SELF-DIFFUSION IN A DILUTE GAS UNDER HEAT AND MOMENTUM TRANSPORT

Diffusion of tagged particles in a dilute gas in a stationary state with temperature and velocity gradients (planar Couette flow) is analyzed. The results are obtained from a kinetic model for a multicomponent gas constructed in the same spirit as in the Bhatnagar-Gross-Krook equation for a single gas. The kinetic equation for the velocity distribution function of the tagged particles is solved by using a Chapman-Enskog-like expansion around the steady-Couette-flow state. Up to first order in the concentration gradient of tagged particles, explicit expressions for the self-diffusion coefficient and the partial pressure have been derived. Both quantities are nonlinear functions of the shear rate. In addition, the distribution function of tagged particles is explicitly obtained. It exhibits a highly nonlinear dependence on both the shear rate and the thermal gradient. In the absence of shear rate, self-diffusion in pure heat flow is also considered with more detail.