Extended hydrodynamic equations for binary granular mixtures

¹ Department of Sciences, Mathematics and Education, St. Joseph University In Tanzania, P.O Box 11007, Dar es Salaam, Tanzania
² Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O, Bangalore 560064, India

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Published online: 1 December 2025

Abstract

The derivation of 2 × 14-moment equations for a dilute binary granular mixture is outlined, following Grad’s moment method. In addition to the mass, momentum and energy equations for each species, the deviatoric stress tensor, the heat flux vector and the fully contracted fourth moment are treated as separate hydrodynamic fields for each species, with the last field variable is known to be important for granular gases even at the leading-order for the homogeneous cooling state of a granular gas. The expression for the nonequilibrium velocity distribution function of each species is obtained by employing an Hermite expansion in terms of fourteen hydrodynamic fields around the species Maxwellian. The production terms of each hydrodynamic equations have been calculated by including the respective quadratic-order nonlinear terms in contrast to most previous works that evaluated source terms by retaining only linear terms. The extended hydrodynamic equations are then used to analyse the homogeneous cooling state of granular mixtures.