Following on from the work presented in Part I. this Part II paper presents a new mathematical description for water and solute transfer in pressure-driven membrane separation processes, the Molecular Trap (MT) model. This model incorporates the outcomes from the Analytical Solution-Diffusion Pore-Flow (ASDPF) model, which explains the effects of the operational conditions on membrane microstructure and the permeated fluid physical properties, with the solute molecular properties. The new theory, which is found to be qualitatively in agreement with the experimental findings, may be useful for further process understanding and future development. (C) 2011 Elsevier B.V. All rights reserved.