Unsteady gravity-driven slender rivulets of a power-law fluid

Yatim, Yazariah Mohd; Wilson, S. K.; Duffy, Brian

doi:10.1016/j.jnnfm.2010.06.017

Cited by 13 publications

(8 citation statements)

References 24 publications

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“…Rare exceptions include the work by Rosenblat 39 on rivulet flow of a viscoelastic fluid, and that by Wilson, Duffy, and Ross 40 on rivulet flow of viscoplastic material. In addition, similarity solutions have been obtained and analysed for steady 41,42 and unsteady 43 flows of non-uniform rivulets of a power-law fluid.…”

Section: Introductionmentioning

confidence: 99%

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

2015

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Locally unidirectional steady gravity-driven flow of a thin rivulet of a power-law fluid with prescribed volume flux down a locally planar substrate is considered. First the solution for unidirectional flow of a uniform rivulet down a planar substrate is obtained, and then it is used to obtain the solution for a slowly varying rivulet with prescribed constant (nonzero) contact angle down a slowly varying substrate, specifically flow in the azimuthal direction around the outside of a large horizontal circular cylinder. The solution is shown to depend strongly on the value of the power-law index of the fluid. For example, a rivulet of strongly shear-thinning fluid "self-channels" its flow down a narrow central channel between two "levees" of slowly moving fluid that form at its sides, and in the central channel there is a "plug-like" flow except in a boundary layer near the substrate. On the other hand, in a rivulet of a strongly shear-thickening fluid the velocity profile is linear except in a boundary layer near the free surface. Another notable qualitative departure from Newtonian behaviour is that, whereas the mass of a rivulet of a Newtonian or a shear-thinning fluid is theoretically infinite, the mass of a rivulet of a shear-thickening fluid is finite

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Section: Introductionmentioning

confidence: 99%

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

2015

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“…Subsequently Holland, Wilson, and Duffy 17 obtained four steady similarity solutions for a slender dry patch in a thin fluid film in the presence of thermocapillarity effects. All of these works concern steady dry patches, but recently the present authors have obtained unsteady similarity solutions for an opening or closing slender dry patch with a fixed apex in a thin fluid film driven by a prescribed constant surface shear stress (Yatim, Duffy, and Wilson 18 ); somewhat unexpectedly, it turns out that there is no corresponding solution for a dry patch in a thin film of either a Newtonian fluid or a non-Newtonian power-law fluid that is driven by gravity (Yatim et al 19,20 ). Earlier, Betelú and Diez 21 obtained a rather different unsteady similarity solution that describes two semi-infinite contact lines that meet to form a "dry line" (rather than a dry patch); the dry line vanishes at a "welding point" which moves at constant velocity.…”

Section: Introductionmentioning

confidence: 84%

Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

2013

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A novel family of three-dimensional travelling-wave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform far-field value. The two most practically important cases of purely gravity-driven flow and of purely surface-shear-stress-driven flow are analysed separately.

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“…The unsteady similarity solution for gravity-driven rivulet of a non-Newtonian power-law fluid on an inclined plane has been studied by Yatim et. al 5 , both for converging sessile rivulet and diverging pendent rivulet. The solution predicts that the evolution of the width and the height of rivulets at any time vary according to | | (2 +1)/2( +1) and | | /( +1) , respectively, while at any position vary according to | | − /2 (2 +1) and | | − /( +1) , respectively, with cross-sectional profiles that are either singlehumped or double-humped.…”

Section: Introductionmentioning

confidence: 99%

Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid

Abas¹,

Yatim²

2018

IJET

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Unsteady travelling-wave similarity solution describing the flow of a slender symmetric rivulet of non-Newtonian power-law fluid down an inclined plane is obtained. The flow is driven by gravity with strong surface-tension effect. The solution predicts that at any time and position , the rivulet widens or narrows according to , where is velocity of a rivulet, and the film thickens or thins according to a free parameter , independent of power-law index . The rivulet also has a quartic transverse profile which always has a global maximum at its symmetrical axis.

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Unsteady gravity-driven slender rivulets of a power-law fluid

Cited by 13 publications

References 24 publications

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

A rivulet of a power-law fluid with constant contact angle draining down a slowly varying substrate

Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

Travelling-Wave Similarity Solution for Gravity-Driven Rivulet of a Non-Newtonian Fluid

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