Colloidal suspensions are widely used in industry, medicine and in natural environments, and encompass systems as diverse as toothpaste, paints, the interior of a cell and sprayable solar panels. Understanding the rheological properties of suspensions is critical to their processing, dispensing, durability and performance. Most studies of suspension rheology have been at fixed volume (or fixed volume fraction). While this may be adequate for many applications, often suspension flows are not at fixed volume but rather at fixed stress (or fixed pressure or pressure drop). Is the flow behavior the same at fixed volume and fixed pressure? If the volume fraction of suspended particles is low enough it should be possible to covert one measurement into the other. But as the maximum flowing fraction is approached, it is no longer clear that the two conditions will lead to the same flow behavior. A simulation study of colloidal suspensions at fixed pressure, allowing the system to dilate or contract and the volume fraction fluctuate as necessary, is proposed. The Accelerated Stokesian dynamics simulation methodology will be adapted to permit the simulation volume to change and used to study the flow behavior of Brownian hard-sphere suspensions as the strength of the shearing forces compared to thermal Brownian forces is varied over a wide range. Complete microscale detail is available from simulation, including particle distribution functions, order parameters, short- and long-time particle displacements, etc., and will connect the observed macroscopic behavior to the underlying particle dynamics. Particular attention will be focused on the flow behavior as the maximum flowing fraction is approached and the scaling of the flow properties near this point.
Understanding suspension rheology is an important subject in its own right, but examining the flow behavior as the maximum flowing fraction is approached may have important implications for glassy and jammed systems. Colloidal dispersions at rest are known to form a glass at volume fractions near 0.58, well below random close packing (0.64 for monodisperse spheres). Experiment on both rapid granular flows and viscous non-Brownian suspensions at fixed pressure and shear stress have shown very similar behaviors: the ratio of shear to normal stress - the friction coefficient - is the same in the two systems, as is the maximum flowing volume fraction, despite the very different microscale physics - inertial dynamics versus viscous forces. It is quite possible that Brownian colloidal dispersions will display a similar behavior, which would then make an important link between jammed granular media and colloidal glasses. If demonstrated, such a connection would transform our understanding of glasses and jammed systems, and possibly provide a universal understanding of jamming.
This research will enable the design, at the particle scale, of colloidal dispersions to meet the flow requirements of specific applications in, for example, the paints and coatings industry, thus reducing energy consumption and product waste. Contributing to the understanding of glasses and glass-forming systems, and particular their dynamic properties, would have broad impact across disciplines from fundamental physics and chemistry to biology - the motion of proteins and protein complexes in the crowded interior of a cell has strong similarities with the hindered and heterogeneous motion in colloidal glasses. Finally, the graduate student supported by this research will be well-trained in continuum and statistical mechanics, colloidal physics and computational science, and will join the scientific workforce of the nation.
