The separation of one component from a multicomponent fluid solution is commonly achieved by bringing the solution into contact with a second immiscible phase, as in liquid-liquid or gas-liquid contactors. Counter-current flow of the phases allows high purity separations and existing approaches typically force one of the phases to disperse into the other, producing the close contact necessary for the solute species to be distributed by diffusion throughout the volume of each phase. This phase mixing leaves the contacting strongly dependent on fluid and interface mechanical properties. Thus an approach that suits one phase and solute system will not necessarily suit others. In addition, it is then necessary to separate the dispersed phase which can be a major drawback of the operation sometimes posing substantial difficulties in easily emulsified liquid-liquid systems or in easily foamed gas-liquid systems. A new approach, which has recently been demonstrated experimentally for microchannels, uses a rotating spiral channel to allow controlled contacting giving a very high ratio of interfacial surface area to fluid volume but avoids phase mixing. Its application to larger channels, up to millimetres in size, is considered here. The two phases are forced to flow side by side in parallel layers along the narrow spiral channel. Selection of spiral parameters, rotation rate and pressure gradient along the channel controls the flow rate ratio of the phases and the relative thickness of the phase layers. This allows adjustment to reach the optimum mass transfer (limited strongly neither by one phase nor the other) and adaptation to phase and solute systems having widely differing fluid viscosities, densities, solute diffusivities and interface equilibria. With appropriate control over these parameters, a single device is, in principle, capable of application to a wide range of separation requirements. This rotating spiral contacting is, however, a new technology and remains to be investigated and tested in detail. The present work develops a model yielding both quantitative prediction of flow and mass transfer in the contacting channel and a framework for determining suitable designs, operating conditions and mass transfer performance for liquid-liquid and gas-liquid operations. (C) 2011 Elsevier Ltd. All rights reserved.