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 ε. For the strongly immiscible condition, the typical domain size is shown to be proportional to ε^{-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.
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