Pendent steady rivulets and droplets: from lubrication to bifurcation

We consider the shape of the free surface of steady pendent rivulets (or equivalently, two-dimensional droplets) beneath a planar substrate. We formulate the governing equations in terms of two closely related dynamical systems and use classical phase-plane techniques, in particular time maps, to an...

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Bibliographic Details
Published inIMA journal of applied mathematics Vol. 89; no. 4; pp. 725 - 744
Main Authors Grinfeld, Michael, Pritchard, David
Format Journal Article
LanguageEnglish
Published Oxford University Press 11.12.2024
Subjects
bifurcation analysis
rivulets
surface tension
time maps
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Summary:We consider the shape of the free surface of steady pendent rivulets (or equivalently, two-dimensional droplets) beneath a planar substrate. We formulate the governing equations in terms of two closely related dynamical systems and use classical phase-plane techniques, in particular time maps, to analyse the bifurcation structure of the problem. Our results explain why lubrication theory is unable to capture this bifurcation structure for pendent rivulets, although it is successful in the related problem of sessile rivulets.
ISSN:0272-4960
1464-3634
DOI:10.1093/imamat/hxae028