Traditionally, batch filtration experiments and steady state compression permeability (C-P) cell measurements have been used to determine the constitutive relationships -- void ratio (e) vs. solid pressure (ps) and specific flow resistance, alpha vs. ps. Conventional filtration theory is applied to determine the parameters in the constitutive equations. Many batch experiments that cover a range of ps are required to determine the two relationships. Consequently, these methods are tedious and time-consuming. For a compressible cake, the assumptions made in the conventional filtration theory can only are approximately correct, which affects the accuracy of the results.;In this dissertation new dynamic methods have been developed. The two constitutive equations are determined over a range of ps in two experiments. A cake that is formed at zero-stress is expressed at a very slow rate, and the compressibility relationship is experimentally determined over a void ratio range, 2.5--20 from this experiment. A second cake is expressed at a higher rate, and alpha vs. ps is determined by applying the solution to the governing equations. The solution does not make the simplifying assumptions of the conventional filtration theory. A search procedure is developed to determine the optimum parameters to fit the experimental data. The method is demonstrated on recycled news slurry, and news-clay slurry. The technique is validated by 3 different independent methods. The steady state permeation results are within 40% of those determined by the dynamic method. The liquid pressure measured on top of the cake agrees within 20% of the simulated results using the estimated constitutive parameters in the governing equations. Dynamic experiments carried out at two different expression rates and water viscosities give results with 5% of each other.;With the new dynamic technique, only two parameters are required to be estimated, which makes the analytical procedure simple and easy. The simplicity of the experimental and analytical technique, without compromise in accuracy, makes this method practical and useful for industrial applications.
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