Experiments on the thermophoretic force on particles in the transition regime of rarefied flows

Thermophoresis is a force exerted on particles in nonisothermal flows, acting opposite to the thermal gradient and potentially dominant in rarefied conditions. This force is not well understood in the transition regime, where the mean-free path of gas molecules, λ, is comparable to the particle radius, r. The rarefaction is quantified by the particle Knudsen number, Kn=λ/r. To determine the thermophoretic force in the transition regime, we conducted experiments by measuring the settling velocities of spherical melamine particles in argon or helium under rarefied conditions, where a thermal gradient was applied. The ratio of the thermal conductivities of the particle to the gas Λ is 21 for argon and 2.4 for helium with respect to the melamine particles. Drag force measurements resulted in momentum accommodation coefficients of 0.9±0.1 and 1.0±0.1 for argon and helium, respectively. Subsequently, the thermophoretic forces were measured in the range 0.07≲Kn≲60 for argon and 0.05≲Kn≲35 for helium. The experimental data were compared with several theoretical predictions of the thermophoretic force covering the transition regime. An important conclusion is that the energy accommodation coefficient, α_{e}, cannot be neglected when predicting the thermophoretic force, as it is found that the approximation of α_{e}≈1 is seldom accurate.