  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.
