Segregation in a sheared binary mixture of nearly elastic, smooth disks under gravity

Few studies exist on the kinetic theory of mixtures of inelastic disks. Jenkins & Mancini (1987) derived constitutive laws for a dense binary mixture of smooth, nearly elastic disks by assuming a Maxwellian velocity distribution, introducing Enskog’s correction to the collision frequency, and distinguishing between the position of the centers of two colliding disks. Willits & Arnarson (1999) developed a more precise theory using the Revised Enskog Theory derived by van Beijeren & Ernst (1973). They followed the path set by López de Haro et al. (1983) and Jenkins & Mancini (1989) who worked with sphere mixtures. They used the Chapman-Enskog procedure to solve the appropriate kinetic equations and derived explicit expressions for the transport coefficients. Their theory was in remarkable agreement with numerical simulations for systems of moderate densities.