The inertio-elastic planar entry flow of low-viscosity elastic fluids in micro-fabricated geometries
Lucy E. Rodda, c, , , Timothy P. Scottc, David V.
Bogera, Justin J. Cooper-Whitea, b and
Gareth H. McKinleyc
aDepartment of Chemical and Biomolecular Engineering, The University of Melbourne, Vic. 3010, Australia
bDivision of Chemical Engineering, The University of Queensland, Brisbane, Qld 4072, Australia
cHatsopoulos Microfluids Laboratory, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Received 4 January 2005; revised 13 April 2005; accepted 13 April 2005. Available online 22 September 2005.
The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through micro-fabricated planar abrupt contraction–expansions is investigated. The small lengthscales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. By considering the definition of the elasticity number, El = Wi/Re, we show that the lengthscale of the geometry is key to the generation of strong viscoelastic effects, such that the same flow behaviour cannot be reproduced using the equivalent macro-scale geometry using the same fluid. We observe significant vortex growth upstream of the contraction plane, which is accompanied by an increase of more than 200% in the dimensionless extra pressure drop across the contraction. Streak photography and video-microscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.44 ≤ Re ≤ 64) associated with these high Weissenberg number (0 ≤ Wi ≤ 548) micro-fluidic flows results in the exploration of new regions of the Re–Wi parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in micro-fluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = Wi/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.
Keywords: Contraction–expansion; Polyethylene oxide (PEO); Elasticity number; Flow instability