Thermophoresis-Brinkman flow of an aerosol particle within a spherical
cavity

A semi-analytical study is presented for the thermophoretic migration of
a spherical particle located at an arbitrary position in a porous medium
inside a spherical cavity. A uniform applied temperature gradient
parallel to the line connecting the particle and cavity centres. The
porous medium is modeled as a Brinkman fluid with a characteristic Darcy
permeability $K$ that can be obtained directly from the experimental
data. The porous medium is assumed to be homogenous, isotropic and the
solid matrix is in thermal equilibrium with the fluid through the voids
of the medium. The Knudsen number is supposed to be small so that the
fluid flow through the porous medium can be described by a continuum
model with a temperature jump, a thermal creep, a frictional slip and
thermal stress slip at the surface of the aerosol particle. The Reynolds
number of the fluid is assumed to be small enough to justify the use of
the Brinkman equation, which is always satisfied because the aerosol
particle is so small. The P{\’e}clet number for heat
transfer in thermophoresis is also assumed to be small. The
dimensionless thermophoretic velocity and the mobility coefficients are
tabulated and represented graphically for various values of the
permeability parameter, relative thermal and surface properties of the
particle and cavity. Results are in good agreement with the analytical
solution of the particular case of a particle located at the centre of
the cavity.