An elastohydrodynamic theory for the rheology of concentrated suspensions of deformable particles

The equations which govern thin films of a Newtonian liquid confined between deformable solid surfaces are applied to the regions of near contact in a concentrated suspension of deformable particles.For the case of slightly deformable elastic particles, one obtains the socalled "elastohydrodynamic" equations of lubrication theory.The appropriate asymptotic solution of these equations yields estimates for the viscosity, of a form proposed earlier by Frankel and Acrivos [1] for rigid particles, as well as a relaxation time for a suspension of near spheres. The present method, which goes beyond the dissipation calculation of Frankel and Acrivos to a derivation of the full stress tensor, yields the same form of dependence of viscosity on particle concentration. However, there is an as yet unexplained difference between the methods in the value of a numerical coefficient determined by the assumed packing of the spheres.While further work is needed on the kinetic theory for fluid suspensions, the methods employed here for the derivation of the stress tensor should have direct utility for certain solid dispersions, where it is possible to specify a priori the particle-packing in the system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22965/1/0000532.pd