Abstract: Non-Newtonian fluids are characterized by complex rheological behaviour that affects the hydrodynamic features, such as the flow rate–pressure drop relation. While flow rate–pressure drop measurements of such fluids are common in the literature, a comparison of experimental data with theory is rare, even for shear-thinning fluids at low Reynolds number, presumably due to the lack of analytical expressions for the flow rate–pressure drop relation covering the entire range of pressures and flow rates. Such a comparison, however, is of fundamental importance as it may provide insight into the adequacy of the constitutive model that was used and the values of the rheological parameters. In this work, we present a theoretical approach to calculating the flow rate–pressure drop relation of shear-thinning fluids in long, narrow channels that can be used for comparison with experimental measurements. We utilize the Carreau constitutive model and provide a semi-analytical expression for the flow rate–pressure drop relation. In particular, we derive three asymptotic solutions for small, intermediate and large values of the dimensionless pressures or flow rates, which agree with distinct limits previously known and allow us to approximate analytically the entire flow rate–pressure drop curve. We compare our semi-analytical and asymptotic results with the experimental measurements of Pipe et al. (Rheol. Acta, vol. 47, 2008, pp. 621–642) and find excellent agreement. Our results rationalize the change in the slope of the flow rate–pressure drop data, when reported in log–log coordinates, at high flow rates, which cannot be explained using a simple power-law model.
Bio: Dr. Evgeniy Boyko completed his Ph.D. in the Faculty of Mechanical Engineering at the Technion, where he studied fluid mechanics of Newtonian liquids at the microscale and their interaction with elastic boundaries, actuated by electrokinetic forces. He is currently a postdoc at the Department of Mechanical and Aerospace Engineering at the School of Engineering and Applied Science at Princeton, and will then be spending two years as a postdoc at Purdue Engineering. In his postdoctoral studies, Dr. Boyko hopes to address major gaps in our understanding of microscale hydrodynamics of complex non-Newtonian fluids, such as colloidal suspensions, blood, and polymeric solutions, which can exhibit shear-thinning and viscoelastic characteristics. These complex fluids are widely used in various microfluidic applications, which are often fabricated from soft materials and thus may deform due to fluid flow within the device, giving rise to a coupled fluid-structure interaction. Dr. Boyko is interested in studying this yet-poorly-understood microscale interaction between complex non-Newtonian fluids and elastic substrate and elucidating the influence of the viscoelastic effects on such interaction and deformation. He believes that building a proper physical understanding of complex fluid flows holds the potential for the development of new applications beyond microfluidics, leveraging unique properties of non-Newtonian fluids.