Asymmetric flow of polymer solutions around microfluidic cylinders: Interaction between shear-thinning and viscoelasticity

Abstract

Viscoelastic flow around a cylinder is a model problem representing a wide range of relevant industrial processing and biological applications. Reducing the cylinder to microscopic dimensions conveniently enables the problem to be examined in the absence of inertia. Recently, we have developed glass microfluidic geometries containing long and slender, yet rigidly fixed, microfluidic cylinders, which present a low blockage ratio β=2r/W=0.1, where r=20μm is the cylinder radius and W=400μm is the channel width. Using a shear-banding viscoelastic wormlike micellar (WLM) solution, we showed how the flow around such a cylinder could destabilize beyond a critical Weissenberg number (Wi=λU/r, where λ is a characteristic time of the fluid and U is the average flow velocity), resulting in the asymmetric division of the fluid around either side of the cylinder [Haward et al, Soft Matter15:1927]. In the present work we investigate this flow instability in greater detail using a range of polymer solutions formulated from hydrolyzed poly(acrylamide) (HPAA) dissolved at different concentrations in deionized water. The test fluids present a range of shear-thinning responses under steady shear, and also a wide variety of characteristic times. At low HPAA concentrations, the flow around the cylinder remains essentially symmetric for all Wi, but as the concentration increases, so does the maximum degree of the flow asymmetry observed with increasing Wi. Interestingly, at intermediate concentrations, the flow can resymmetrize at very high Wi. We understand these effects by considering simultaneously both the degree of shear-thinning of the fluid and the imposed Wi, and our analysis shows that both strong shear-thinning and high elasticity are required for the formation of strongly asymmetric flows. Our results represent the first report of this highly asymmetric flow state in polymer solutions, showing that it is a general phenomenon and not only specific to WLM. Our analysis provides a clear insight into the origins of this unusual flow state and may also be relevant to understanding other instances of asymmetries arising in shear-thinning viscoelastic flows.