The roles of particle-wall and
particle-particle interactions are examined for suspensions of spherical
particles in a viscous fluid being confined and sheared at low Reynolds numbers
by two parallel walls moving with equal but opposite velocities. Both
particle-wall and particle-particle interactions are shown to decrease the
rotational velocity of the spheres so that, in the limit of vanishingly small
gaps between the spheres and the walls, the spheres acquire a rotational slip
relative to the walls. The presence of the walls also increases the particle
stresslet and, therefore, the total viscous dissipation. In the limit of
vanishingly small gaps, the increased viscous dissipation in the gaps between
the pairs of spheres aligned in the flow direction is largely compensated by
the reduction in the dissipation in the gaps between the spheres and the walls
due to reduction in the rotational velocity of the spheres. As a result, the
effect of short-range particle interactions on the stresslet is generally
insignificant. On the other hand, the channel-scale particle interactions in
the shear flow induced by the moving walls decrease the particle stresslet,
primarily because the fraction of pairs of spheres that are aligned parallel to
the flow (the presence of which in a shear flow reduces the stresslet) is
relatively higher than in unbounded suspensions. Expressions are also derived
for the total stress in dilute random suspensions that account for both the
particle-wall and the channel-scale particle-particle interactions in
determining the rotational velocities and stresses. The latter are shown to be
consistent with recent numerical [Davit and Peyla, *Europhys. Lett*. **83**,
64001 (2008)] and experimental [Peyla and Verdier, *Europhys. Lett*., in
print] findings according to which, for a range of sphere radius to gap width
ratios, the effect of particle-particle interactions is to decrease the total
dissipation.

**Extended Abstract:**File Not Uploaded

See more of this Group/Topical: Engineering Sciences and Fundamentals