Hydrodynamic theory of wet particle systems
Sudeshna Roy is a PhD student in The Multiscale Mechanics Group. Her supervisor is Stefan Luding from the faculty Engineering Technology.
External forces lead to granular flow under the condition that the applied shear stress reaches the yield (shear) stress while an(other) 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. The velocity profiles exhibit tails that decay as an error function.
In partially saturated systems, in the pendular regime, the formation of liquid bridges between particle pairs leads to the development of microscopic tensile forces, resulting in cohesion at macroscopic scale. For this, macroscopic quantities consistent with the conservation laws of continuum theory are obtained by time averaging and spatial coarse graining of the discrete constituents. Initial studies involve understanding the effects of liquid content and liquid properties on the macroscopic quantities. One research goal is to understand the essential phenomena and mechanisms, which determine the rheology of dry and wet granular flow under a different complex conditions. The rheology is described in terms of different dimensionless numbers that relate the time scales of significant phenomena, namely, the time scales related to confining pressure tp, shear rate tγ̇, particle stiffness tk, gravity tg and cohesion tc, respectively. Those phenomena collectively contribute to the rheology, entering as multiplicative corrective functions (that turn out to be first order linear). Thus, 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. The macroscopic torque measured at the walls, which is an experimentally accessible parameter, is predicted from simulation results and from the model in dependence on the steady state cohesion.
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 of the interstitial liquid. This can strongly change the materials' bulk behavior. I study the transients of this liquid re-distribution, using the Discrete Element Method (DEM) for different initial wetting conditions. The liquid is then re-distributed under shear. For small shear strain, the interstitial liquid is locally re-distributed to a quasi-steady state almost independent of the initial condition, while for larger shear strain, liquid is transported diffusively away from the shear zone. It is observed in earlier studies that depletion of liquid is observed in the shear band during shear. A front of high density of liquid content is observed moving outwards to the tails of the shear band, demarcating the sheared depleted zone from the relatively saturated zone. This front is propagating towards the boundaries, possibly drying out the entire system, but the boundaries in the long run. This 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 a 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. The novel experimental technique used is a combination of Particle Tracking Velocimetry (PTV) and Coarse Graining (CG) to obtain continuum velocity fields of granular flow.
