Abstract

A collection of discrete macroscopic particles which dissipate energy during collisions among themselves is termed as a granular material. Granular materials are ubiquitous in nature and industry alike. They occur in all shapes and sizes ranging from few microns to several hundred kilometres. Sand dunes, debris flow, asteroid belt, dust storm, gravels, cement, food grains, sugar, capsules, pills are some typical examples of granular materials. Depending on the energy supplied, they can exist in the solid, liquid or gaseous state. Due to their dissipative nature, granular materials exhibit several interesting—and often counter-intuitive—phenomena. At the same time, this very feature of granular materials poses many difficulties while modelling processes in granular materials due to the non- conservation of energy.

The present work considers the gaseous state of granular materials, for which, analogous to molecular gases, mathematical tools can be developed within the framework of kinetic theory. In this talk, I shall present my recent work on Grad moment method for modelling a dilute granular gaseous flow of d-dimensional smooth, identical, inelastic spheres interacting with Maxwell interaction potential—referred to as inelastic Maxwell molecules (IMM). Here d = 2 means disk flows while d = 3 means sphere flows. This work is a somewhat generalization of my previous work to arbitrary dimensions. To assess the capabilities of the derived models for IMM , the homogeneous cooling state of a freely cooling granular gas of IMM and its stability to small perturbation is studied. Moreover, the Navier–Stokes level transport coefficients are also obtained from the moment equations and it has been found that the transport coefficients obtained in this work agree exactly with those obtained in previous studies.