Thermophoresis of nanoparticles hotter/colder than the surrounding dilute gases

Aerosol particles suspended in a diluted gas with non-uniform temperature distribution are expected to experience a thermophoretic force. In theoretical treatment of thermophoresis, it is usually assumed that the particle temperature is equal to the surrounding gas temperature. However, this might not always be the case. In some particular applications, the particle temperature can significantly differ from the gas temperature. In the present paper, we theoretically investigate the effect of the particle temperature on the thermophoresis of nanoparticles in the free molecule regime. Theoretical formulas for the thermophoretic force and thermophoretic velocity are obtained based on the gas kinetic theory. As examples, a spherical Ag nanoparticle suspended in a dilute He gas is considered, and the Rudyak–Krasnolutski potential is employed to model the gas–particle interaction. It is found that the influence of the particle temperature on the thermophoresis of nanoparticles can be significant. With increasing particle size, the error due to the equal gas–particle temperature assumption can be neglected.