Impurities in inelastic Maxwell models

Transport properties of impurities immersed in a granular gas undergoing homogenous cooling state are studied. The results are obtained from the Boltzmann-Lorentz kinetic equation for inelastic Maxwell models in d dimensions. The kinetic equation is solved by means of the Chapman-Enskog method up to first order in the density gradient of impurities. The mass and heat fluxes associated with impurities are determined and the corresponding transport coefficients are identified. Both transport coefficients (diffusion and Dufour coefficients) are exactly obtained in terms of the coefficients of restitution for the impurity-gas and gas-gas collisions as well as the ratios of mass and diameters. The results are compared with those obtained for inelastic hard spheres in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows good agreement between both interaction models, especially in the case of the diffusion coefficient.