Journal of Aerosol Science, Vol.26, No.5, 717-734, 1995
SEMIEMPIRICAL MODEL OF PHOTOPHORETIC FORCES FOR THE ENTIRE RANGE OF PRESSURES
Photophoretic forces can be induced both by differences in the surface temperature T-s and by differences in the thermal accommodation coefficient alpha. It is assumed that the particles are spheres, that either a difference Delta T-s or Delta alpha is present, and that the distribution of both quantities is rotationally symmetric (T-s about the direction of incident light, alpha 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) = Phi(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 = Phi B-1 and its pressure dependence are rigorous for the free molecule and continuum limits. For intermediate pressures, the function Phi(p) is constructed according to Hettner's interpolation method which is found to be a good representation of available experimental data. Whereas Phi(p) is common to both types of photophoretic forces, B-1(p) is specific, leading to different force-pressure relationships for Delta T-s- and Delta alpha-forces. These results are discussed in the light of available experimental data.