Concentration effects on photophoresis of aerosol spheres

The photophoretic motion of a homogeneous suspension of identical spherical particles of arbitrary thermal conductivity and surface properties exposed to a radiative flux is considered under conditions of small Knudsen, Reynolds, and Peclet numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of energy and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the photophoretic velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as monotonically decreasing functions of the non-vanishing volume fraction of the particles. The normalized photophoretic velocity increases with an increase in the relative conductivity of the particles for a given particle concentration.