Research Summary

Research Projects

• Computational Modelling of Suspensions and Colloidal Systems
  Concentrated suspensions of small particles present challenging research problems in many applications of scientific and technological significance. These systems include paper manufacturing, coating processes, paints, food products, ceramics, and bioparticulates (including blood cells) as well as large macromolecules. We are interested in the dynamics of these particulate systems under the action of hydrodynamic, Brownian, and interparticle forces. Previous studies have focused on the effects of Brownian and interparticle forces but have had limited success in analyzing the strong hydrodynamic interactions in concentrated systems. Accurate solution of the fluid dynamic equations required O(N3) operations, limiting simulations to N = 100 particles or less. In our research, we have reduced the computational cost to O(N ln N) operations, allowing realistic simulations with systems having up to 25,000 particles. With such large-scale systems, we are able to investigate a range of interesting physical phenomena that have previously been beyond the limits of computer simulation. We are currently pursuing research on structure formation in suspensions, order-disorder transitions, and the dynamics of nonspherical particles, such as platelets and long flexible-particle chains.



• Large Scale Simulations of Multiphase Flow: Foams and Emulsions
  Multiphase flows of emulsions and foams are encountered in a wide range of industrial processes. Enhanced oil recovery processes and environmental remediation constitute two important examples in which a multiphase mixture flows through the complex interstitial spaces of a porous medium. Owing to the complexity of the interfacial flows, many multiphase systems can be analyzed only through experiment or computer simulation. Previously, computational methods for solving the hydrodynamic equations required O(MN)2 operations, where N is the number of fluid droplets and M is the number of computational elements per drop. As with the particulate systems discussed above, this computational cost placed severe limitation on the phenomena that could be studied by direct simulation. In our research, we have developed a new algorithm, having a computational cost O[MN ln(MN)]. Computer simulations with this new algorithm promise to significantly extend our understanding of multiphase flows of emulsions and foams. In two major research thrusts, we are analyzing the rheology of multiphase fluid mixtures in shear flows and studying the relative permeability of two fluid phases in flow through porous media.