Elastic instability in stratified core annular flow

Abstract

We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Suprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.PACS numbers: 83.80. Rs, 83.60.Wc, 83.85.Cg Polymer solutions exhibit purely elastic flow instabilities even in the absence of inertia [1]. The almost ubiquitous ingredient of such an elastic instability is the curvature of streamlines: polymers that have been extended along curved streamlines are taken by fluctuations across shear rate gradient in the unperturbed state which, in turn, couples the hoop stresses acting along the curved streamlines to the radial and axial flows and amplifies the perturbation [2,3]. Flat interfaces between two fluids with different viscoelastic properties can also become unstable [4-6] due to the normal stress imbalance across the interface. These instabilities often occur in coextrusion where different polymers are melted in separate screw extruders and then flown simultaneously in the extrusion nozzle. Undesirable wavy interfaces are sometimes observed between the adjacent polymer layers both during the flow and in the final product [7]. Since these instabilities set severe limits to the industrial processes such as film or fiber fabrication, they have been extensively studied before [7,8]. Although previous experiments and theory agree reasonably well [7,9], a comprehensive description of the flow is still lacking [10].In this Letter we propose a quantitative explanation for various flow patterns observed in purely elastic interfacial instabilities. We perform a set of original experiments on co-flow of a polymer solution and water and map the full flow diagram. In contrast to previous experimental studies dealing with macroscopic flows of molten polymers, we focus here on flows of dilute polymer solutions and water in microfluidic devices. The advantage of using dilute polymer solutions is that their elastic properties can easily be tuned by dilution and that most of the theoretical work has been performed for models representing dilute polymeric fluids. The use of microfluidic flow geometries offers simple control and visualisation of the flow.We observe that above some flow rate the interface between the polymer solution and water becomes wavy. Surprisingly, for relatively low velocities...

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