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Apart from the empirical conventional filtration model, a number of rigorous multiphase flow models are available for the description of the dead-end cake filtration of compressible slurries. In this study, Tiller`s and Smiles` models are compared with regard to their quantification of the dynamic filtration behavior of `dilute` flocculated yeast slurry during dead-end constant pressure filtration. Steady-state filtration is employed to obtain the compressive yield stress and specific resistance of the cake as functions of solid fraction. It is found that, by virtue of these cake properties, the governing equations of Smiles` and Tiller`s model can be numerically solved. The results show that Smiles` and Tiller`s models are equivalent in quantifying filterability and specific resistance, as well as solid fraction, superficial liquid velocity and solid pressure profiles. The compressible property of the cake is demonstrated by the dependence of either filterability or average specific resistance on the applied pressure. For dilute slurries, the applied pressure has a significant influence on solid fraction profile but has little influence on superficial liquid velocity profile with the maximum variance in superficial liquid velocity in the cake being determined by the solid fraction of the slurry. In the dead-end filtration of dilute slurry, the superficial liquid velocity through the cake is almost uniform and the specific resistance can be approximately obtained from correlation of filtration data by the conventional model. © 2007 Elsevier B.V. All rights reserved.