Modeling and Simulation of a Complex Fluid: Wormlike Micellar SolutionsMichael Cromer, Jr.
University of Delaware, Department of Mathematical Sciences
Tuesday, November 30, 2010 15:00-16:00,
In wall-driven shearing flows such as circular Taylor-Couette flow, it is known that many wormlike micellar solutions exhibit a shear-banding transition resulting in a high shear-rate region near the inner, rotating cylinder and a low shear-rate region located towards the outer, fixed wall. These solutions consist of long self-assembled micellar aggregates (`wormlike micelles') which entangle in solution, thus exhibiting viscoelastic properties; these aggregates can also break and reform. The VCM model (Vasquez, McKinley and Cook, Journal of Non-Newtonian Fluid Mechanics, 2007) describes the coupled evolution of two chain species: long chains which can break in half to form shorter chains, which can themselves recombine to form a long worm. In this presentation, predictions of the VCM model are examined in time-dependent, one-dimensional filament stretching and in pressure-driven flow through a straight channel. The resulting velocity profile deviates from the parabolic profile expected for a Newtonian fluid, exhibiting an interior layer that connects high and low shear-rate bands. An adaptive spectral method is developed to track and resolve the spatial and temporal evolution of this thin interior layer. Linear stability analysis of the steady pressure-driven flow shows that at banding an interfacial instability can arise resulting in a 2D sinuous (snake-like) perturbation flow in the flow/gradient plane, with local fluctuations along the interface between bands. Further analysis shows that decreasing the channel height leads to a critical height at which the flow stabilizes.
Speaker Bio: Mike Cromer is currently a graduate student in the Department of Mathematical Sciences at the University of Delaware. He received his B.S. in mathematics from York College of Pennsylvania in 2005 and is on course to receive his Ph.D. in applied mathematics from UD in May 2011. Mike's current research involves the analysis and simulation of nonlinear mathematical models developed for complex fluids with particular interest in how these models compare with flows of wormlike micellar solutions. His research is under the advisement of Prof. Pam Cook in collaboration with Prof. Gareth McKinley (Dept. of Mechanical Engineering, MIT). He was a visiting graduate student at the Institute for Mathematics and its Applications at the University of Minnesota in the fall of 2009 during the special year on complex fluids and complex flows. Mike has been supported under a National Science Foundation collaborative research grant and is currently supported by a University Dissertation Fellowship.
Contact: G. B. McFadden
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