The decline in permeate flux due to fouling is attributed to the flow resistance offered by cake layer and enhanced concentration polarization. The adverse effects on permeate flux can be negated by increasing the fluid shear over the membrane. Roto-dynamic filtration systems, where a rotating disk over a membrane generates high strain rates, have been previously implemented in the ultra and microfiltration regimes. The present work provides a detailed mathematical description of colloidal fouling and cake-enhanced concentration polarization in cross-flow reverse osmosis (CFRO) systems. The mathematical model is numerically implemented in a commercial Computational Fluid Dynamics (CFD) package by employing several subroutines. The proposed model is able to predict the spatio-temporal variation of permeate flux and cake layer thickness in a CFRO filtration system for the first time, the primary focus being a high shear roto-dynamic RO filtration system. The effects of feed pressure, Reynolds number and foulant properties on the permeate flux and salt rejection are discussed in detail. Eventually, the temporal variation of the performance of a roto-dynamic RO filtration system is compared with that of a channel CFRO filtration system and hence the advantages of employing a roto-dynamic RO filtration system have been highlighted. © 2019 Elsevier B.V.