DOI: 10.1017/s0022112099005352. On the stability of liquid ridges

10.1017/s0022112099005352

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

We consider the stability of a rectilinear liquid region whose boundary is composed of a solid cylindrical substrate of arbitrary shape and a free surface whose cross-section, in the absence of gravity, is a circular arc. The liquid–solid contact angle is a prescribed material property. A variational technique, using an energy functional, is developed that predicts the minimum wavelength for transverse instability under the action of capillarity. Conversely, certain configurations are absolutely stable and a simple stability criterion is derived. Stability is guaranteed if, for given substrate geometry and given contact angle, the unperturbed meniscus pressure is an increasing function of the liquid cross-sectional area. The analysis is applied to a variety of liquid/substrate configurations including (i) a liquid ridge with contact lines pinned to the sharp edges of a slot or groove, (ii) liquid ridges with free contact lines on flat and wedge-shaped substrates as well as substrates of circular or elliptical cross-section. Results are consistent with special cases previously treated including those that employ a slope-small-slope approximation.

Bibliography

ROY, R. V., & SCHWARTZ, L. W. (1999). On the stability of liquid ridges. Journal of Fluid Mechanics, 391, 293â318.

Authors 2

R. VALÉRY ROY (first)
LEONARD W. SCHWARTZ (additional)

References 0 Referenced 55

None

Dates

Type	When
Created	23 years, 1 month ago (July 27, 2002, 5:23 a.m.)
Deposited	6 years, 2 months ago (June 7, 2019, 12:23 p.m.)
Indexed	1 year ago (Aug. 27, 2024, 7:49 a.m.)
Issued	26 years, 1 month ago (July 25, 1999)
Published	26 years, 1 month ago (July 25, 1999)
Published Online	26 years, 1 month ago (July 25, 1999)
Published Print	26 years, 1 month ago (July 25, 1999)

Funders 0

None

BibTeX

@article{ROY_1999, title={On the stability of liquid ridges}, volume={391}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112099005352}, DOI={10.1017/s0022112099005352}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={ROY, R. VALÉRY and SCHWARTZ, LEONARD W.}, year={1999}, month=jul, pages={293–318} }

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