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Difficulties with existing approaches to the modelling of filtration of compressible materials under constant flux conditions are addressed in this paper and a new approach to modelling simultaneous consolidation and cake build-up based on dewatering theory is presented. Flocculated yeast is used as the test system with the predicted trans-membrane pressure rise as a function of time under constant flux conditions compared with experimental data. Good agreement is observed between model and experimental trends. The close correspondence between experimental and predicted results also suggests that it may be possible to predict trans-membrane pressure rise during constant flux filtration on the basis of material properties determined through simple constant pressure steady-state experiments. © 2008 Elsevier B.V. All rights reserved.