Nonlinear hydrodynamics and rheology of granular and gas-solid suspensions

Abstract

Granular matter is a collection of large number of solid particles where the particle size ranges from 1mm to meters (Saturn’s ring) and it is found everywhere in nature (avalanche, debris flows, Planetary rings, etc.) as well as in industry (Jackson 2000; Rao & Nott 2008). At rest the ‘dry’ granular materials (for which the effect of interstitial fluid can be neglected) behave like a solid, having a compressive strength but no tensile strength, and hence dubbed a ‘peculiar’ solid. On the other hand, a collection of particles can flow like a liquid as in an hour-glass or behave like a gas under strong shaking (Forterre & Pouliquen 2008; Rao & Nott 2008). In the case of a granular gas (Campbell 1990; Goldhirsch 2003; Brilliantov & Pöschel 2004), the particle collisions are inelastic, leading to the dissipation of the kinetic energy of colliding particles. The inelastic dissipation is known to be the progenitors of many interesting properties of a granular fluid, and is also responsible for the loss of ‘microscopic’ reversibility at the level of Liouville and Boltzmann equations that calls for non-standard statistical mechanics (Jenkins & Richman 1985a; Sela & Goldhirsch 1998; Garzó & Dufty 1999; Lutsko 2005; Rongali & Alam 2014) to develop coarse-grained theories for flowing granular matter. Because of its rich properties it is still an interesting and unexplored topic of research.