Photophoresis of aerosol particles with nonuniform gas–surface accommodation in the free molecular regime

Abstract

The problem of calculating the photophoretic force acting on an aerosol particle, with nonuniform distributions of accommodation coefficients over the particle's surface in a rarified equilibrium gas medium in the free molecular regime, is considered within the framework of perturbation theory, using the assumption that the variations of accommodation coefficients are sufficiently small. In general, the expression for the force acting on a convex particle involves four contributions. The energy accommodation coefficient and the radiometric accommodation coefficient for normal momentum are used.The formulae for calculating all four contributions to the photophoretic force are presented for a uniform spherical particle with finite thermal conductivity and a nonuniform axisymmetric distribution of accommodation coefficients over its surface. According to our estimates, the photophoretic force is defined with good accuracy by only two contributions: the “delta-alpha” force and “delta-T” force. The other contributions are small corrections to these two prevailing forces of order 1% or less.The ratio between the “delta-alpha” and “delta-T” forces depends on the particle size, Knudsen number, and the differences in the accommodation coefficients. For micron-sized spherical particles, the photophoretic “delta-alpha” force exceeds the “delta-T” force, and also exceeds gravity if the variation in the radiometric accommodation coefficient over the particle's surface is more than 0.055. Thus, levitation of particles in the Earth's stratosphere is possible due to gravito-photophoresis. For centimetre-sized particles, the “delta-T” force is a few orders of magnitude larger than the “delta-alpha” force due to the influence of IR radiation on the particles' temperature.