Related Experiment Video
Updated: Jan 19, 2026

The Preparation of Electrohydrodynamic Bridges from Polar Dielectric Liquids
Published on: September 30, 2014
The shape of two-dimensional liquid bridges
Paulo I C Teixeira1,2, Miguel A C Teixeira3
1ISEL-Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa Rua Conselheiro Emídio Navarro 1, 1959-007 Lisbon, Portugal.
Abstract:
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 [Formula: see text]) for which the liquid bridge can exist, for given contact angles at the top and bottom substrates ([Formula: see text] and [Formula: see text], respectively). In particular, we find that the absolute maximum span of a liquid bridge is four capillary lengths, for [Formula: see text] and [Formula: see text]; whereas for [Formula: see text] and [Formula: see text] 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.
Related Concept Videos
Surface Tension of Fluid
Surface tension varies...
Newman Projections
The organic molecules rotate across the single bonds leading to numerous temporary three-dimensional structures of varying energy known as...
Surface Tension, Capillary Action, and Viscosity
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded by other molecules and are attracted equally in all directions by the cohesive forces within the liquid. However, the molecules on the surface of a liquid are attracted only by about one-half as many molecules. Because of the unbalanced molecular attractions on the surface molecules, liquids contract to form a shape that minimizes the number...
Molecular Shapes
Two regions of electron density in a diatomic...
Cohesion
On a...
The Fluid Mosaic Model

