The Simplest Complex Fluid? The Remarkable Rheology of Hard-sphere Suspensions
Jeffrey F. Morris, Levich Institute and Dept. of Chemical Engineering, City College of the City University of New York



Dense suspensions of solid spherical particles in a Newtonian liquid solvent provide a crucial basic model system for development of mixture flow and complex fluid theory. By complex fluid, we mean that there is a dependence of the properties of the fluid upon the shear rate.  In practice, suspensions and slurries appear in coatings, ceramic precursors, mud flows, among numerous examples.    In this work, we see to understand the surprisingly rich rheology, i.e. the stresses, of flowing suspensions under conditions of large particle loading.  Motivations include particle migration phenomena and secondary flows induced by normal stresses as well as the observation of extreme shear rate dependence of the viscosity called “discontinuous shear thickening” (DST).  The phenomenon of DST is known popularly in corn-starch suspensions, on which a person can run if quick enough (solid-like behavior art a high rate of forcing) but will rapidly sink if standing still (liquid behavior at a low rate).

We will consider the underlying microstructure of dense suspensions of Brownian particles (i.e. small enough to be influenced by thermal fluctuations in the solvent), based on our own simulations and theory.  This theory [1] predicts highly anisotropic structure and hydrodynamically-driven normal stresses when the flow dominates Brownian motion.  Migration driven by normal stresses is now well-established, as will be briefly developed by description of the continuum approach.     A key feature of the microstructure is that the probability of particles directly adjacent to contact is extremely large (and strongly singular in the limit of maximum packing) so the role of surface friction is expected to play a role in experiments.  We show  in recent simulations [2] that a combination of hydrodynamic interactions and surface contact and frictional interactions are able to reproduce well the experimentally observed features of discontinuous shear thickening.   

1. E. Nazockdast & J. F. Morris 2012 Microstructural theory and rheological analysis for concentrated colloidal dispersions. J. Fluid Mech. 713, 420-452.

2. R. Seto, R. Mari, J. F. Morris & M. M. Denn 2013 Discontinuous shear thickening of frictional hard-sphere suspensions. Phys. Rev. Lett. 111, 218301.