Hydrodynamic limit Of a binary mixture Of rigid spheres

Abstract

In this paper, we study the hydrodynamic limit of a binary mixture of rigid spheres. When Knudsen numbers of two different species are equal and go to zero, we show formally that the hydrodynamic variables satisfy the compressible Euler and Navier-Stokes equations. Like single species gas, we develop Enskog-Chapman theory up to the second order. It turns out that the macro velocities corresponding to the different spheres are equal and the ratio of the temperatures is the mass ratio of the spheres. However, the macro mass densities satisfy independent conservation laws in the case of the compressible flows. Explicit formulas of viscosity, heat conductivity and heat diffusion coefficient are established in term of particle parameters.