An energy loss coefficient in fluid buckling

Cruickshank, J. O.

doi:10.1063/1.863681

Cited by 13 publications

(13 citation statements)

References 3 publications

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“…The bouncing [137] of a jet raises similar questions about fluid elasticity and surface tension as well as about the mathematical nature of the flow as a boundary-value problem and the particular issue of the influence of down-stream boundary conditions on the flow of the jet as a whole. A quantitative investigation of the coiling (or buckling) of the fluid jet is presented by Cruickshank [138] who refers to earlier work by G.I. Taylor.…”

Section: Discussionmentioning

confidence: 99%

One hundred years of extensional flow

Petrie

2006

Journal of Non-Newtonian Fluid Mechanics

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This historical review takes a few selected issues from the rheological studies of extensional flow that fill the literature, starting with extracts from the seminal papers of Trouton (Proc. Roy. Soc. A77 (1906) 426-440) and Fano (Archivio di fisiologio, 5 (1908) 365-370). Work in the first half of the twentieth century on spinnability and extensional viscosity measurement is highlighted, followed by a discussion of the blossoming of studies on extensional flow. As a case study, a project on anti-misting additives in aviation fuel is taken; whether the rheology or the politics is the more interesting is an open question. Finally some current issues surrounding spinnability and other extensional flow phenomena are discussed.

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Section: Discussionmentioning

confidence: 99%

One hundred years of extensional flow

Petrie

2006

Journal of Non-Newtonian Fluid Mechanics

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“…Physically, the buckling of a viscous plume can be attributed to the fact that the stress changes from tension to compression as the fluid approaches the surface, and in the region of compression its behaviour does indeed have some superficial characteristics in common with that of an elastic column. Following Taylor's paper there was little quantitative work on this problem until Cruickshank & Munson (1981, 1982a) made a thorough study of both axisymmetric and plane jets. They presented experimental results for jets of viscous silicone oil pumped through a circular orifice or a slit and impinging on a flat plate held a known distance H below the orifice.…”

Section: Methodsmentioning

confidence: 99%

Folding of Viscous Plumes Impinging On A Density Or Viscosity Interface

Griffiths

Turner

1988

Geophysical Journal International

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S U M M A R YThe possibility that slabs of subducted oceanic lithosphere may buckle and fold under longitudinal compressive stresses when they encounter the major seismic discontinuity near a depth of 670 km in the mantle has led us to explore experimentally the behaviour of very viscous plumes falling onto a density interface or a viscosity step. We begin with the case of axisymmetric and planar streams falling through air onto the free surface of a viscous fluid which has the same or smaller density, and observe the conditions under which they coil or fold. In order to remove surface tension and to introduce effects of a viscous environment we study plumes falling onto a density interface between two (generally very viscous) liquid layers. Stability to buckling is found to depend largely on a geometrical criterion based on the length to thickness ratio of plumes, but also the tendency to buckle is greater for large density differences across the interface and larger viscosity contrasts between plume and upper layer.When plumes are unstable, coils or folds are laid down with a horizontal scale in a fixed proportion to the thickness of the plume, and the frequency of folding is determined by the velocity and thickness of the slab as it enters the region of compressive stress. Entrainment of upper layer fluid can have a marked effect on the fate of the folded plume material, which may spread at the interface or continue to descend into the lower layer. Similar behaviour is observed at a viscosity interface. Application of results to the mantle depends on the nature of the 670 km discontinuity and is therefore inconclusive. However, cool slabs are likely to be unstable if mantle circulation involves two layers separated by a density interface or if whole-mantle circulation involves a large viscosity increase with depth near 700 km.

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“…He recognized that a longitudinal compressive stress is a primary factor of the folding instability. A quasi one-dimensional analysis was developed for buckling of an axisymmetric (Tchavdarov et al 1993;Yarin 1993;Entov and Yarin 1984;Cruickshank andMunson 1983, 1982b) and thin plane jets (Yarin and Tchavdarov 1996) and for both cases (Cruickshank 1988;Cruickshank and Munson 1982a). Cruickshank and Munson (1982a) reported that the compressive stress associated with fluid buckling was related with energy loss which was experimentally determined for the axisymmetric and the plane jets.…”

Section: Introductionmentioning

confidence: 98%

“…A quasi one-dimensional analysis was developed for buckling of an axisymmetric (Tchavdarov et al 1993;Yarin 1993;Entov and Yarin 1984;Cruickshank andMunson 1983, 1982b) and thin plane jets (Yarin and Tchavdarov 1996) and for both cases (Cruickshank 1988;Cruickshank and Munson 1982a). Cruickshank and Munson (1982a) reported that the compressive stress associated with fluid buckling was related with energy loss which was experimentally determined for the axisymmetric and the plane jets. According to the perturbation analysis (Cruickshank 1988), the slenderness ratio of the viscous thread was found to determine the onset of buckling, where the slenderness can be defined as the ratio of the thickness and height of the thread.…”

Section: Introductionmentioning

confidence: 98%

Numerical and experimental studies on the viscous folding in diverging microchannels

Chung

Choi

Kim

et al. 2009

Microfluid Nanofluid

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We performed numerical and experimental studies on the viscous folding in diverging microchannel flows which were recently reported by Cubaud and Mason (Phys Rev Lett 96:114501, 2006a). We categorized the flow patterns as ''stable'', ''folding,'' and ''chaotic'' depending on channel shape, flow ratio, and viscosity ratio between two fluids. We focused on the effect of kinematic history on viscous folding, in particular, by changing the shape of diverging channels: 90°, 45°, and hyperbolic channel. In experiments, the proposed power-law relation (f $ _ c 1 ; where f is the folding frequency, and _ c is the characteristic shear rate) by Cubaud and Mason (Phys Rev Lett 96:114501, 2006a) was found to be valid even for hyperbolic channel. The hyperbolic channel generated moderate flows with smaller folding frequency, amplitude, and a delay of onset of the folding compared with other two cases, which is considered to be affected by compressive stress when compared to the simulation results. In each channel, the folding frequency increases and the amplitude decreases as the thread width decreases since higher compressive stress is applied along the thin thread. The secondary folding was also reproduced in the simulation, which was attributed to locally heterogeneous development of compressive stresses along the thread. This study proves that the viscous folding can be controlled by the design of flow kinematics and of the compressive stresses at the diverging region.

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An energy loss coefficient in fluid buckling

Cited by 13 publications

References 3 publications

One hundred years of extensional flow

One hundred years of extensional flow

Folding of Viscous Plumes Impinging On A Density Or Viscosity Interface

Numerical and experimental studies on the viscous folding in diverging microchannels

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