Hydrodynamic Coarsening of Binary Fluids

By suitable interpretation of results from the linear analysis of interface dynamics, it is found that the hydrodynamic growth of the size $L$ of domains that follow spinodal decomposition in fluid mixtures scales with time as $L\sim t^{\alpha }$, with $\alpha =4\mathrm{}/7$ in the inertial regime. The previously proposed exponent $\alpha =2\mathrm{}/3$ is shown to indicate only the scaling of the oscillatory frequency ${\omega }^{-2\mathrm{}/3}\sim L$ of the largest structures of the system. The viscous dissipation in the system occurs within a layer of thickness $L_d$ that also follows a power law of the form $L_d\sim L^{3/4}$ in the inertial regime. In the viscous regime the growth is linear in time $L\sim t$ and the dissipative region remains constant $L_d\sim L^0$.