Analytical Model of Suspensions Separation in Hydrodynamic Filter with Pivoting Perforated Partition

Abstract

The article develops a stochastic model of suspensions separation in hydrodynamic filter. Suspensions separation in the filter is carried out due to hydrodynamic force action on suspension flow (first stage of separation) and filtering through a porous membrane (second stage). Pivoting perforated partition is put into filter in front of the porous filtering membrane to increase effectiveness of suspensions separation at stage one. Complex Couette flow develops in the gap between filter bowl and the perforated partition. Specific modes of flow in the gap produce Taylor vortex, size and intensity of which depend on parti-tion’s rotation speed and flow velocity. It produces a flow currently known as Couette-Taylor flow. Multidirectional Taylor vortex arising in the mainstream disrupts its hydrodynamics and creates turbulence. Given such flow, calculation of hard phase separation with use of determinate models can be an error as does not include stochastic processes. The article presents a new analytical model of suspensions separation, which takes in stochastic (probabilistic) separation processes and is based on the theory of Markovian processes. Equations of diffusion type, particularly the Fokker-Planck-Kolmogorov equation, are offered to describe process of suspensions separation in hydrodynamic filters with pivoting perforated partition.