468a A Kinetic-Based Model for a Non-Isothermal Granular Gas with Mono- and Bi-Dispersed Particles

Alberto Passalacqua, Department of Chemical and Biological Engineering, Iowa State University, 2114 Sweeney Hall, Ames, IA 50011-2230, Prakash Vedula, School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019-0601, Christine M. Hrenya, Chemical and Biological Engineering, University of Colorado at Boulder, Boulder, CO 80309-0424, and R. O. Fox, Department of Chemical & Biological Engineering, Iowa State University, 2114 Sweeney Hall, Ames, IA 50011-2230.

A granular gas between two stationary Maxwellian walls at different temperatures is studied by means of numerical simulations of the Boltzmann equation with a hard-sphere collision kernel for mono- and bi-dispersed particles.

The behaviour of a granular gas in these conditions is influenced by the thickness of the wall Knudsen layers: if its thickness is comparable to the characteristic length scale of the system, the traditional description based on the hydrodynamic equation is invalid, and it is necessary to account for the presence on the Knudsen layers.

In this work the system is described by solving the full Boltzmann equation using a third-order quadrature-based moment method (Fox, 2008).

These results are compared with the predictions of molecular dynamics simulations of an equivalent system with finite-size particles (Galvin et al., 2007; Hrenya et al., 2008). Results for constitutive quantities such as the heat flux and the stress tensor are provided, and show the capability of the quadrature-based approach to predict them in agreement with the molecular dynamics simulations.

Fox, R. O., A quadrature based third-order moment method for dilute gas-particle flows, Journal of Computational Physics, 227, 6313 – 6350, 2008.

Galvin J. E., Hrenya C. M., Wildman R. D., On the role of the Knudsen layer in rapid granular flows, Journal of Fluid Mechanics, Vol. 585, pp. 73 – 92, 2007.

Hrenya C. M., Galvin J. E., Wildman R. D., Evidence of higher-order effects in thermally-driven, rapid granular flows, Journal of Fluid Mechanics, 598, 429 – 450, 2008.

Vedula, P., Fox, R. O., A quadrature-based method of moments for solution of the collisional Boltzmann equation, Journal of Statistical Physics, Submitted, 2008.