Analytic Calculation of Capillary Bridge Properties Deduced as an Inverse Problem from Experimental Data

Laplace pressure evolution and four instabilities in evaporating two-grain liquid bridges

“…12a (middle image), according to Plateau's nomenclature, the free liquid surface evolves from nodoid (Δp b 0) into catenoid (Δp = 0), with Δp developing further into positive values (and the surface transitioning from catenoid into unduloid, see Fig. 14a and [37]. This (Δp reaching zero) constitutes a second pressure instability.…”

“…At the same time, over the initial volume loss from 4 to 3 μl, there is very little (b1/10th for D = 0.4 mm and b 1/5th for D = 0.7 mm) of r g change, and over half of the volume loss, there is a still small change in κ g , and as long as CD is pinned, the CA decrease, is the main geometrical change of relevance of the water body. However, (a) Bridge external profile transition during evaporation; images for separation of 0.7 mm compared to: 1 -nodoid, 2 -catenoid, 3 -unduloid , 4 -cylinder (profiles marked follow algebraic expressions as in [37]), Transition from unduloid into cylinder during liquid bridge evaporation in vertical (b) and horizontal (c) for tall and slim bridge of separation of 2 mm; d) transition from unduloid -cylinder as described by Plateau [38] for originally cylindrical fluid jet; e) the actual evolution of the shape into cylinder supported by two conical volumes: top-an early stage; bottom-terminal phase of pinching of the cylindrical water-wire, for separation of 2 mm. over the same range, κ ext does increase.…”

Theoretical and experimental study of pendular regime in unsaturated granular media

“…This article addresses the experimental study of the capillary bridge properties with use of the analytical calculation of bridge profile, based on solution of Young-Laplace equation (Gagneux and Millet, 2014). In this method, the parameters of pendular bridge and the shape of the meridian may be estimated using theoretical solutions of YoungLaplace equation, based on an inverse problem as the capillary pressure 1 is unknown (Gagneux & Millet 2014).…”

“…In this method, the parameters of pendular bridge and the shape of the meridian may be estimated using theoretical solutions of YoungLaplace equation, based on an inverse problem as the capillary pressure 1 is unknown (Gagneux & Millet 2014). However, this pressure may be recovered with experimental measurements of three geometrical parameters: gorge radius y à , contact angle h, half-filling angle d. This will be done using experimental set-up similar to one described in Mielniczuk, Hueckel, El Youssoufi (2013, 2015.…”

“…For several distances D, a photo of the capillary bridge is recorded and the geometric parameters (y à ; d; h) are measured from image processing. Then shape of the capillary bridge, and its exact analytical parameterisation, are deduced, according to the criterion given in Gagneux and Millet 2014 and recalled in Section 2. The shapes obtained correspond, first to a portion of nodoid (from the creation of the capillary bridge to some distance D).…”