Hydrodynamic theory of wet particle systems

Abstract

External forces lead to granular flow under the condition that the applied shear stress reaches the yield (shear) stress while another stress must be maintained for continuous flow in steady state. Most studies in granular physics focus on dry granular materials and their flow rheology. However, wet granular materials are ubiquitous in geology and many real world applications where interstitial liquid is present between the grains. There are several proposals for flow rules of dry and wet granular materials available in the literature. These flow rules differ in complexity and in the number of parameters, which are combined in the equations. The main focus areas of my research are (i) the formulation of suitable constitutive equations for the hydrodynamic density-stress-strain relations, specifically for wet granular materials, (ii) the deduction of the constitutive equations from discrete element simulations, and (iii) the validation of the micro-macro transition with numerical, theoretical and experimental results. The geometrical set-up of split-bottom shear cell used in my research is most appropriate for assessing the shear band originating from the split position that widens near the free surface. My research proposes a modified generalized flow rule/rheology to close the fundamental conservation laws for mass and momentum. Subsequently, a correlation is developed between the micro parameters and the {steady state cohesion in the limit} of very low confining pressure. Another aspect of studying unsaturated granular media is the movement of interstitial liquid due to the rupture of existing and formation of new liquid bridges. Shearing a wet granular system causes a re-distribution and transport of the interstitial liquid. The liquid transport can be modeled by a diffusion equation with a space-dependent diffusive coefficient in the split bottom geometry. Alternatively, it is shown here that this is an advective-diffusive process with constant diffusivity coefficient and a space-dependent drift, when transformed to an appropriate set of variables that can be solved analytically. The final chapter of this thesis concerns the experimental work exploring the surface flow profile for different dry and wet granular materials.