Cephalosporin C (CPC) fermentation broth is a typical fluid which is filtrated hardly. In order to optimize the CPC diafiltration process under constant yield and constant concentration, a mathematic model is developed to estimate the operation time, where the membrane permeation performance is given by the gel polarization model. The expressions of t(min) and the optimal conditions are put forward respectively. Based on the model, the optimization processes for CPC diafiltration to achieve desired yield and concentration have been investigated. Under the conditions of C-0 = 0.1 and the steady state, the values C-G= 0.65 and beta = 28.65 m(3) m(-2) h(-1) are extrapolated based on the experiment results. The optimal range of pre-concentration ratio 0.5 a <= a <= 0.8 is confirmed. Compared with the overall process time under C-0/C-G = 1/6.5, the fluctuation range of that is more than 40% in the range of 0.08 < C-0/C-G < 0.23. Under the time-optimal conditions, both of the desired CPC yield xi and the average concentration of CPC in filtrate C-t can be controlled properly. (c) 2013 Elsevier B.V. All rights reserved.