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  • Bifurcation phenomena in viscoelastic flows through a symmetric 1: 4 expansion
    Publication . Rocha, Gerardo N.; Poole, R. J.; Oliveira, Paulo J.
    In this work we present an investigation of viscoelastic flow in a planar sudden expansion with expansion ratio D/d = 4. We apply the modified FENE–CR constitutive model based on the non-linear finite extensibility dumbbells (FENE) model. The governing equations were solved using a finite volume method with the high-resolution CUBISTA scheme utilised for the discretisation of the convective terms in the stress and momentum equations. Our interest here is to investigate two-dimensional steady-state solutions where, above a critical Reynolds number, stable asymmetric flow states are known to occur.We report a systematic parametric investigation, clarifying the roles of Reynolds number (0.01 < Re < 100),Weissenberg number (0 < We < 100) and the solvent viscosity ratio (0.3 < β < 1). For most simulations the extensibility parameter of the FENE model was kept constant, at a value L2 = 100, but some exploration of its effect in the range 100–500 shows a rather minor influence. The results given comprise flow patterns, streamlines and vortex sizes and intensities, and pressure and velocity distributions along the centreline (i.e. y = 0). For the Newtonian case, in agreement with previous studies, a bifurcation to asymmetric flow was observed for Reynolds numbers greater than about 36. In contrast viscoelasticity was found to stabilise the flow; setting β = 0.5 and We = 2 as typical values, resulted in symmetric flow up to a Reynolds number of about 46. We analyse these two cases in particular detail.
  • Purely Elastic Flow Asymmetries
    Publication . Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.
    Using a numerical technique we demonstrate that the flow of the simplest differential viscoelastic fluid model (i.e., the upper-convected Maxwell model) goes through a bifurcation to a steady asymmetric state when flowing in a perfectly symmetric ‘‘cross-slot’’ geometry. We show that this asymmetry is purely elastic in nature and that the effect of inertia is a stabilizing one. Our results are in qualitative agreement with very recent experimental visualizations of a similar flow in the microfluidic apparatus of Arratia et al. [Phys. Rev. Lett. 96, 144502 (2006)].
  • Laminar flow of a viscoelastic shear-thinning liquid through a plane sudden expansion preceded by a gradual contraction
    Publication . Poole, R. J.; Escudier, M. P.; Oliveira, Paulo J.
    Experimental observations are reported for the laminar flow of a viscoelastic liquid through a symmetrical plane sudden expansion preceded by a gradual contraction from a square duct. As is well known, for Newtonian fluid flow above a critical Reynolds number the flowfield downstream of an expansion becomes asymmetric. For the viscoelastic liquid investigated here the asymmetry is greatly reduced, with very similar reattachment lengths for the two recirculation regions. More significantly, the flow unexpectedly develops a strongly three-dimensional jet-like structure, with side-to-side symmetry centred on the ‘vertical’ symmetry plane of the contraction/expansion geometry. Especially interesting is the flow within the contraction itself, where the nature of the flow field for the viscoelastic liquid is also fundamentally different to that for a comparable Newtonian fluid flow: large velocity overshoots with very strong gradients occur near to the sidewalls that, due to their appearance, we have termed ‘cat’s ears’. The fully developed approach flow in the square duct is unremarkable.
  • Enhanced Microfluidic Mixing via a Tricritical Spiral Vortex Instability
    Publication . Haward, Simon J.; Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.; Goldenfeld, Nigel; Shen, Amy Q.
    Experimental measurements and numerical simulations are made on fluid flow through cross-slot devices with a range of aspect (depth:width) ratios, 0.4 < alpha < 3.87. For low Reynolds numbers Re, the flow is symmetric and a sharp boundary exists between fluid streams entering the cross-slot from opposite directions. Above an alpha-dependent critical value Re_c, the flow undergoes a symmetry-breaking bifurcation (though remains steady and laminar) and a spiral vortex structure develops about the central axis of the outflow channel. An order parameter characterizing the instability grows according to a sixth-order Landau potential, and shows a progression from second order to first order transitions as alpha increases. A tricritical point occurs for alpha ~ 0.55. The spiral vortex acts as a mixing region in the flow field and this phenomenon can be used to drive enhanced mixing in microfluidic devices.
  • Plane sudden expansion flows of viscoelastic liquids
    Publication . Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.; Pinho, Fernando
    We report a systematic numerical investigation of the creeping flow of three different viscoelastic models, the UCM, Oldroyd-B and the linear form of the PTT model, through a 1:3 planar sudden expansion. Although the effect of elasticity is to reduce both the length and intensity of the recirculation region downstream of the expansion, we show that this reduction is much lower than previous studies have suggested and that, at high Deborah number, a significant region of recirculation still exists for all of the models studied.
  • Lid-driven cavity flow of viscoelastic liquids
    Publication . Sousa, R. G.; Poole, R. J.; Afonso, A. M.; Pinho, F. T.; Oliveira, P. J.; Morozov, A.; Alves, M. A.
    The lid-driven cavity flow is a well-known benchmark problem for the validation of new numerical meth- ods and techniques. In experimental and numerical studies with viscoelastic fluids in such lid-driven flows, purely-elastic instabilities have been shown to appear even at very low Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation formulation, is used in this work to probe the effect of viscoelasticity on the appearance of such instabilities in two-dimensional lid-driven cavities for a wide range of aspect ratios (0.125 ≤ = height/length ≤4.0), at different Deborah numbers under creeping-flow conditions and to understand the effects of regularization of the lid velocity. The effect of the viscoelasticity on the steady-state results and on the critical conditions for the onset of the elastic instabilities are described and compared to experimental results.
  • On extensibility effects in the cross-slot flow bifurcation
    Publication . Rocha, Gerardo N.; Poole, R. J.; Alves, M. A.; Oliveira, Paulo J.
    The flow of finite-extensibility models in a two-dimensional planar cross-slot geometry is studied numerically, using a finite-volume method, with a view to quantifying the influences of the level of extensibility, concentration parameter, and sharpness of corners, on the occurrence of the bifurcated flow pattern that is known to exist above a critical Deborah number. The work reported here extends previous studies, in which the viscoelastic flow of upper-convected Maxwell (UCM) and Oldroyd-B fluids (i.e. infinitely extensionable models) in a cross-slot geometry was shown to go through a supercritical instability at a critical value of the Deborah number, by providing further numerical data with controlled accuracy.We map the effects of the L2 parameter in two different closures of the finite extendable non-linear elastic (FENE) model (the FENE-CR and FENE-P models), for a channel-intersecting geometry having sharp, “slightly” and “markedly” rounded corners. The results show the phenomenon to be largely controlled by the extensional properties of the constitutive model, with the critical Deborah number for bifurcation tending to be reduced as extensibility increases. In contrast, rounding of the corners exhibits only a marginal influence on the triggering mechanism leading to the pitchfork bifurcation, which seems essentially to be restricted to the central region in the vicinity of the stagnation point.
  • The effect of expansion ratio for creeping expansion flows of UCM fluids
    Publication . Poole, R. J.; Pinho, Fernando; Alves, M. A.; Oliveira, Paulo J.
    A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER≥4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER≤3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases.