One principal output of fluid mechanics research is the quantitative understanding of the relationship between flow rate and pressure drops (power requirements). While such relationships are well understood from first principles for Newtonian flows, it is hardly the case for viscoelastic, polymeric flows. Significant advances in this area will undoubtedly have pronounced impact on knowledge-based design of polymer processing operations and polymer-based products that constitute a significant portion of the U.S. manufacturing economy. The central goal of this research is the development of a quantitative understanding of the flow-microstructure coupling mechanisms in viscoelastic polymer solutions that in turn determine their friction drag behavior under conditions of negligible inertia. Specifically, the PIs plan a highly integrated research program that will leverage from recently developed multiscale (micro-macro) and continuum-level computational tools within the PIs' groups to investigate the intriguing phenomenon of friction resistance enhancement (FRE), where the pressure drop increases abruptly as the flow rate of a viscoelastic polymer solution through variable conduit, exceeds a critical value. Depending on the flow geometry, this pressure drop saturates at a value that greatly exceeds that for a Newtonian liquid of identical viscosity. While FRE has been known experimentally since the 1960s, it has not been explained based on first principles primarily due to the computational bottlenecks associated with the simulation of multi-dimensional and/or time-dependent viscoelastic flows using realistic models. Two hypotheses have been put forward to explain FRE, namely stress-conformation hysteresis (attributed to the inherent asymmetry in molecular unraveling and relaxation when an elastic polymer solution is subjected to contraction/expansion) and nonlinear flow transitions caused by a series of purely elastic flow instabilities. Both will be put to rigorous test in these studies. This study will develop much needed large-scale multiscale or 'micro-macro' simulations, integrating continuum-level finite element or spectral solvers with fast integrators of stochastic differential equations to describe the evolution of polymer configuration. This will require efficient parallel algorithms to track nonlinear flow transitions in inertialess, viscoelastic flows and their use to understand the effect of elastically-induced flow modifications on friction drag. The two PIs share complementary expertise and are ideally placed to undertake these efforts. NSF-supported TLSAMP, Pipeline Engineering Diversity Program and GEM will be used to ensure participation of African-American, Hispanic-American, Native-American and female students. Internet-ready instruction modules will be developed for enhancing curriculum in the broader areas of complex fluids, scientific computing and within an existing NSF-REU program that focuses on complex fluids dynamics. The PIs will also use the extensive outreach infrastructure at their respective institutions to involve K-12 teachers and high school students in the research program.
