A model capable of predicting concentration polarisation and cake formation in cross-flow membrane filtration is proposed. The cross-flow hydrodynamics is resolved by solving the Navier–Stokes equations and convection–diffusion equation is used to resolve the solute distribution. A Lattice-Boltzmann (LB) scheme is used for the hydrodynamics and this is coupled with an LB scheme or a finite volume (FV) scheme for modelling the cake formation. The equations are coupled through the velocity and the viscosity, which is assumed to vary with the solute concentration. Concentration polarisation is modelled for interacting nano-particles by using concentration dependence on diffusion coefficient and osmotic pressure gradient as a function of solute concentration. Cake formation phenomenon is predicted for interacting nano-particles and non-interacting solute particles using the same approach. The proposed model is validated by comparing the results obtained for a number of problems with the predictions produced by other computational models and experimental results available in literature.