A numerical simulation is presented of the filtering/dewatering of structured suspensions. In the model the constitutive properties that are needed include : (1) the membrane permeability as a function of the solidosity of the deposited particulates (this is obtained by analysing the experimental data of the initial stages of the flow for a wide range of solids concentrations); (2) the effective drag coefficient which is found as a function of the solidosity from a least squares cell model; and (3) the stiffness of the solids matrix due to the interparticle repulsion. For this the double layer interaction is used, combined with recent advances in techniques of micromechanics, as well as improved estimates for the interparticle distance in dense suspensions. The resulting stiffness function is valid over a wide range of solidosities and contains two easily measurable parameters. Experimental data are presented for tests on anatase at initial solidosities in the range 0.07 < phi(0) < 0.3. The filtrate collected from the slurry as a function of time is recorded and used for analysis of the initial stage of the experiment to obtain the membrane permeability as a function of solidosity. Then a nonlinear numerical simulation is presented using the aforementioned constitutive relations and the results of this are compared to the Volume vs Time curves. The comparison shows that all experiments can be adequately described with the same set of constants for the suspension flow. Only two parameters need to be introduced : the effective thickness of the double layer (related to the zeta-potential) and one phenomenological constant that describes the effective interparticle potential strength in a suspension. With the aid of the simulation, cake formation is studied; the evolution of various internal parameters, such as the solidosity, pressure, skeletal stress and fluid and particle velocities is presented.