AbstractThe nonlinear problem of reverse osmosis in annular conduits is solved by a series expansion method which is very accurate in the diffusion entrance region near the inlet of the membrane section. It is found that polarization at the outer membrane surface is significantly greater than at the inner wall.In the diffusion entrance region, for the problem considered, the degree of polarization depends on the three parameters, σ, and B2, which are known once the operating conditions and the physical properties of the system are specified. The quantities θi (0) are tabulated for a wide range of ηk and B2. With these quantities known one can apply Equation (17) at β = 0 to calculate the wall concentration distribution and, with Equation (4), the flux distribution along the system. Then, by using Equation (26), the water produced by the system can be determined explicitly in terms of prescribed operating conditions.