Using a 2D fully coupled numerical model, the limiting flux phenomenon in the ultrafiltration of dextran was directly simulated assuming neither constant permeate velocity nor constant wall concentrations. It was found that the average permeate velocity agrees well with the permeate flux of Jonsson's experiment [G. Jonsson, Boundary layer phenomena during ultrafiltration of dextran and whey protein solutions, Desalination 51 (1984) 61-77], while significant axial variations of wall concentration and permeate velocity are maintained. This suggests that the limiting flux is actually the result of such axial variations, and therefore, assuming constant wall concentration or constant permeate velocity to interpret the experiment is inappropriate under the conditions investigated. The effects of osmotic pressure coefficients on permeate flux and wall concentrations, and the role of concentration-dependent viscosity in reaching the limiting flux, were further assessed. It was found that the permeate flux, and therefore the limiting flux, is not significantly affected by the osmotic pressure coefficients, although the magnitude of the wall concentration is considerably affected by osmotic pressure estimations. The concentration-dependent viscosity was found to be a critical factor for reaching the limiting flux under the simulation conditions. These findings imply that, in interpreting the results of limiting flux experiments, it is vital to include the axial variations of the wall concentration and permeate velocity and the impact of the variations of fluid properties.