Thermophoresis of an Aerosol Sphere with Chemical Reactions

Abstract

The thermophoretic motion of a spherical aerosol particle undergoing a chemical reaction in a uniformly prescribed temperature gradient is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The chemical reaction taking place within the particle can be either endothermic or exothermic. The Knudsen number is assumed to be small (of the order 0.1) so that the fluid flow is described by a model with a thermal slip, a temperature jump, and a frictional slip at the surface of the particle. The energy and momentum equations governing the system are solved analytically, and explicit expressions for the thermophoretic velocity of the particle are obtained. Results of the effect of the chemical reaction inside the particle on its thermophoresis are presented for various distributions of the composition-dependent factor or heat generation parameter of the chemical reaction as well as the relative thermal and surface properties of the aerosol sphere. When the composition-dependent factor is not a function of position, the thermophoretic velocity of the particle is enhanced when the reaction is exothermic and reduced when the reaction is endothermic. In general, the effect of the chemical reaction on the thermophoretic velocity can be significant in appropriate situations.

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

“…This thermal creep phenomenon (Maxwell 1879) provides a mechanism in the slip-flow regime for the thermophoresis of aerosol particles and thermoosmosis of bounded gases with the Knudsen number l 6 a of the order 0.1, where a is the linear dimension of the particles or boundaries and l is the mean free path of the gas molecules. Thermophoresis (viz., the Soret effect), which is the particle motion caused by a bulk-gas temperature gradient against its direction (i.e., from hot to cold), plays an important role in many practical applications such as aerosol sampling, air cleaning, microelectronic manufacturing, scale formation on heat exchanger surfaces, nuclear reactor safety, modified chemical vapor deposition, and catalysis-driven plasmonic nanomotors (Balsara and Subramanian 1987;Williams and Loyalka 1991;Chang and Keh 2010a,b;Hsieh and Keh 2012;Sagot 2013;Guha and Samanta 2014;Wu et al 2015;Bhusnoor et al 2017;Qin et al 2017).…”

Thermophoretic Motion of a Cylindrical Particle with Chemical Reactions

“…Extending an early analysis on the thermophoresis of an aerosol sphere with a chemical reaction in its interior but without the effect of thermal stress slip at its surface (Hsieh and Keh 2012), we obtain a formula corresponding to Equation (20) for the thermophoretic velocity of a sphere of radius a with the effect of thermal stress slip at the particle-gas interface as…”

“…[32] R 1 (1) are given by Equation (13) in Hsieh and Keh (2012) and generally smaller than those for a corresponding aerosol cylinder. Both Equations (23) and (32) show that L increases linearly with the thermal stress slip coefficient C h (and thermal creep coefficient C s ) under an otherwise specified condition.…”

“…Recently, the thermophoresis of an aerosol sphere undergoing chemical reactions in an imposed temperature gradient is analyzed with the consideration of the effects of temperature jump, thermal creep, and frictional slip at the particle surface (Hsieh and Keh 2012). When an endothermic/exothermic reaction takes place within the particle, a higher reaction rate with more heat consumption/generation on its hot side than on its cold side leads to a reduction/enhancement of its thermophoretic velocity.…”