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

Photophoretic forces can be induced both by differences in the surface temperature Ts and by differences in the thermal accommodation coefficient α. It is assumed that the particles are spheres, that either a difference ΔTs or Δα is present, and that the distribution of both quantities is rotationally symmetric (Ts 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) B1 (p) which covers the entire range of p. A key to this is the introduction of the temperature Ta in the gas next to the surface in place of the surface temperature Ts. There, B1 is the first-order coefficient of a Legendre expansion of Ta. The derivation of the expression F = ΦB1 and its pressure dependence are rigorous for the free molecule and continuum limits. For intermediate pressures, the function Φ (p) is constructed according to Hettnerʹs 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, B1(p) is specific, leading to different force-pressure relationships for ΔTs- and Δα-forces. These results are discussed in the light of available experimental data.