Kolmogorov-Hinze scales in turbulent superfluids

When a two-component mixture of immiscible fluids is stirred, the fluids are split into smaller domains with more vigorous stirring. We numerically investigate the sizes of such domains in a fully-developed turbulent state of a two-component superfluid stirred with energy input rate $\epsilon$. For the strongly immiscible condition, the typical domain size is shown to be proportional to $\epsilon^{-2/5}$, as predicted by the Kolmogorov-Hinze theory in classical fluids. For the weakly immiscible condition, quantum effects become pronounced and the power changes from $-2 / 5$ to $-1 / 4$.