Secondary flows of viscoelastic fluids in serpentine microchannels
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Secondary flows are ubiquitous in channel flows, where small velocity components perpendicular to the main velocity appear due to the complexity of the channel geometry and/or that of the flow itself such as from inertial or non-Newtonian effects. We investigate here the inertialess secondary flow of viscoelastic fluids in curved microchannels of rectangular cross-section and constant but alternating curvature: the so-called “serpentine channel” geometry. Numerical calculations (Poole et al. J Non-Newton Fluid Mech 201:10–16, 2013) have shown that in this geometry, in the absence of elastic instabilities, a steady secondary flow develops that takes the shape of two counter-rotating vortices in the plane of the channel cross-section. We present the first experimental visualization evidence and characterisation of these steady secondary flows, using the complementary techniques of quantitative microparticle image velocimetry in the centreplane of the channel, and confocal visualisation of dye-stream transport in the cross-sectional plane. We show that the measured streamlines and the relative velocity magnitude of the secondary flows are in qualitative agreement with the numerical results. In addition to our techniques being broadly applicable to the characterisation of three-dimensional flow structures in microchannels, our results are important for understanding the onset of instability in serpentine viscoelastic flows.
KeywordsPolymer solutions Non-Newtonian fluids Vortices Confocal microscopy Particle image velocimetry
AL and LD acknowledge funding from the ERC Consolidator Grant PaDyFlow (Grant Agreement no. 682367). RJP acknowledges funding for a “Fellowship” in Complex Fluids and Rheology from the Engineering and Physical Sciences Research Council (EPSRC, UK) under grant number EP/M025187/1, and support from Chaire Total. SJH, AQS and LD gratefully acknowledge the support of the Okinawa Institute of Science and Technology Graduate University (OIST) with subsidy funding from the Cabinet Office, Government of Japan, and funding from the Japan Society for the Promotion of Science (Grant nos. 17K06173, 18H01135 and 18K03958). SL acknowledges funding from the Institut Universitaire de France. We would also like to acknowledge discussions on the nature of the secondary flow with Philipp Bohr and Christian Wagner. This work has received the support of Institut Pierre-Gilles de Gennes (Équipement d’Excellence, “Investissements d’avenir”, program ANR-10-EQPX-34).
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