Shear flow in da Vinci fluids
Working in collaboration with Prof. Rafi Blumenfeld, this project attempted to model horizontal shear flow of granular matter with the da Vinci fluid model, which proposes that the primary mechanism of energy dissipation in a granular fluid is solid friction between infinitesimal layers. The threshold nature of this process - static friction has greater magnitude than dynamic friction - leads naturally to formation of sections of granular fluid that move together as though a solid, known as plugs. We investigated the predictions of this model by formulating the da Vinci fluid equations for a two dimensional system representing an infinite horizontal slab of fluid, bounded by surfaces that can be sheared at some velocity, as shown in the diagram opposite. Through mathematical analysis and construction of a computaitonal solver we were able to investigate how this system evolves in time.
Further to these predictions we considered how the density of the fluid may vary with fluid velocity and pressure, how the effective frictional coefficient between layers may depend on this variation in density, and how such relationships might affect formation and splitting of plugs.