Dynamics of cavitation bubbles near granular boundaries

We study the dynamics of a cavitation bubble near beds of sand of different grain sizes. We use high-speed imaging to observe the motion of the bubble and the sand for different values of the stand-off parameter gamma (dimensionless bubble-boundary distance) between 0.3 and 5.3. Compared with a rigid boundary, we find that a granular boundary leads to bubbles with shorter lifetimes and reduced centroid displacements. Above gamma approximate to 1.3, the behaviour of the bubble is almost independent of the granularity of the sand. When the stand-off parameter lies between 0.6 and 1.3, a mound of sand develops beneath the bubble, which can force the latter to assume a conical shape as it collapses. For gamma less than or similar to 0.6, the bubble develops a bell-shaped form, leading to the formation of thin and surprisingly fast micro-jets (v(jet) > 1000 m s(-1)). Moreover, between gamma approximate to 1.3 and gamma approximate to 0.3, granular jets erupt from the sand surface following the bubble collapse. We additionally develop a simple numerical model, based on the boundary integral method, to predict the dynamics of a cavitation bubble near a bed of sand, which we replace by an equivalent liquid. The simulations are remarkably consistent with experimental observations for values of gamma down to 1.3. We also show how the anisotropy parameter a dimensionless version of the Kelvin impulse, can be adapted for the case of a nearby bed of sand and predict the displacement of the bubble centroid for zeta less than or similar to 0.08.