The performance of industrial membrane processes is affected by the time dependence of permeate flux, which includes both the absolute value and the rate of decrease in permeate flux at a given time. In particular, long-term fouling will affect the performance of industrial membrane processes that operate continuously for long periods of time, such as industrial whey ultrafiltration processes that can operate for up to 14 h every day. Results of whey ultrafiltration experiments conducted on a pilot scale membrane rig were used to establish a unified model for the time dependence of permeate flux during long-term ultrafiltration. Experimental results indicate that the effects of trans-membrane pressure and feed concentration on the rate of decrease in the permeate flux due to long-term fouling are statistically insignificant. The unified model from this paper can be applied in conjunction with the process dynamics models to study the performance of automatic controllers prior to controller design. (C) 2009 Elsevier B.V. All rights reserved.