Stokes flow inside a porous spherical shell: Stress jump boundary condition

Abstract

An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkman's equation for the flow in the porous region is discussed. At the interface of the clear fluid and porous region stress jump boundary condition for tangential stresses is used. The drag and torque are found by deriving the corresponding Faxen's laws. It is found that drag and torque not only change with the varying permeability, but also change for different values of stress jump coefficient. Critical permeability is found for which drag and torque change their behavior. As a limiting case the corresponding Faxen's laws for the rigid spherical shell with internal singularities has been obtained. Mathematics Subject Classification (2000). 76xx, 76D07, 76S05

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

“…The latter figure shows that with the increase in dimensionless resistance σ the hydrodynamic permeability is decreasing. An almost similar observation for the drag force has been reported by Bhattacharya and Raja-Shekhar [53]. Fig.11 shows the decay in hydrodynamic permeability with viscosity ratio which agrees with previous results for spherical particles and cylindrical particles for flow across the membrane.…”

“…Srivastava and Srivastava [52] studied the Stokes flow around a porous sphere using stress jump condition at the liquid-porous layer interface and concluded that drag on porous sphere decreases with increase of permeability of the medium. Recently, Bhattacharya and Raja Sekhar [53] have used the same jump boundary conditions to discuss Stokes flows inside a porous spherical shell.…”

Steady rotation of a composite sphere in a concentric spherical cavity

“…Figure 3 shows the variation of torque with permeability in absence of solid core. Here similar behaviour is also observed, however, for some positive values of stress jump coefficient σ, there is a reversal in the behaviour of torque at a particular value of permeability (critical permeability K c [19]). Beyond this value of K c , the value of torque becomes negative which is not physically possible.…”

“…Kuznetsov [17,18] used this stress jump boundary condition at the interface between a porous medium and a clear fluid to discuss flow in channels partially filled with porous medium. Bhattacharyya and RajaSekhar [19] have used stress jump boundary condition while discussing the stokes flow of a viscous fluid inside a sphere with internal singularities, enclosed by a porous spherical shell. They concluded that the fluid velocity at a porous-liquid interface varies with the stress jump coefficient and it plays an important role in describing the flow field associated with porous medium.…”

Stokes flow of an assemblage of porous particles: stress jump condition

“…At the porous-liquid interface, we use the stress jump condition that has been proposed by Ochoa-Tapia et al [15,16]. This has been widely used in various models [17][18][19][20][21]. Ochoa-Tapia et al [15,16] reasoned that due to spatial changes of the local porous structure that characterize the interface region, the macroscopic conservation equations in both homogeneous fluid and porous regions may not be satisfied.…”