Effect of blockage ratio on flow of a viscoelastic wormlike micellar solution past a cylinder in a microchannel.

Abstract

We present experiments on the flow of a viscoelastic wormlike micellar solution around cylinders (radius R) confined in straight microchannels (width W). Thirteen flow geometries are tested where the blockage ratio is varied over a wide range 0.055 ≤ BR = 2R/W ≤ 0.63. Experiments are performed at negligible Reynolds number, and for Weissenberg numbers Wi = λU/R up to 1000, where U is the average flow speed and λ is the relaxation time of the fluid. Micro-particle image velocimetry is used to characterise the flow state at each BR and Wi. In all of the geometries, a first critical Weissenberg number marks a transition from symmetric flow to an asymmetric but time-steady flow state, while a second higher critical Weissenberg number marks the onset of time-dependent flows. However, we report a clear shift in behaviour over a narrow intermediate range of 0.33 ≲ BR ≲ 0.41. Channels with BR ≤ 0.33 fall in a 'low' BR regime, with instabilities that originate from the downstream stagnation point, while those with BR ≥ 0.44 fall in a 'high' BR regime, with instabilities developing at the upstream stagnation point. Behaviour within the newly-identified intermediate BR regime is complex due to the competing influence of the two stagnation points. We summarise all our results in a flow state diagram covering Wi-BR parameter space, clearly defining the different regimes of blockage ratio for the first time. Our results contribute to the understanding of the complexities of viscoelastic flow in this benchmark geometry.