is the ratio of the sphere radius to the distance of the sphere center from the wall.…”

“…For the corresponding thermophoretic motion of an aerosol sphere of radius a perpendicular to a large plane wall, a combined analytical-numerical solution was developed by using a boundary collocation method (Keh and Chang, 2006). The results of the wall-corrected thermophoretic mobility of the sphere (normalized by that given by Eq.…”

“…Later, the thermophoretic motions of an aerosol sphere in a spherical cavity (Keh and Chang, 1998) and in a cylindrical pore (Lu and Lee, 2003) were also theoretically studied. Recently, the thermophoretic motions of an aerosol sphere parallel (Keh and Chen, 2003) and perpendicular (Keh and Chang, 2006) to one plane wall or to two plane walls at an arbitrary position between them have been investigated by using both a boundary collocation technique and a method of reflections. Exact numerical results and approximate analytical solutions of the wall correction to Eq.…”

Thermophoresis of an Aerosol Particle in a Microtube

“…The thermophoretic motions of a spherical particle parallel and perpendicular to a single plane wall or a pair of plane walls were examined by using the methods of boundary collocation and successive reflections [3,4]. Beyond that, the thermophoresis of a spherical particle in a spherical cavity was also analytically investigated [5].…”

Thermophoresis of axisymmetric aerosol particles along their axes of revolution

“…8 at the particle surface to these distributions to yield where To satisfy the boundary condition 16 exactly along the entire semicircular generating arc of the sphere in a meridian plane would require the solution of the entire infinite array of the unknown constants H n and H n . However, the boundary‐collocation technique37–40 enforces the boundary condition at a finite number of discrete points on the particle's generating arc and truncates the infinite series in Eqs. 7, 9, and 16 into finite ones.…”