  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 stirred two-component superfluid in
a fully-developed turbulent state 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 $-1 / 4$. The domain
size scaled by the interface thickness collapses into a universal line.
