Review of the entry flow problem: Experimental and numerical

White, Scott A.; Gotsis, A. D.; Baird, Donald G.

doi:10.1016/0377-0257(87)85007-3

Cited by 179 publications

(64 citation statements)

References 82 publications

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“…The viscoelastic entry flow through a sudden planar contraction with a contraction ratio of 4:1 is widely used for benchmarking numerical methods; cf. the literature reviews [56,42]. We restrict attention to the flow of Oldroyd-B and PTT fluids in the planar 4:1 contraction benchmark for which quantitative numerical results have been provided in [45,1,4,15,32], using the stress tensor representation (STR).…”

Section: Numerical Studies and Discussionmentioning

confidence: 99%

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

Niethammer

Marschall

Kunkelmann

et al. 2017

Numerical Methods in Fluids

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Abstract. A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full combinatorial flexibility between different kinds of rheological models on the one hand, and effective stabilization methods on the other hand. A special emphasis is put on the velocity-stress-coupling on co-located computational grids. Using special face interpolation techniques, a semi-implicit stress interpolation correction is proposed to correct the cell-face interpolation of the stress in the divergence operator of the momentum balance. Investigating the entry-flow problem of the 4:1 contraction benchmark, we demonstrate that the numerical methods are robust over a wide range of Weissenberg numbers and significantly alleviate the high Weissenberg number problem. The accuracy of the results is evaluated in a detailed mesh convergence study.

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Section: Numerical Studies and Discussionmentioning

confidence: 99%

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

Niethammer

Marschall

Kunkelmann

et al. 2017

Numerical Methods in Fluids

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“…This type of flow is relevant for many industrial polymer processing applications, and at high flow rates, it displays a range of interesting dynamics not seen in Newtonian contraction flows and still not completely understood. Comprehensive reviews of the research in this field are, for example, the ones by Boger (1987), White et al (1987), and Owens and Phillips (2002).…”

Section: Introductionmentioning

confidence: 99%

Hele-Shaw rheometry

Drost¹,

Westerweel²

2013

Journal of Rheology

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SynopsisIn this paper, we describe a novel approach to determine the flow behavior index of a power-law fluid by means of a microfluidic device. The concept of this method is based on a mathematical analysis by Aronsson and Janfalk [Eur. J. Appl. Math. 3, 343-366 (1992)] of Hele-Shaw flow of power-law liquids. We implement this approach by driving a non-Newtonian fluid through a glass microfluidic chip with a 100:1 contraction. The flow in this chip satisfies the Hele-Shaw flow conditions in most of the device. Two conjugate p-Laplace equations describe the pressure and stream function in such flows. These equations depend on the flow behavior index, n. Therefore, by fitting the p-Laplace equation to the velocity field obtained from a micro particle image velocimetry measurement of the flow, the flow behavior index of the fluid in the chip can be determined. Because in practice, fluids rarely show perfectly inelastic power-law behavior, conditions under which the assumption of inelastic flow is valid were derived by analyzing Hele-Shaw flow of an Oldroyd-B fluid. The concept was tested using three different classes of model fluids, a Newtonian fluid, an inelastic power-law fluid, and a Boger fluid. In all three cases, satisfactory results were obtained, with values of n deviating at most 4% from values measured using conventional rheometry. The method presented here is expected to be potentially useful in online quality control in, for example, polymer or food processing. V C 2013 The Society of Rheology. [http://dx

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“…[82][83][84] 4. Coil-stretch transition at high Wi in random flow and flow around obstacles Polymeric flows above Wi of O(1), typically exhibit a number of intriguing flow phenomena such as vortex formation and wobble, die swelling, and drag reduction in industrially relevant flows.…”

Section: Dynamics Of Dna In Contraction Flowmentioning

confidence: 99%

Flow of DNA in micro/nanofluidics: From fundamentals to applications

et al. 2016

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Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil–stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.

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Review of the entry flow problem: Experimental and numerical

Cited by 179 publications

References 82 publications

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes

Hele-Shaw rheometry

Flow of DNA in micro/nanofluidics: From fundamentals to applications

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