Elastic-plated gravity currents

Hewitt, Ian; Balmforth, N. J.; Bruyn, John R. de

doi:10.1017/s0956792514000291

Cited by 68 publications

(132 citation statements)

References 30 publications

(71 reference statements)

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“…When deflections are smaller than the thickness of the pocket, the pocket is bent and analytical solutions developed in previous works were sought (Koialovich, 1902;Boobnoff, 1902;Amon and Widera, 1969;Chandrashekhara, 2001;Meleshko, 1997;Hewitt et al, 2015), while when the deformations are greater than the thickness, the pocket is stretched and numerical solutions were extended using Finite Element Analysis.…”

Section: Discussionmentioning

confidence: 99%

“…In the case of a ring, when α tends to 1, Hewitt et al (2015) obtained an asymptotical approximation of γ b equal to (1 − σ 2 )/32. In the stretching regime, the maximum deflection reduces as well when the size of the hole (α) increases for both shapes.…”

Section: Maximum Displacementsmentioning

confidence: 99%

“…In the case of a ring, γ s can be rewritten as approximately (3(1 − σ 2 )) 1/3 /4 when α tends to 1 (Hewitt et al, 2015). Details of γ s and γ b for both doubly-connected shapes are given in figure 13.…”

Section: Maximum Displacementsmentioning

confidence: 99%

“…One of the limitations of their model is that the stretch ratio can be considered as averaged, as their model assumed a uniform inflation over the surface of the disk. More recently, Hewitt et al (2015) developed an elastohydrodynamic lubrification theory that characterise deflection of elastic sheets under different conditions. Lister et al (2013) applied an optical method to measure deflection with high resolution along a line when peeling sheets are bent or stretched.…”

Section: Introductionmentioning

confidence: 99%

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Pursing of planar elastic pockets

Bouremel

Madaan

Lee

et al. 2017

Journal of Fluids and Structures

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The pursing of a simply-or doubly-connected planar elastic pocket by an applied pressure is analysed from the bending to the stretching regimes. The response is evaluated in terms of maximum deflection and profiles across a range of simply-and doubly-connected circular and square shapes. The study is conducted using experimental and numerical methods and supported by previous analytical results. The experimental method is based on an original 2D optical method that gives access to the pursing direction perpendicular to each image across the field of view. The equations for maximum pursing deflections are developed and compared for a range of thicknesses of silicone samples and shapes from the bending to the stretching regimes. In the case of doubly-connected shapes, dependence of maximum pursing deflection on clamped central circular and square areas or holes is quantified for both regimes. Good agreement is established between the three methods and the study also shows that the optical method may as well be successfully applied to problems of pursing of rubber pockets.

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Section: Discussionmentioning

confidence: 99%

Section: Maximum Displacementsmentioning

confidence: 99%

Section: Maximum Displacementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pursing of planar elastic pockets

Bouremel

Madaan

Lee

et al. 2017

Journal of Fluids and Structures

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“…The solution for γ (υ) is discussed below, but first, we translate the result back to the notation of the ruck problem. We have determined 11) and so the energy constraint (2.11) is…”

Section: (B) a Thermodynamic Adhesion Modelmentioning

confidence: 99%

The speed of an inclined ruck

Balmforth

Hewitt

2015

Proc. R. Soc. A.

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Steady rucks in an elastic beam can roll at constant speed down an inclined plane. We examine the dynamics of these travelling-wave structures and argue that their speed can be dictated by a combination of the physical conditions arising in the vicinity of the 'contact points' where the beam is peeled off the underlying plane and stuck back down. We provide three detailed models for the contact dynamics: viscoelastic fracture, a thermodynamic model for bond formation and detachment and adhesion mediated by a thin liquid film. The results are compared with experiments.

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Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Anand

Christov

2020

Z Angew Math Mech

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A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross‐sectional area. The latter gives rise to a non‐constant pressure gradient in the flow‐wise direction and, hence, to a nonlinear flow rate–pressure drop relation (unlike the Hagen–Poiseuille law for a rigid tube). Many biofluids are non‐Newtonian, and are well approximated by generalized Newtonian (say, power‐law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a “generalized Hagen–Poiseuille law” for soft microtubes. We benchmark the mathematical predictions against three‐dimensional two‐way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow‐induced deformation of a blood vessel, which is featured in some textbooks.

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Elastic-plated gravity currents

Cited by 68 publications

References 30 publications

Pursing of planar elastic pockets

Pursing of planar elastic pockets

The speed of an inclined ruck

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

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