Semi-empirical model of photophoretic forces for the entire range of pressures

Abstract Photophoretic forces can be induced both by differences in the surface temperature T s and by differences in the thermal accommodation coefficient α. It is assumed that the particles are spheres, that either a difference ΔT s or Δα is present, and that the distribution of both quantities is rotationally symmetric ( T s about the direction of incident light, α about an axis fixed to the particle). Then, the photophoretic force F as a function of pressure p is described for both types by the expression F ( p ) = Φ ( p ) B 1 ( p ) which covers the entire range of p . A key to this is the introduction of the temperature T a in the gas next to the surface in place of the surface temperature T s . There, B 1 is the first-order coefficient of a Legendre expansion of T a . The derivation of the expression F = ΦB 1 and its pressure dependence are rigorous for the free molecule and continuum limits. For intermediate pressures, the function Φ ( p ) is constructed according to Hettner's interpolation method which is found to be a good representation of available experimental data. Whereas Φ( p ) is common to both types of photophoretic forces, B 1 ( p ) is specific, leading to different force-pressure relationships for ΔT s - and Δα-forces. These results are discussed in the light of available experimental data.