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The shape of two-dimensional liquid bridges

Teixeira, P. I. C. and Teixeira, M. A. C. (2020) The shape of two-dimensional liquid bridges. Journal of Physics: Condensed Matter, 32 (3). 034002. ISSN 1361-648X

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To link to this item DOI: 10.1088/1361-648X/ab48b7


We have studied a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates of given wettabilities. For this simple geometry, the Young-Laplace equation can be solved (quasi-)analytically to yield the equilibrium bridge shape under gravity. We establish the range of gap widths (as described by a Bond number ${\rm Bo}$) for which the liquid bridge can exist, for given contact angles at the top and bottom substrates ($\theta_c^t$ and $\theta_c^b$, respectively). In particular, we find that the absolute maximum span of a liquid bridge is four capillary lengths, for $\theta_c^b=180^\circ$ and $\theta_c^t=0^\circ$; whereas for $\theta_c^b=0^\circ$ and $\theta_c^t=180^\circ$ no bridge can form, for any substrate separation. We also obtain the minimum value of the cross-sectional area of such a liquid bridge, as well as the conditions for the existence and positions of any necks or bulges and inflection points on its surface. This generalises our earlier work in which the gap was assumed to be spanned by a liquid film of zero thickness connecting two menisci at the bottom and top substrates.

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:86418
Uncontrolled Keywords:Thin films, Liquid Interfaces, Surface tension, Gravity
Publisher:Institute of Physics Publishing


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