In a particular type of centrifugal rotor for dividing a liquid mixture into one liquid phase having a low viscosity and one concentrate phase having a high viscosity, the concentrate phase on its way towards an outlet chamber (17) in the rotor has to flow through a vortex device (20). The vortex device has a property of admitting therethrough a larger flow of a liquid if this has a high viscosity than if it has a low viscosity. For making an operation for cleaning of the rotor and conduits for concentrate phase downstream of the rotor more efficient, a cleaning liquid, which has a low viscosity, is conducted not only through the vortex device (20) to said outlet chamber (17) for concentrate phase but to this outlet chamber (17) also through a separate passage (34). Thereby, it is guaranteed that a sufficient flow of cleaning liquid enters the concentrate outlet chamber (17) and from there can be pumped out of the rotor to the concentrate phase conduits downstream of the rotor.