Predicting Bubble Fragmentation in Superfluids

In classical fluids, the Weber number is a dimensionless parameter that characterises the flow of a multi-phase fluid. The superfluid analogy of a classical multi-phase fluid can be realised in a system of two or more immiscible Bose-Einstein condensates. These superfluid mixtures have been shown to display a wider variety of exotic dynamics than their single component counterparts. Here we systematically study the dynamics of a binary immiscible Bose-Einstein Condensate in two dimensions, where a small bubble of the second component is used to "stir" the first component. We begin by rigorously mapping out the critical velocity for vortex shedding as a function of the size of the bubble, in analogy to the critical velocity of a laser spoon. Observing that the dynamics of the system depend on the initial size and velocity of the bubble, we then show that a dimensionless parameter with the same form as the Weber number accurately predicts the resulting bubble fragmentation.