Phase-separation of miscible liquids in a centrifuge

We show that a liquid mixture in the thermodynamically stable homogeneous phase can undergo a phase-separation transition when rotated at sufficiently high frequency $\omega$. This phase-transition is different from the usual case where two liquids are immiscible or where the slow sedimentation process of one component (e.g. a polymer) is accelerated due to centrifugation. For a binary mixture, the main coupling is due to a term $\propto \Delta\rho(\omega r)^2$, where $\Delta\rho$ is the difference between the two liquid densities and $r$ the distance from the rotation axis. Below the critical temperature there is a critical rotation frequency $\omega_c$, below which smooth density gradients occur. When $\omega>\omega_c$, we find a sharp interface between the low density liquid close to the center of the centrifuge and a high density liquid far from the center. These findings may be relevant to various separation processes and to the control of chemical reactions, in particular their kinetics.