Microstructure and rheology of colloidal suspension in simple shear and dynamic oscillatory flows: theory and simulation.
Ehssan Nazockdast (CUNY), Stéphanie Marenne (City College of New York), Jeffrey Morris (Levich Institute and Dept. of Chemical Engineering, CCNY)
Complex Fluids: Suspensions, Emulsions, and Gels
Tue 10:45 - 12:15
Barus-Holley 160
A theoretical framework is developed for analytical prediction of structure and rheology of sheared colloidal suspensions. The theory computes either the steady or transient pair distribution function, $g(\mathbf{r})$ or $g(\mathbf{r},t)$, as a solution to the pair Smoluchowski equation (SE) where $\mathbf{r}$ is the pair separation vector. The interactions of the surrounding ``bath'' particles on the pair dynamics are modeled through third particle integrals; as a result the steady theory is able to give predictions of pair microstructure over a wide range of volume fractions, $\phi$, and P\'eclet numbers, $Pe$. Here $Pe$ is the ratio of hydrodynamic to Brownian forces. The prediction of $g(\mathbf{r})$ is used to compute the steady-state simple shear flow rheology, namely shear viscosity and first and second normal stress differences. The predictions of microstructure and rheology are compared against Accelerated Stokesian Dynamics (ASD) simulations in a wide range of $Pe$ and $\phi$. The theory is then extended to study time-dependent behavior of colloidal suspensions in two flow conditions: 1- startup of steady shear, and 2- oscillatory shear flows. In case of oscillatory flows, the behavior is defined by $\phi$, $Pe_{\omega}$ and $\gamma_{0}$ where $\omega$ is the frequency of oscillatory straining motion, and $\gamma_{0}$ is the strain amplitude of the oscillation. Here $Pe_{\omega}$ is the ratio of the time required for a single particle to diffuse a particle radius with Brownian motion to the oscillation time period. The predictions of $g(\mathbf{r},t)$ and time-dependent rheology are carried out for a wide range of $Pe$ and $\phi$ in startup flow and $\phi$, $Pe_{\omega}$ and $\gamma_{0}$ in oscillatory flows. The results are compared against ASD simulations or experiments where possible.