Our understanding of the physics and mechanics of materials in particulate, granular, or powder form is still in relative infancy despite intense interest for well over a century. Why are particulate systems proving such a challenge? The answer is quite simple. In fluid and solid state mechanics, it is possible for the most part to use continuum mechanical formalism without recourse to molecular or microstructural physics. With granular dynamics, a universal theory based on continuum mechanics has so far proved illusive because these materials behave neither in an entirely solid-like nor entirely fluid-like way. For example, the simple everyday operation of getting salt granules or powdered spices out of a shaker requires a transition from static granular packed bed to a fluid stream carrying particles! It is possible to model the static bed using soil mechanics and the fluid/particle system using complex fluid mechanics, but how do we model the transition from the solid-like state to the fluid-like state? Similar arguments could be advanced for snow avalanches and geological landslides, where sudden transitions from solid-like to fluid-like state are the trigger for many, often unforeseen, human disasters.
In process industries worldwide, the operations involving storage, handling, and transport of granular solids account for well over a third of the capital costs and well over half of all the operating costs. Additionally, the physics and mechanics of granular matter has become the pivot for mesoscopic modeling of nano-matter and bio-matter. Examples include colloidal suspensions, vapor plasmas used to manufacture nano-powder compacts and coatings, and biological fluids, such as blood or protein solutions.
A convenient starting point is to assume an assembly of perfect spheres moving randomly around each other. This approach follows closely the prescription of widely applied theories including the kinetic theory of gases and molecular theories of fluid density and viscosity. It is then possible to advance new theories describing the ‘granular state’ by making use of the entire mathematical toolkit developed for these earlier theories. The ‘rapid granular flow theory’ has been used to model simple granular flows down inclined chutes and in rotating drums to reasonable, but varying, degrees of agreement with experiment. Or, starting with a static packed bed of spherical particles and initiating a quasi-static, slow flow, it is possible to arrive at assembly equations of flow. Such models are used to describe sliding, rotational, and spin interactions that evolve during enduring contacts between particles.
Irrespective of whether a theoretical approach uses solid-like or fluid-like reference states, the question still remains as to the relevance of perfect sphere assemblies to the dynamics of real granular matter. How many powder formulations, natural granular materials, and biomaterials come with spherical particles? Salt, sand, clay, many minerals, sugar, coffee, and grains of wheat are decidedly non-spherical, while others are also significantly angular in shape. Many man-made foods and pharmaceutical products also show significant variations of particle shape and size. Furthermore, many of the process routes to produce nano or bio-matter results in structured materials with nonspherical building blocks. It is quite clear from these varied examples that perfect spheres are as illusive as ever in real life.
The practicing engineer is immediately put off by the highly mathematical theory base, which only engages with perfect sphere assemblies. In industrial materials handling operations, the engineering solutions then refer to the heuristic, recipe-based, or trial and error-based methods, much to the delight of the experienced consultant who can demand large fees for educating the engineer in the required ‘black art’! In hi-tech applications, the geometric properties of the particles are often glossed over in the designing and manufacturing of complex materials. Would an angular nonspherical particle rotate as much as a perfect sphere when a solid bulk matrix is deformed? Would collisional contacts occur at the same frequency as between perfect spheres? The theoretical argument is that these geometric differences will be ‘averaged out’ when ensemble mechanical calculations are performed over sufficiently large length scales. I have yet to see a rigorous scientific study validating this gross theoretical supposition, even for an apparently simple application such as the emptying of an hourglass!
If we should expect theory to lead novel technology development and subsequent industrial application, the theoretician must convince the engineer that it is sufficient to use the theories based on perfect sphere assemblies. However, I believe that the budding theoretician is instead expecting to see the innovative engineering of more and more spherical particles, so that a tighter scientific remit can be established between theory and practice. Therein lies a yet to be resolved dilemma of universal proportion!