Geometry-induced capillary emptying

When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we pre...

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Published inProceedings of the National Academy of Sciences - PNAS Vol. 113; no. 45; pp. 12633 - 12636
Main Authors Rascón, Carlos, Parry, Andrew O., Aarts, Dirk G. A. L.
Format Journal Article
LanguageEnglish
Published United States National Academy of Sciences 08.11.2016
Subjects
Laplace transforms
Liquids
Physical Sciences
Surface tension
contact angle
Young–Laplace equation
surface tension
capillarity
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Summary:When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary crosssectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.
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Edited by Jean-Christophe Baret, CNRS, University Bordeaux, CRPP, UPR 8641, Pessac, France, and accepted by Editorial Board Member John D. Weeks September 16, 2016 (received for review April 18, 2016)
Author contributions: C.R., A.O.P., and D.G.A.L.A. designed research; C.R. and A.O.P. performed research; C.R. and A.O.P. analyzed data; D.G.A.L.A. performed Surface Evolver computations; and C.R. and A.O.P. wrote the paper.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1606217113