Role of the elasticity number in the entry flow of dilute polymer solutions in micro-fabricated contraction geometries

Abstract

We explore the interplay of fluid inertia and fluid elasticity in planar entry flows by studying the flow of weakly elastic solutions through micro-fabricated planar contraction geometries. The small characteristic lengthscales make it possible to achieve a wide range of Weissenberg numbers (0.4 < Wi < 42) and Reynolds numbers (0.03 < Re < 12), allowing access to a large region of Wi– Re space that is typically unattainable in conventional macroscale entry flow experiments. Experiments are carried out using a series of dilute solutions (0.78 < c/ c * < 1.09) of a high molecular weight polyethylene oxide, in which the solvent viscosity is varied in order to achieve a range of elasticity numbers, 2.8 < El = Wi/ Re < 68. Fluorescent streak imaging and micro-particle image velocimetry (μ-PIV) are used to characterize the kinematics, which are classified into a number of flow regimes including Newtonian-like flow at low Wi, steady viscoelastic flow, unsteady diverging flow and vortex growth regimes. Progressive changes in the centreline velocity profile are used to identify each of the flow regimes and to map the resulting stability boundaries in Wi– Re space. The same flow transitions can also be detected through measurements of the enhanced pressure drop across the contraction/expansion which arise from fluid viscoelasticity. The results of this work have significant design implications for lab-on-a-chip devices, which commonly contain complex geometric features and transport complex fluids, such as those containing DNA or proteins. The results also illustrate the potential for using micro-fabricated devices as rheometric tools for measuring the extensional properties of weakly elastic fluids.