A general numerical method using the boundary integral equation technique o
f Pozrikidis (1994) for Stokes how in an axisymmetric domain is used to obt
ain the first solutions to the Brinkman equation for the motion of a partic
le in the presence of planar confining boundaries. The method is first appl
ied to study the perpendicular and parallel motion of a sphere in a fibre-f
illed medium bounded by either a solid wall or a planar free surface which
remains undeformed. By accurately evaluating the singular integrals arising
from the discretization of the resulting integral equation, one can effici
ently and accurately treat flow problems with high alpha defined by r(s)/K-
p(1/2) in which r(s) is the radius of the sphere and K-p is the Darcy perme
ability. Convergence and accuracy of the new technique are tested by compar
ing results for the drag with the solutions of Kim & Russell (1985a) for th
e motion of two spheres perpendicular to their line of centres in a Brinkma
n medium. Numerical results for the drag and torque exerted on the particle
moving either perpendicular or parallel to a confining planar boundary are
presented for epsilon greater than or equal to 0.1, in which epsilon r(s)
is the gap between the particle and the boundary. When the gap width is muc
h smaller than r(s), a local analysis using stretched variables for motion
of a sphere indicates that the leading singular term for both drag and torq
ue is independent of alpha provided that alpha = O(1). These results are of
interest in modelling the penetration of the endothelial surface glycocaly
x by microvilli on rolling neutrophils and the motion of colloidal gold and
latex particles when they are attached to membrane receptors and observed
in nanovid (video enhanced) microscopy. The method is then applied to inves
tigate the motion of a sphere translating in a channel. The drag and torque
exerted on the sphere are obtained for various values of alpha, the channe
l height H and particle position b. These numerical results are used to des
cribe the diffusion of a spherical solute molecule in a parallel walled cha
nnel filled with a periodic array of cylindrical fibres and to assess the a
ccuracy of a simple multiplicative formula proposed in Weinbaum et al. (199
2) for diffusion of a solute in the interendothelial cleft.