Flow and structure of dense granular materials

Abstract

Granular materials are frequently encountered in our daily lives and are widely processed forms of matter in various industries. Despite decades of research, the mechanical behavior of granular materials is not well understood. This thesis focuses on two problems in granular materials, flow in a cylindrical Couette geometry, and emergence of the force network. Recent experiments on granular materials sheared in a cylindrical Couette device revealed a puzzling anomaly, wherein all components of the stress rise nearly exponentially with depth. In this thesis, using particle dynamics simulations and imaging experiments, we show that the stress anomaly arises from a remarkable vortex flow. For the entire range of fill heights explored, we find a single toroidal vortex that spans the entire Couette cell, and whose sense is opposite to the uppermost Taylor vortex in a fluid. In addition, we show that the vortex is driven by a combination of shear-induced dilation, a phenomenon that has no analogue in fluids and gravity flow. We also find that the secondary flow exhibits interesting features like dual vortices in flow conditions where the inertia of grains is relevant. Dilation is a well-known characteristic of a flowing granular medium, but not adequately represented in existing models. This thesis makes a case for properly incorporating cross-streamline dilation in constitutive models. In the second part of this thesis, we focus on force transmission in amorphous materials. Force transmission in amorphous materials like grains, suspensions, emulsions, and foams is primarily characterised by a complex network of inter-particle contact forces called the force network. Important transport and mechanical properties of these forms of matter have been experimentally shown to be associated with the underlying force network. The origin and features of the force network has remained elusive. By defining connectivity in particle packings based on linearity of particle contacts, we show the existence of a criticality. The paths with critical linearity are shown to be mechanically important and constitute the strong force network observed in experiments. The origin of this criticality is shown to be a feature that emerges out of geometric constraints inherent to particle packings. We explain how this critical feature helps us understand particulate matter better, like the stress dip in granular piles and Janssen effect in silos. With a simple path linearity dependent random walk model, we provide insights about force transmission in amorphous materials.