An Axisymmetric Problem of Suspension Filtering with Formation of Elastic–Plastic Cake Layer

Abstract

The paper considers an axisymmetric problem of filtering suspensions with the formation of a cake on the filter surface. It is supposed that the cake has elastic–plastic properties. Using the mass conservation equation and Darcy’s law, the suspension filtration equations at the elastic–plastic regime are derived, which characterize the partial irreversibility of the filtration characteristics when the system is unloaded after loading. An equation is also derived that describes the increase in the thickness of the cake. Problems of suspension filtering for the derived equations are posed and numerically solved. The role of partial irreversibility of deformation on the filtration characteristics is estimated. Distributions of compression pressure, the concentration of solid particles in the cake, relative permeability in the mode of primary and secondary loading of the system, as well as in the mode of unloading after the first loading are obtained. The growth dynamics of the cake thickness are also established. The parameters of plasticity in terms of particle concentration and permeability mainly affect the corresponding indicators, i.e., on the particle concentration distribution and on the relative permeability of the cake. It is shown, that depending on the change in the model parameters characterizing the elastic–plastic properties of the cake, the filtration characteristics change significantly. This indicates a significant effect of the elastic–plastic deformation of the cake on the suspension filtration characteristics.

An Axi-Symmetric Problem of Suspensions Filtering with the Formation of a Cake Layer

“…, m Figure 4 illustrates the dynamics of the cake thickness (t) = R L (t) − R. One can see its monotonous growth. This is a typical feature of cake filtration [1][2][3]5,6,11,16,17,20]. In all cases, due to the accumulation of solid particles in the cake on the filter surface despite its compaction (consolidation), i.e., an increase in the concentration of the solid particles and a change in its porosity, the growth of the cake thickness occurs.…”

“…To solve the problems in ( 25) and ( 26), we use the finite differences method [19,20,23,24]. We introduce a uniform grid using t with the step τ:…”

“…Since in the process of filtering, the sediment-suspension interface is mobile, the models are usually reduced to Stefan problems [1,4,7], the numerical solution of which, as is known, has a number of specific features [18][19][20][21][22][23][24].…”