October 16, 2025 -- October 16, 2025
Student : Gautam Vatsa- Ph.D, Chem. Engg. IISc.
Date & Time: Thursday-16th -Oct. 2025 at 4 PM.
Venue: Seminar Hall, Chemical Engg.
Continuum Modeling of Slow Granular Flow.
Granular materials are central to both natural and industrial processes—they underlie geophysical hazards such as landslides and debris flows and are fundamental to diverse engineering applications ranging from soil mechanics and powder transport to food processing and pharmaceutical manufacturing. Despite their ubiquity, predicting and optimizing granular flows remain a formidable challenge. Unlike conventional fluids or solids, the macroscopic behavior of granular assemblies emerges from discrete particle interactions, leading to complex phenomena such as flow localization, segregation, and jamming that defy classical continuum descriptions. Understanding slow granular flow is particularly critical for improving the efficiency and safety of industrial processes such as hopper discharge, silo storage, and screw feeding, as well as for assessing the stability of geophysical materials.
Granular materials consist of large, nearly rigid particles whose collective motion is non-Brownian. Their collective flow behavior spans a wide range of regimes for which no single governing framework exists. At one extreme, rapid granular flows are dominated by collisional momentum transfer and are effectively described by kinetic theories for dissipative particles. At the other, slow or quasistatic flows involve enduring contact networks and correlated particle motion, where inertia is negligible. Continuum modeling in this slow-flow regime has been especially challenging.
Slow granular flows exhibit distinctive features absent in conventional fluids—rate independence (stress insensitive to strain rate), shear localization, and shear dilatancy, the volume change that accompanies shear deformation. Capturing these behaviors within a continuum framework has remained an open problem. Classical rate-independent plasticity, such as that used in critical state soil mechanics, incorporates rate independence but suffers from kinematic indeterminacy. Recent non-local continuum models have overcome this limitation by introducing spatial derivatives of kinematic quantities, but most assume incompressibility and thus cannot account for dilatancy. The non-local model developed by Dsouza and Nott (2020) overcomes both issues by extending critical state plasticity to incorporate dilatancy and remove indeterminacy. Prior to this work, the model had been validated only against discrete element (DEM) simulations of steady plane shear flow.
This thesis investigates slow granular flow using the non-local model of Dsouza and Nott. First, the model is validated against experimental data from steady, axisymmetric flow in a two-dimensional Couette rheometer containing bidisperse granular material. The model’s steady-state predictions show excellent agreement with measured velocity and packing fraction fields—constituting the first experimental validation of this non-local constitutive model. To elucidate the role of dilatancy within the model, transient simulations are conducted. A physically motivated boundary condition for the dilation rate normal to solid boundaries is proposed and later used in more complex two-dimensional simulations.
The thesis then examines the transient evolution of dilatancy-driven secondary flows in a slowly sheared granular medium. DEM studies have shown that the coupling of dilatancy with gravity can generate system-spanning vortices in plane Couette flow with a free surface. Initially, computations are performed with a fixed top boundary and prescribed mean volume fraction. The model successfully reproduces the emergence and qualitative evolution of secondary vortices, demonstrating that shear-induced dilatancy alone can drive such flows even under constant-volume conditions. The analysis is subsequently extended to free-surface boundary conditions, where the model captures dynamic surface deformation—representing, to our knowledge, the first continuum simulations that simultaneously resolve all velocity components and density in such a system.
Finally, the model is applied to the slow flow of dry, cohesionless granular materials in screw feeders. Experiments (PRN Lab) reveal that the volumetric discharge rate depends on the screw’s pitch-to-diameter ratio. A prior macroscopic analysis by Gupta (2021) used integral force and torque balances under a plug-flow assumption to identify an optimal pitch to diameter ratio for a frictionless screw. Here, the governing conservation and momentum equations are derived rigorously in a helical coordinate system aligned with the screw geometry. The resulting analysis recovers Gupta’s prediction in the frictionless limit and clarifies the assumptions under which their simplified model holds. Incorporating a minimal constitutive law based on critical state plasticity and solving the equations numerically confirms that the plug-flow solution indeed emerges asymptotically in this limit.
In summary, this thesis advances the continuum modeling of slow granular flow by:
1. Establishing the non-local model of Dsouza and Nott as a robust constitutive framework validated against both experiments and complex transient flows, and
2. Extending continuum modeling to the helical geometry of screw feeders—providing new physical insights into a widely used industrial process.