In this collaborative project, the investigators and a colleague study the motion of complex fluids, especially flows of wormlike micellar fluids and of monodisperse polymer solutions in a variety of geometries and under a variety of forcings. Surfactant systems consist of amphiphilic molecules with hydrophilic heads and hydrophobic tails. Under suitable chemical conditions these molecules can self-assemble in aqueous solution into long aggregates known as worm-like micelles. These long flexible structures entangle to form a network and lead to viscoelastic properties similar to those of polymer melts and concentrated solutions, but with the added complexity that the worms continuously break and reform (i.e. they are "living polymers"). External deformations can enhance the local rate of micellar breakage, thus the macroscopic flow affects the microscopic structure which in turn further modifies the global velocity field. Due to these multi-scale interactions these fluids exhibit flow inhomogeneities even in simple geometries. Development and analysis of new constitutive models and comparison with experimental results is generating new insight and understanding into the multi-scale nature of these flows and of the influence of the evolution in the microscopic structure on the macroscopic measurables. The governing mathematics is that of a nonlinear system of partial differential equations describing conservation of mass and linear momentum, coupled to equations governing the number densities of the entangled molecules and constitutive (stress) equations for each species. Specifically, the investigators study a pair of two-species network models that they recently proposed: a two species model with chain scission and reforming effects (the VCM model) physically appropriate for wormlike micellar solutions, and a simplified non-interacting model (PEC+M model) appropriate to monodisperse entangled polymer solutions. The investigators study the time evolution of the solutions in strong extensional flow and in rapidly time-varying flow using a combination of asymptotics and computation as well as experiments. Approximate closed form solutions are generated to enable an understanding of the flows and of sharp spatial transitions (microstructural boundary layers).
The investigators study the material properties of complex fluids such as those constituting shampoos, liquid detergents, molten plastics, and fluids utilized in enhanced oil recovery. On the microscopic scale these polymeric fluids consist of large aggregates or macromolecules and the shape and orientation of these molecules control the properties of the fluid and how it performs in the desired application. It is very difficult to characterize these fluids experimentally because their flow properties, unlike those of Newtonian fluids such as water, become inhomogeneous even in simple geometries. This means that the usual types of measurements (in which the fluid properties are measured at the flow boundaries) are not sufficient to understand and characterize the material response. The investigators have formulated a new equation of state -- a mathematical model -- that more fully describes the microstructural properties of these fluids and how they flow. They now investigate the predictions of this model in various complex flows and compare this with experimental findings. This in turn enables them to develop new means to probe and characterize the properties of the fluids. The complex fluids listed above are used commercially in a variety of geometries that may involve both stretching flows (such as the motion of a jet, flow out of a nozzle) as well as shearing flows (for example pumping of the fluids in a pipe). To ensure that their analytical and experimental results are relevant to researchers in industry, the investigators investigate both steady and time-dependent examples of both types of flow conditions.
