Experiments on the thermophoretic force on particles in the transition regime of rarefied flows: An extension to diatomic gases

In a non-isothermal flow, small particles experience a force in the opposite direction of the thermal gradient, known as thermophoresis, which can become dominant in rarefied conditions. In the transition regime, where the mean free path of gas molecules, λ, is comparable to the particle size, r, the thermophoretic force is not well understood. The Knudsen number defines the rarefaction and is given by Kn = λ/r. Analytical predictions in the transition regime (0.1 ≲ Kn ≲ 10) are limited to monatomic ambient gases, while in many applications the gas is polyatomic. The force on a particle is the result of a statistical accumulation of momentum exchange due to many molecule-particle collisions. For a diatomic gas, we assume validity of an orientation-averaged approach to evaluate the force on a particle, which allows the use of monatomic models for the drag and thermophoretic force on the particle. To explore the feasibility of this approach, we conducted experiments to measure the thermophoretic force in the transition regime with nitrogen as an ambient gas. The force is determined by measuring the settling velocities of microparticles under rarefied conditions with a vertical thermal gradient in the gas. By measuring the drag force, we found a momentum accommodation coefficient of 0.96 ± 0.08. Subsequently, the thermophoretic force is measured over the entire transition regime and beyond (0.14 ≲ Kn ≲ 35). In the free-molecular regime, using an analytical monatomic model, we find a proxy of the energy accommodation coefficient with value 1.18 ± 0.01.