Influence of concentration on thermophoresis of spherical aerosol particles within a Brinkman medium

Abstract

Abstract We are examining the thermophoretic movement of a uniform mixture of spherical aerosol particles, all with the same properties, as they are situated within a porous material. These particles can have various thermal conductivity and surface characteristics. This analysis focuses on situations where the Péclet and Reynolds numbers are small. The influence of particle interactions is carefully considered by using a unit cell model, a well-established method known for its accurate predictions in the context of sedimentation for monodisperse suspensions of spherical particles. The porous medium is represented as a Brinkman fluid characterized by a Darcy permeability, which can be determined directly from experimental observations. This medium is considered to be uniform and isotropic, and the solid matrix is in thermal equilibrium with the fluid flowing through the voids of the medium. The Knudsen number is assumed to be low, enabling the description of fluid flow through the porous medium using a continuum model that includes temperature jump, thermal creep, frictional slip, and thermal stress slip at the aerosol particle’s surface. The conservation equations for energy and momentum are individually tackled within each cell. In this model, each cell represents a spherical particle enclosed by a concentric shell of surrounding fluid. The thermophoretic particle migration velocity is determined across different cases. We derive analytical expressions for this average particle velocity, expressing it in terms of the particle volume fraction. It is observed that different cell models yield somewhat varied results for particle velocity. Generally, with a fixed permeability parameter characterizing the porous medium, an increase in the thermal stress slip coefficient tends to decrease the normalized thermophoretic velocity across the different cell models. The results are in good agreement with the available data as documented in the existing literature. Additionally, a parallel examination of aerosol sphere sedimentation is provided.