A method and apparatus for separating immiscible liquids in a dispersion containing an aqueous liquid and at least one dispersed non-aqueous liquid by passing the dispersion through a series of absorbents, preferably polymeric. The direction of the flow through the absorbent is periodically changed. The period required before a change of the flow direction is established by the differential pressure. There is a gradual increase in the differential pressure across the absorbents which indicates a blockage due to viscous oil and/or solids. The product produced by the method and the apparatus of the invention is a polished non-aqueous phase and a polished aqueous phase both having low contaminant levels. In a preferred embodiment when solids are also present in the dispersion, a solids stream is also recovered.