Apparatus for carrying out a process between first and second immiscible fluids comprises channels defining first and second primary flow paths for permitting fluid flow of the respective first and second fluids therethrough. Portions of the flow paths are disposed close to or adjacent one another and communicate with one another at a region where the flow paths are constructed and arranged so as to permit the fluids to form a stable interface between them. At least one of the fluids is induced to flow in a secondary direction perpendicular to the direction of its primary flow path at the region either by bending the primary flow path around a curve, or by positioning flow detectors within the flow path.