Turbulent flows in highly elastic wormlike micelles

Abstract

This work reports on an experimental study of elastic turbulence in a semi-dilute wormlike micelle system made of a highly elastic betaine surfactant solution. The temporal evolution of both rheological quantities and local flow properties is monitored by combining global rheology, optical visualization, and ultrasonic velocimetry. Even at the smallest applied shear rates or shear stresses, we find that the micellar sample develops large Weissenberg (Wi) numbers, leading the flow to undergo a transition to elastic turbulence. Three-dimensional flows are indeed observed all along the flow curve, which therefore cannot be interpreted in the framework of classical shear banding. Strong fluctuations are also recorded in the rheological quantities, in the reflected light intensity, and in velocity profiles. We show that the power spectral densities (PSDs) of these fluctuations display power law behaviours with exponents ranging from −1 to −3 depending on the applied shear stress or shear rate. The exponents inferred from local velocity measurements are found to be spatially dependent, pointing to inhomogeneous turbulence. The nature of the instability and of the transition to elastic turbulence is further discussed in light of recent experimental and theoretical works on wormlike micelles and polymers.