Pressure-driven flow in thin domains

Fabricius, John; Miroshnikova, Elena; Tsandzana, Afonso Fernando; Wall, Peter

doi:10.3233/asy-191535

Cited by 5 publications

(5 citation statements)

References 9 publications

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“…This dimensional reduction will be achieved by using an adaptation of a technique called two-scale convergence for thin domains which was developed by Marušić and Marušić-Paloka [1]. The present results generalize [2] where the Newtonian case was considered without any obstacle in the geometry. Moreover, we generalize the classical Poiseuille law, see e.g.…”

Section: Introductionsupporting

confidence: 55%

“…16-22] or [30, p. 55]. The parameter p is dimensionless while μ 0 has units which depend on the value of p. When p = 2 we recover the case of a Newtonian fluid studied in [2].…”

Section: Power-law Fluidmentioning

confidence: 99%

“…In this appendix, we generalize the Korn inequalities proved in [2], where the case p = 2 was considered. Let be the cube in R 3 defined by = (−1/2, 1/2) 3 and let ε be the cube defined by ε = (−ε/2, ε/2) 3 .…”

Section: Appendices Appendix 1 Proof Of Theorem 21mentioning

confidence: 99%

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On pressure-driven Hele–Shaw flow of power-law fluids

Fabricius

Manjate

Wall

2021

Applicable Analysis

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We analyze the asymptotic behavior of a non-Newtonian Stokes system, posed in a Hele-Shaw cell, i.e. a thin three-dimensional domain which is confined between two curved surfaces and contains a cylindrical obstacle. The fluid is assumed to be of power-law type defined by the exponent 1 < p < ∞. By letting the thickness of the domain tend to zero we obtain a generalized form of the Poiseuille law, i.e. the limit velocity is a nonlinear function of the limit pressure gradient. The flow is assumed to be driven by an external pressure which is applied as a normal stress along the lateral part of the boundary. On the remaining part of the boundary we impose a no-slip condition. The two-dimensional limit problem for the pressure is a generalized form of the p -Laplace equation, 1/p + 1/p = 1, with a coefficient called 'flow factor', which depends on the geometry as well as the power-law exponent. The boundary conditions are preserved in the limit as a Dirichlet condition for the pressure on the lateral boundary and as a Neumann condition for the pressure on the solid obstacle.

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Section: Introductionsupporting

confidence: 55%

“…16-22] or [30, p. 55]. The parameter p is dimensionless while μ 0 has units which depend on the value of p. When p = 2 we recover the case of a Newtonian fluid studied in [2].…”

Section: Power-law Fluidmentioning

confidence: 99%

See 1 more Smart Citation

On pressure-driven Hele–Shaw flow of power-law fluids

Fabricius

Manjate

Wall

2021

Applicable Analysis

Self Cite

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“…They obtained exact solutions corresponding to periodic, solitary and kink-type bidirectional travelling waves, which, from the Reynolds equation with a Dirichlet boundary condition for the pressure, were found to be in better agreement with engineering practice. The study of asymptotic pressure-driven flow in a thin domain was studied by Fabricius et al [8]. They discovered that by prescribing the external pressure as normal pressure, the Dirichlet condition for a limit pressure was discovered.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of flow and pressure variation inside a horizontalfilter chamber using Lie symmetry analysis

Itumeleng

Magalakwe

Motsepa

et al. 2023

Preprint

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Physical model exact solutions improve crucial industrial production processes by giving operatorsand designers a greater grasp of how systems operate in practice. The current casestudy aims to find exact momentum and pressure variation solutions during the unsteadystatefiltration process to advance fluid purification. Lie symmetry analysis is used to transforma system of PDEs representing the flow and pressure variation into solvable ODEswithout changing the dynamics of the case study. The velocity (momentum) and pressuresolutions are then determined by integrating the obtained solvable ODEs. The effects ofphysical parameters resulting from the process dynamics are examined using the exact solutionsacquired to identify the parameter combination that results in the maximum permeatesoutflow. Graphical representations of the flow velocity and pressure are presented and analysedas well as the skin friction tabular. The results indicate that as time evolves, permeateoutflow decreases because internal momentum, work done, and pressure diminish over timedue to the clustering of particles. In addition, low wave speed, small porosity, more chamberspace, high injection rate, and stronger magnetic effects are ideal for minimising the effectsof no-slip condition at the bottom wall during operation.

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“…Linear reaction-diffusion-convection equations coupled with non-linear surface chemical reactions for infinitely thin layers were studied in [17] in the context of smoldering combustion. In [16], the authors studied pressure-driven Stokes flow through a infinitely thin layer. A double porosity scenario with jumps at sharp heterogeneities was studied in [9].…”

Section: Introductionmentioning

confidence: 99%

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

Raveendran¹,

Cirillo²,

Bonis³

et al. 2021

Preprint

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We study the question of periodic homogenization of a variably scaled reaction-diffusion problem with non-linear drift posed for a domain crossed by a flat composite thin layer. The structure of the non-linearity in the drift was obtained in earlier works as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) process for a population of interacting particles crossing a domain with obstacle.Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive the homogenized evolution equation and the corresponding effective model parameters for a regularized problem. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interface in essentially two different situations: (i) finitely thin layer and (ii) infinitely thin layer.This study should be seen as a preliminary step needed for the investigation of averaging fast non-linear drifts across material interfaces -a topic with direct applications in the design of thin composite materials meant to be impenetrable to high-velocity impacts.

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Pressure-driven flow in thin domains

Cited by 5 publications

References 9 publications

On pressure-driven Hele–Shaw flow of power-law fluids

On pressure-driven Hele–Shaw flow of power-law fluids

Exact solutions of flow and pressure variation inside a horizontalfilter chamber using Lie symmetry analysis

Scaling effects on the periodic homogenization of a reaction-diffusion-convection problem posed in homogeneous domains connected by a thin composite layer

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