Our group's research interests are in fluid mechanics and transport processes, with a special interest in problems at the interface between continuum mechanics and statistical mechanics. One area of research concerns fundamental studies of complex fluids. Complex fluids is a generic label for materials that are composed of microstructural elements that interact via colloidal, hydrodynamic, and Brownian forces. Familiar examples of such fluids are suspensions, colloidal dispersions, liquid crystals, ferrofluids, electrorheological fluids, and polymer solutions and melts. In these systems the basic question is one of understanding and predicting the relationship between the material's microstructure and its macroscopic properties. To carry out this task, we have developed a novel computational method known as Stokesian Dynamics that allows us to make quantitative predictions of the structure-properties relations under processing conditions. These numerical experiments have opened up a new approach to study complex fluids and, combined with analytical statistical mechanical theories, are leading the way to the rational design and use of complex fluids.

Another area of research is the development and solution of macroscopic equations to describe transport in heterogeneous media. In heterogeneous media, such as an oil reservoir, a packed bed reactor, or the flow of a suspension, the physics of the transport mechanisms on the microscale (the scale of individual grains or particles) is well known, but the average or macroscopic scale transport processes are not known and are generally the quantity of interest. The key problem is to pass from one scale to the next, deriving the appropriate laws on the macroscale and relating these to the underlying microscale physics. Once model equations have been proposed, the challenge is in the computational fluid dynamics of multiphase flows.

Another area of research is the development and solution of macroscopic equations to describe transport in heterogeneous media. In heterogeneous media, such as an oil reservoir, a packed bed reactor, or the flow of a suspension, the physics of the transport mechanisms on the microscale (the scale of individual grains or particles) is well known, but the average or macroscopic scale transport processes are not known and are generally the quantity of interest. The key problem is to pass from one scale to the next, deriving the appropriate laws on the macroscale and relating these to the underlying microscale physics. Once model equations have been proposed, the challenge is in the computational fluid dynamics of multiphase flows.