Photophoresis on particles hotter/colder than the ambient gas in the free molecular flow

•New approximation for longitudinal photophoresis for non-equilibrium.•To be used for high intensities (e.g. laser irradiation) or optically thin gases.•Best statistical properties compared to existing approximations.

Aerosol particles experience significant photophoretic forces at low pressure. Previous work assumed the average particle temperature to be very close to the gas temperature. This might not always be the case. If the particle temperature or the thermal radiation field differs significantly from the gas temperature (optically thin gases), given approximations overestimate the photophoretic force by an order of magnitude on average with maximum errors up to more than three magnitudes. We therefore developed a new general approximation which on average only differs by 1% from the true value.