J. Feng et S. Weinbaum, Flow through an orifice in a fibrous medium with application to fenestral pores in biological tissue, CHEM ENG SC, 56(18), 2001, pp. 5255-5268
Slow viscous flow through a circular orifice in a plane wall bounded by a f
ibrous medium is studied using an effective medium approach, based on the B
rinkman equation, using an integral equation technique. The solution is of
more general interest because it describes the transition in behavior from
the classic Sampson solution for creeping flow through an orifice to a pote
ntial flow solution for Darcy flow as the permeability parameter increases.
Asymptotic analytical results for the total flux through the orifice for a
given pressure difference are obtained for both small and large values of
the permeability parameter alpha defined by a/rootK(p), where a is the orif
ice radius and K-p the Darcy permeability. For intermediate values of alpha
, the integral equation is solved numerically for the flux and velocity pro
file at the opening. For alpha much greater than O(1), the velocity profile
at the opening has a minimum at the orifice center, rises dramatically nea
r the edge of the orifice and then experiences a boundary-layer-like correc
tion of thickness O(1/alpha) to satisfy the no-slip boundary condition. The
close relation between pressure driven flow through a circular orifice and
broadside translation of the complementary geometry, namely a circular dis
k in Stokes flow, is also discussed. The effect of the finite thickness of
the orifice is taken into account using a simple model proposed by Dagan et
al. (J. Fluid Mech. 115 (1982)) for Stokes flow through a pore of finite l
ength. The present results are used to estimate the hydraulic conductance o
f orifice like pores in fenestrated capillaries and fenestral pores in the
internal elastic lamina of the arterial intima. (C) 2001 Elsevier Science L
td. All rights reserved.