Numerical investigation of surface level instability due to a tube in a vibrating bed of powder

We investigate numerically surface level instability originally found in experiments when a tube is injected into a vibrating bed of powder. It turns out that a thicker (thinner) tube makes the surface level inside the tube higher (lower) than the surface level outside the tube. With a fixed acceleration amplitude of vibration, the surface level inside the tube becomes higher as the amplitude of vibration increases, which can be explained by considering the dependence of flow patterns upon control parameters.