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The rheology and microstructure of complex fluids are intimately related, and this relationship is explored to gain a deeper understanding of the physics of colloidal dispersions, emulsions and polymer solutions.

The nonequilibrium microstructure and rheological properties of dispersions in steady, simple shear flow are calculated by solving the Smoluchowski equation as a function of dimensionless shear rate. The particles have a purely repulsive interaction with an hydrodynamic radius, a, and a thermodynamic radius, b. For hard spheres, b/a --> l, shear thinning is caused by a decrease in the Brownian contribution since Brownian motion becomes less important with increasing shear. Shear thickening occurs because of an increase in the hydrodynamic viscosity caused by the increased probability of finding particles near contact with increasing shear when particles hydrodynamically interact. The first normal stress difference changes sign since Brownian and hydrodynamic contributions have opposite signs, while the second normal stress difference is always negative. Scaling arguments are made to extend these dilute results for concentrated dispersions. Similar calculations and analyses are performed to study the effects of hydrodynamic interactions and varying b/a ratios on rheology and microstructure.

Scaling arguments for the volume-fraction dependence of the bulk stress of emulsions at the critical capillary number are presented along with experimental evidence using an unstabilized emulsion of polymerized castor oil dispersed in polydimethylsiloxane. It is shown that the droplet contribution to both the relative shear viscosity and first normal stress difference is linear in volume fraction for a given viscosity ratio for dilute to moderately-concentrated emulsions in steady, simple shear flow.

Stress jump measurements are performed for the first tune for (i) shear startup and (ii) polymer solutions in shear. The startup viscosity of a polymer solution of polyacrylamide in fructose-water at equilibrium is equal to the measured high frequency dynamic viscosity, as expected, since both methods measure the viscous contribution to the viscosity associated with the equilibrium microstructure. Since polymer solutions exhibit stress jumps different from the solvent viscosity, effects of shear on the hydrodynamic viscosity can be investigated.

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