Research in Rafi Blumenfeld's group

My group's main research interests have focused in recent years on the behaviour of particulate media (PM), consisting of particles sufficiently large to make thermal fluctuations irrelevant, inter-particle forces non-central, energy dissipation on collision relevant, and friction important. Beyond posing a number of fundamental theoretical challenges, understanding the physics of PM is important to a wide range of technological applications and to mitigating natural hazards. Our work involves mainly theoretical and numerical modelling of the following.

• Formulation of a continuum stress field theory
  Current continuum models are empirical and phenomenological and not one explaining how the inter-particle force field, which is often highly non-uniform on the particle scale, is upscaled to a continuum stress field. This is a challenging theoretical and practical problem. Selected publications on it so far are [1-8].



• Flow and structural self-organisation of dense PM
  Dense flow of PM is notoriously difficult to model theoretically, with one difficulty being that slow such flows often generate stagnant regions, aka plugs, which move as large rigid clumps in otherwise fluid media. The conditions for plug nucleation, formation and growth are still not understood. We have been working on the flow equations with and without plugs. Even in the absence of plugs, the evolving structure is driven by the inter-granular forces and, although it is almost always disordered it is nevertheless has typical characteristics. A recent first-principles theory has been constructed, which provides good predictions so far and an astonishing theoretical prediction. Some of our work in this direction is in [9-22].



• Statistical mechanics of PM
  Statistical mechanics is a powerful theoretical formalism to deal with large assemblies of particles even in the absence of thermal fluctuations. It is the ultimate coarse-graining technique from the particle level to equations of state and constitutive properties. In the context of PM, this formalism is based on entropy, i.e. the number of structural and stress configurations that static and quasi-static PM can have. We have derived several important results so far, some of which are in [23-31].