Roles of particle-wall and particle-particle interactions in highly confined suspensions of spherical particles being sheared at low Reynolds numbers

Abstract

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 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 a 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 [Y. Davit and P. Peyla, Europhys. Lett. 83, 64001 (2008)] and experimental [P. Peyla and C. Verdier, Europhys. Lett. 94, 44001 (2011)] 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.