Light-scattering studies of phase separation in isobutyric acid + water mixtures: Hydrodynamic effects

The growth of droplets in a binary fluid mixture undergoing phase separation has been studied by light scattering. The measurements have focused on the dependence of growth rate on the overall composition of the mixture. For mixtures of the critical composition, there is a crossover: $k_m$, the wave number corresponding to the maximum in the scattering, decreases initially as $t^{-\frac{1}{3}}$ and at long times as $t^{-1\mathrm{}}$. In accordance with hydro-dynamic arguments of Siggia [Phys. Rev. A 20, 595 (1979)], the existence of the crossover can be related to the volume fraction of the new phase $v$. Only for $v\gtrsim 0.10$ are cross-overs observed. In more dilute mixtures we find $\left|k_m\right|=A{t}^{\frac{-1\mathrm{}}{3}}$ with $A$ proportional to $v$ for $0.10\gtrsim v\gtrsim 0.02$. Lifshitz-Slyozov growth, for which $A$ is independent of $v$, is found for $v<\mathrm{}0.02\mathrm{}$.