The limiting flux phenomena in ultrafiltration were studied. The experiments were carried out using an asymmetric membrane in a radial cross-flow cell. The permeate flux was predicted for black liquor, a paper plant effluent, in comparison to the results using a standard macromolecular solution of poly(ethylene glycol) (PEG 6000). The governing equations for the simulation of radial cross-flow ultrafiltration cell were solved. The differential equations were coupled with an osmotic pressure model and they were solved successively. The fluxes were predicted employing two different techniques. The first technique was an approximate solution using a simplified velocity field and a similarity transformation, called here the simplified approach. The second technique was a detailed simulation using perturbation theory and orthogonal collocation, the so-called detailed approach. The overall average fluxes obtained by the two approaches were compared. The results showed agreement between the two approaches and with the experimental data.