Stokes Flow Through a Membrane Built up by Nonhomogeneous Porous Cylindrical Particles
P. K. Yadav1, P. Singh2, A. Tiwari3, S. Deo4
1Motilal Nehru National Institute of Technology Allahabad, Prayagraj, 211004, India
2National Institute of Technology Patna, Patna, 800005, India
3BITS Pilani, Pilani Campus, Rajasthan, 333031, India
4University of Allahabad, Prayagraj, 211002, India
Keywords: ячеечная модель, функция тока, закон Дарси, гидродинамическая проницаемость, cell model, stream function, Darcy equation, hydrodynamic permeability
Abstract
This work deals with the creeping flow of an incompressible viscous fluid through a membrane. It is assumed that the membrane is composed of nonhomogeneous porous cylindrical particles with radially varying permeability enclosing a cavity. The flow within the nonhomogeneous porous medium is governed by the Darcy equation. The flow inside the cavity and outside the nonhomogeneous porous region is governed by the Stokes equations. An analytical solution of the problem is obtained by using the cell model technique. Exact expressions for the drag force acting on the membrane and hydrodynamic permeability of the membrane are derived. The influence of radially varying permeability on flow parameters is considered. The effects of various parameters of the problem on hydrodynamic permeability of the membrane are discussed for four models. Some previous results for hydrodynamic permeability are verified as special limiting cases.
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