Flow Past a Porous Spherical Particle

Let us consider the problem about a porous particle of radius a in a translational fluid flow with velocity U. We assume that the flow outside the particle obeys the Stokes equations (2.1.1) with viscosity /z. We also assume that the percolation flow of an incompressible fluid inside the particle satisfies Darcy s law [97, 346,423]  

To complete the statement of the problem, along with condition (2.2.2) of remote flow uniformity and condition (2.2.10) of boundedness of the solution, we need some boundary conditions on the interface. One of these conditions is obtained by substituting /j.2-0 and 7 = 0 into (2.2.8) and means that the normal stress is equal to the internal pressure. Furthermore, the normal velocity must be continuous across the interface, 

By solving the stated hydrodynamic problem, we arrive at the following expressions for the velocity components outside and inside a porous particle [372]  

In the limit cases K 0 and A - 0, formula (2.2.29) is reduced to (2.2.5) and corresponds to a Stokes flow around a solid sphere. 

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