Gautam Vatsa

Continuum Modeling of Shear dilatancy driven secondary flow in granular media

This study focuses on slow granular flows and demonstrates the ability of the non-local constitutive model by Dsouza and Nott (2020, J. Fluid Mech.) to capture shear dilatancy-driven secondary flow in granular media—a phenomenon observed in the discrete particle simulations of Krishnaraj and Nott (2016, Nat. Commun.) but elusive to other constitutive models. Shear dilatancy, first observed by Sir Osborne Reynolds, refers to the density change in a granular medium due to shear. While most constitutive models treat granular flow as incompressible and neglect dilatancy, the non-local model by Dsouza and Nott uniquely incorporates this effect, capturing the density variations that are critical to granular flow behavior. Previously validated against DEM simulations of plane Couette flow (Dsouza and Nott, 2020, J. Fluid Mech.) and laboratory experiments on cylindrical Couette flow (Vatsa et al., 2024, J. Fluid Mech.), the model is applied here to the more complex scenario of transient 2D plane Couette flow under gravity. The transient flow reveals the mechanism through which secondary flow emerges and transitions to a sustained system-spanning vortex at the steady state. Our result supports the hypothesis of Krishnaraj and Nott (2016, Nat. Commun.) that both shear dilatancy and gravity are essential for sustaining secondary flows. These findings underscore the critical role of dilatancy in continuum models, advancing the theoretical understanding of dense, slow granular flows and providing valuable insights for practical applications.