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

In this paper, we consider a vertically positioned cylindrical filtering element. Filtering occurs in the radial direction, therefore, the direction of the velocities of the liquid and suspended particles coincide with this radial direction. The flow can be considered to be one-dimensional and radially axisymmetric. To describe such a filtering process, the axisymmetric Stefan problem will be formulated. The radial mass balance formalism and Darcy's law are utilized to obtain a basic equation for cake filtration. The boundary condition at the moving surface is derived and the cake filtration is formulated in a Stefan problem. Equations are derived that describe the dynamics of cake growth in the cake filtration, and they are numerically solved. The influence of different model parameters on the compression and fluid pressure across the cake and the growth of its thickness are studied.

Automated summary

In this paper, the authors investigate the filtering process of a vertically positioned cylindrical filtering element. By considering the radial direction, the flow is assumed to be one-dimensional and radially axisymmetric. The axisymmetric Stefan problem is formulated to describe the filtering process, and the dynamics of cake growth are analyzed numerically. The study explores the influence of different model parameters on compression, fluid pressure, and thickness growth of the cake.