Pressure measurements in an elastically turbulent co-moving Kelvin-Helmholtz-like shear flow inside a straight Hele-Shaw cell

Abstract

As an experimental model to mimic the flow of bio-fluids in the cell and the flow in tiny blood capillaries, we study the co-moving shear flow of dilute polymeric solutions. An inflection point shear flow profile is created by parallel streams moving at different speeds inside a pressure-driven Hele-Shaw cell. The broad aim is to explore the possible instability mechanisms that lead to Elastic Turbulence, discovered two decades ago (Groisman & Steinberg 2000). The Reynolds number is kept very low ($Re < 0.1$) to eliminate any effects of inertia, ensuring that any present instabilities are purely elastic in nature. The interface is stable if the two co-moving fluids are Newtonian, but the interface becomes wavy (Varshney & Steinberg 2019; David & Steinberg 2024) and elastically turbulent with polymer solutions. Pressure spectra show clear transitions, and the spectral decays have a well-defined form ($S(P) \sim f^{-3.3}$), typical of Elastic Turbulence. Pressure drop measurements ($\Delta P$) across the channel show an increase in drag up to 80% compared to the purely viscous case and exhibit transitions consistent with pressure spectra measurements. These measurements have led to an understanding that Elastic Turbulence in dilute polymeric flows can be excited at Reynolds numbers as low as 0.1, even with parallel shear flows and straight channels. This new finding overturns the two-decade understanding, that Elastic Turbulence could be achieved only in the presence of externally or internally imposed curvature/perturbation in the flow and supports the recent growing body of evidence (Steinberg 2022) which points to the presence of Elastic Turbulence in straight channels with weak perturbations and no curvatures.