Photophoresis on particles hotter/colder than the ambient gas for the entire range of pressures

• New approximation for longitudinal photophoresis for strong non-equilibrium conditions.
• To be used for high intensities (e.g. laser irradiation) or optically thin gases.
• Comprises the entire range of pressure.

Small, illuminated aerosol particles embedded in a gas experience a photophoretic force. Most approximations assume the mean particle surface temperature to be effectively the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field strongly differs from the gas temperature (optically thin gases), given approximations for the free molecule regime overestimate the photophoretic force by an order of magnitude on average and for individual configurations up to three magnitudes. We apply the radiative equilibrium condition from the previous paper (Paper 1) – where photophoresis in the free molecular flow regime was treated – to the slip flow regime. The slip-flow model accounts for thermal creep, frictional and thermal stress gas slippage and temperature jump at the gas–particle interface. In the limiting case for vanishing Knudsen numbers – the continuum limit – our derived formula has a mean error of only 4% compared to numerical values. Eventually, we propose an equation for photophoretic forces for all Knudsen numbers following the basic idea from Rohatschek by interpolating between the free molecular flow and the continuum limit.