Transient Flows of Colloidal Dispersions

Transient development of the microstructure in colloidal hard- and soft-sphere dispersions is studied using simulation by the Accelerated Stokesian Dynamics algorithm. The cases of startup of a steady shear flow, cessation of steady shear flow, and large-amplitude oscillatory shear (LAOS) have been examined. A methodology for use of simulation to extract time-resolved ensemble averages of structure and properties is presented and the findings of the study are summarized. The flows have been studied for monodisperse spherical particles over a range of solid volume fractions varying from 30-55%, at Peclet numbers (characterizing the relative strength of shear to Brownian motion) from Pe << 1 (near equilibrium) to Pe = 1000. In each case, the time-resolved structure is related to the rheological response during the transient flow. For soft spheres interacting through long-range electrostatic repulsion, the solid fractions examined are lower.

It is found that during startup from an isotropic equilibrium configuration that both the shear stress and normal stress differences in hard-sphere dispersions exhibit an overshoot before returning to their steady values. This overshoot is particularly pronounced for the second normal stress difference, N₂, and is found to be correlated to a development of a strong pair correlation along the compressional axis, which is relaxed through rotational flow and diffusion. Upon flow cessation, the hydrodynamic stress relaxes immediately while the Brownian stress relaxes due to Brownian motion (and through repulsive forces in the soft-sphere case). The relaxation of the first normal stress difference, N₁, is found to be comparable to the shear stress, with both relaxing significantly more slowly than slower than N₂; this is explained in part by N₂ being controlled by the very small length scale structural feature of the pair correlation boundary layer scaling roughly as aPe^-1 where a . The primary features of the LAOS study are reviewed using the higher harmonics of the Fourier transform description of the nonlinear rheology for a wide range of Pe and maximum imposed strain of 0.1 to 5.