(454f) Leveraging Elasto-Inertial Instabilities in Curvilinear Geometries for Advanced Liquid Cooling Applications

It is well known that the steady shearing flow of a viscoelastic fluid, such as the torsional flow between a cone and plate or the curvilinear flow in a Taylor-Couette geometry, becomes unstable to a three-dimensional time-dependent instability. This instability is driven by the elastic stresses in the fluid acting along curved streamlines resulting in a secondary motion beyond a critical Deborah (De) or Weissenberg (Wi) number. In the absence of inertia, i.e., in the low Reynolds number (Re) regime, shear thinning delays the onset of such instability to a higher critical De, thus, stabilizing the flow. In the presence of inertia, (i.e., the high Re regime), these elastic instabilities lead to the onset of elasto-inertial turbulence well below the critical value of Re for the onset of purely inertial turbulence, thus destabilizing the flow. However, the combined effects of fluid elasticity, shear-thinning and finite inertia on the onset of elasto-inertial instabilities are not completely understood. To this end, we experimentally explore the entire Wi – Re phase space plane for a number of canonical viscoelastic fluids with varied levels of shear thinning (quantified using a shear thinning parameter β_P) in torsional shear flows.

Particularly, we tune the strength of shear thinning by varying the concentration of the polymer in the solution. For dilute solutions, this inherently leads to the presence of finite inertia before the onset of elastic instability, thus, naturally resulting in an elasto-inertial coupling. We perform torsional flow experiments in cone-and-plate and concentric cylinder geometries to investigate the effects of flow geometry. Flow visualizations reveal the coupled effects of varying Wi, Re, and β_P on the emergence and quantify the spatio-temporal dynamics of the different secondary motions observed close to the onset of instability. We compile our results in a state diagram (in Re-Wi space) of critical conditions of instability. This critical state diagram quantitatively depicts the competition between the stabilizing effects of shear thinning and destabilizing effects of inertia. We extend the existing Pakdel-McKinley instability criterion for the onset of a purely elastic instability in curvilinear geometries by incorporating both shear thinning and finite inertial effects. This generalized criterion facilitates predictions of the onset of complex instabilities over a wider range of flow conditions and bridges the gap between purely elastic and purely inertial instabilities. The results elevate our fundamental physical understanding of inertioelastic coupling and the role of shear-thinning on complex three-dimensional flow instabilities. Owing to the ubiquity of viscoelastic and shear-thinning fluids in nature and in industry, these insights will be beneficial in understanding how the fluid rheology and flow conditions can be optimized in advanced energy-material operations. Specifically, we use time-resolved measurements of the pumping power reductions and operational heat transfer enhancements that can be obtained by exploiting curvilinear flows of viscoelastic polymer solutions to realize new liquid coolant solutions that outperform the current state-of-the art Newtonian heat transfer oils in advanced electronics and battery cooling applications.