Two-dimensional dam break flows of Herschel–Bulkley fluids: The approach to the arrested state

Dam break flows of viscoplastic fluids are studied theoretically using a Herschel–Bulkley constitutive law and a lubrication model of the motion. Following initiation these fluids are gravitationally driven out of the lock in which they had resided. Their motion is eventually arrested because they exhibit a yield stress and they attain a stationary state in which the gravitational forces are in equilibrium with the yield stress. We study the evolution of these flows from initiation to arrest by integrating the equations of motion numerically. We demonstrate that the final arrested state is approached asymptotically and find analytically that the perturbations to the final state decay algebraically with time as 1/tn1/tn, where n is the power index of the Herschel–Bulkley model.