Can the washing curve be predicted

Yes it can be estimated from theory if the right data are available but the results are subject to simplifying assumptions, which do not hold in practice. Experimental, direct determinations are always more reliable if carried out under correct conditions. 

For reasons of clarity in demonstrating the use, a simplified version of the model is shown here, as used by Hermia and Rahier, for example . This is applicable to washing fully saturated cakes containing non-porous solids, at relatively high washing rates, i.e. with more porous cakes and/or at higher applied pressures (high Pe see later). For the full model which is more complex mathematically but applied in much the same way, see ref. 2. 

The dispersion model takes into account diffusion. In modelling, the Peclet number Pe is used as a ratio of the convective transport to diffusive transport. Here we can define two different Peclet numbers one for the overall flow in the cake Pec and another. Pep, for the flow in the vicinity of a particle of an average size characterizing the particles in the cake. The definitions are as follows  

As may be expected, Pec depends on Pep and this was studied by many workers. Wakeman and Attwood, for example, found the following relationship for relatively thin cakes (up to 10 cm) of fine particles  

The first term represents the effect of molecular diffusion and that dominates up to about Pep = 0.005 whilst the second term, for convective dispersion, dominates for higher Pep numbers. 

---