Normal stress and diffusion in a dilute suspension of hard spheres undergoing simple shear

The complete set of normal stresses in a dilute suspension of hard spheres undergoing simple shear at low Reynolds number is calculated using a path i ntegration approach for the cases where the concentration is uniform and wh ere a small gradient in concentration is present. As expected, the normal s tresses are seen to be a strong function of epsilon (s)=2(b-a)/a, where b i s the hard sphere radius and a is the particle radius. The normal stress di fferences N-1 and N-2, are negative while the osmotic pressure is large and positive, with Pi > parallel toN(2)parallel to and N-1-->0 as epsilon (s)- -> infinity. For epsilon (s)much less than1, the asymmetry in the pair dist ribution function due to a depletion of particles in the extensional side o f a pair interaction leads to \N-1\> \N-2\. On the other hand, for epsilon (s)--> infinity, the additional stresslet induced when hard sphere radii to uch dominates the stress generated in the suspension, and N-2 becomes the p revailing normal stress difference. The self and gradient diffusivities are calculated using da Cunha and Hinch's [J. Fluid Mech. 309, 211 (1996)] tra jectory method. Numerical results for the diffusivities are in agreement wi th those obtained by da Cunha and Hinch for epsilon (s)less than or equal t o0.08 while matching the analytically obtained diffusivities for large epsi lon (s). Finally, we calculate the normal stress in the presence of a small concentration gradient and compare two models of migration for this case, namely the suspension balance model of Nott and Brady [J. Fluid Mech. 275, 157 (1994)] and the diffusive flux model first introduced by Leighton and A crivos [J. Fluid Mech. 181, 415 (1987)]. The results show that although the two models equally describe migration in the presence of a concentration g radient for the case where b much greater thana (or epsilon (s)--> infinity ), the two models are shown to be quantitatively different when near-field hydrodynamics are relevant. (C) 2001 American Institute of Physics.