Fifty years of non‐Newtonian fluid dynamics

Denn, Morton M.

doi:10.1002/aic.10357

Cited by 75 publications

(53 citation statements)

References 143 publications

(155 reference statements)

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“…These relations ensure the elimination of the pressure unknowns in the conservation equations, and the automatic enforcement of the continuity constraint on the discrete level to the machine precision. 2 Note that the line-integrations around the discrete streamfunction variables laying on the boundary Fig. 1.…”

Section: Discrete Curl Operatorsmentioning

confidence: 99%

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Robust simulations of viscoelastic flows at high Weissenberg numbers with the streamfunction/log-conformation formulation

Comminal

Spangenberg

Hattel

2015

Journal of Non-Newtonian Fluid Mechanics

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Section: Discrete Curl Operatorsmentioning

confidence: 99%

“…Viscoelastic fluids exhibit different flow features as compared to purely viscous fluids, such as turbulence drag reduction [1], elastic instabilities [2,3], and elastic turbulence at low Reynold numbers [4,5]. These viscoelastic effects are magnified in micro-fluidics [6].…”

Section: Introductionmentioning

confidence: 99%

Robust simulations of viscoelastic flows at high Weissenberg numbers with the streamfunction/log-conformation formulation

Comminal

Spangenberg

Hattel

2015

Journal of Non-Newtonian Fluid Mechanics

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“…Non-Newtonian fluids have been extensively studied since the 1940s, when investigations carried out during the Second World War showed several interesting phenomena and stimulated numerous industrial applications (Denn, 2004). Thereafter, flows of viscoelastic fluids and consequently the impact of their rheological properties on the flow patterns were the aim of several research studies.…”

Section: Introductionmentioning

confidence: 99%

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

Sousa

Pinho

Oliveira

et al. 2011

Chemical Engineering Science

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a b s t r a c tIn this work we investigate the laminar flow through square-square sudden contractions with various contraction ratios (CR ¼ 2.4, 4, 8 and 12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streak line photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shearthinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes timedependent at De E 200, 300, 70 and 450 for CR ¼2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments.

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“…This geometric separation of length scales leads to a separation of time scales that is at the heart of a range of unusual behaviour arising from the confluence of geometry and physics in these objects. While this interplay has been the subject of much research in the context of simple Newtonian fluids, only recently have analogous questions been asked for complex fluids, such as those encountered commonly in the kitchen when an egg is broken, in the bathroom when shampoo is squirted from a bottle, and in a host of applications such as rheometry and fibre processing of polymer melts and solutions (McKinley & Sridhar 2002;Denn 2004). However, much of this work has been focused on the one-dimensional dynamics of stretching and the accompanying thinning (Keiller 1992;Entov & Hinch 1997;Olagunju 1999).…”

Section: Introductionmentioning

confidence: 99%

Fall and rise of a viscoelastic filament

2006

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When a viscoelastic fluid blob is stretched out into a thin horizontal filament, it sags and falls gradually under its own weight, forming a catenary-like structure that evolves dynamically. If the ends are brought together rapidly after stretching, the falling filament tends to straighten by rising. These two effects are strongly influenced by the elasticity of the fluid and yield qualitatively different behaviours from the case of a purely viscous filament analysed previously (Teichman & Mahadevan, J. Fluid Mech. vol. 478, 2003, p. 71). Starting from the bulk equations for the motion of a viscoelastic fluid, we derive a simplified equation for the dynamics of a viscoelastic filament and analyse this equation in some simple settings to explain our observations.

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Fifty years of non‐Newtonian fluid dynamics

Cited by 75 publications

References 143 publications

Robust simulations of viscoelastic flows at high Weissenberg numbers with the streamfunction/log-conformation formulation

Robust simulations of viscoelastic flows at high Weissenberg numbers with the streamfunction/log-conformation formulation

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square–square contractions

Fall and rise of a viscoelastic filament

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