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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 89
Edited by: M. Papadrakakis and B.H.V. Topping
Paper 98

Viscoelastic Low-Reynolds-Number Flows in Mixing-Separating Cells

A. Afonso1, M.A. Alves1, R.J. Poole2, P.J. Oliveira3 and F.T. Pinho1,4

1Chemical Engineering Department, CEFT, Faculty of Engineering, University of Porto, Portugal
2Department of Engineering, University of Liverpool, United Kingdom
3Department of Electromechanics Engineering, MTP Unit, University of Beira Interior, Covilhã, Portugal
4University of Minho, Braga, Portugal

Full Bibliographic Reference for this paper
A. Afonso, M.A. Alves, R.J. Poole, P.J. Oliveira, F.T. Pinho, "Viscoelastic Low-Reynolds-Number Flows in Mixing-Separating Cells", in M. Papadrakakis, B.H.V. Topping, (Editors), "Proceedings of the Sixth International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 98, 2008. doi:10.4203/ccp.89.98
Keywords: mixing-separating, low Reynolds number, viscoelastic fluids, upper-convected Maxwell model, elastic instabilities, flow bifurcation.

An investigation of Newtonian and viscoelastic flows is carried out on the mixing-separating geometry of Cochrane et al. [1]. This consists of a low Reynolds number flow in two opposed channels sharing a common wall, where a gap allows the interaction between the two flows (Re<40).

For Newtonian fluids the flow is anti-symmetric, due to the anti-symmetry of the fully-developed inlet conditions and the symmetry of the flow geometry. Increasing the gap size increased the reversed flow rate ratio (Rr), here defined as the ratio between the reversed and total flow rates.

The creeping flow of upper-convected Maxwell (UCM) fluids showed two distinct flow patterns and for a combination of critical flow geometries, it was possible to identify a new steady bi-stable bifurcation pattern at low inertia and high elasticity. For normalized gap sizes below a critical value the reversed flow is slightly enhanced by viscoelasticity, followed by a strong decrease in Rr towards zero as the Deborah number De further increases. Above a supercritical gap size, viscoelasticity is responsible for a continuous increase in Rr. For a near-critical gap size it was possible to observe a sudden jump between the two flow conditions at slightly different Deborah numbers.

Flow inertia was found to increase the critical Deborah number for the steady flow bifurcation at a particular value of the gap non-dimensional width. Inertia naturally enhances the straight flow case and at Re=5, Rr always decreased with Deborah number for De<=0.6 and for the investigated gap sizes.

These predictions suggest the need for experiments with very viscous elastic fluids in order to detect the supercritical behavior, which has so far not been reported in the literature.

A.T. Cochrane, K. Walters, M.F. Webster, "On Newtonian and non-Newtonian flow in complex geometries", Philos. Trans. R. Soc. London, A301, 163-181, 1981. doi:10.1098/rsta.1981.0103

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