Abstract: In order to facilitate diffusive transfer of an entity such as a solute between immiscible fluids and subsequent separation of the liquids without mixing, a method and an apparatus are disclosed and have first and second flow paths carrying first and second immiscible fluids on opposite sides of a foraminous sheet. The height of the apertures in the sheet is not greater than 200 micrometers (measured perpendicular to the width of the sheet and to the direction of fluid flow), and a stable interface is formed between the fluids within each aperture with a significant amount of fluid flow immediately adjacent the interface. Diffusive transfer takes place across the interface, and subsequently the fluids flow away from the region without mixing. The width of the flow paths measured perpendicular to sheet lies between 10 and 500 micrometers. The walls of each aperture may be parallel or tapered.