Understanding pressure drop-flow rate relationships in inertialess viscoelastic flows: effects of flow instability and stress-conformation hysteresis

Bamin Khomami (University of Tennessee, USA), Mahdy Malakzadeh (University of Tennessee, USA), and Rahdakrishna Sureshkumar (Washington University, USA)

One of the principal outputs of fluid mechanics research is the quantitative understanding of the relationship between flow rate (throughput) and pressure/friction losses (power requirements). While such relationships are well understood from first principles analysis 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, we are investigating the intriguing phenomenon of friction resistance enhancement (FRE) that manifests experimentally in the following fashion: when a viscoelastic polymer solution flows, under creeping (inertialess) flow conditions, through conduits with cross sectional area variations (e.g., geometries with contraction/expansion as in the case of die flows used in polymer processing), the pressure drop recorded is seen to increase abruptly as the flow rate exceeds a critical value and, depending on the flow geometry, saturates at a value that greatly exceeds that for a Newtonian liquid of identical viscosity. While the FRE phenomenon has been known experimentally since the 1960s, it has not been explained based on first principles theory/simulations, 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 of which will be put to rigorous test in our studies.