Gérard Gagneux

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

In this work, we propose an original resolution of Young–Laplace equation for capillary doublets from an inverse problem. We establish a simple explicit criterion based on the observation of the contact point, the wetting angle and the gorge radius, to classify in an exhaustive way the nature of the surface of revolution. The true shape of the admissible static bridges surface is described by parametric equations; this way of expressing the profile is practical and well efficient for calculating the binding forces, areas and volumes. Moreover, we prove that the inter-particle force may be evaluated on any section of the capillary bridge and constitutes a specific invariant.

Theoretical and experimental study of pendular regime in unsaturated granular media

This article addresses the experimental study of capillary bridge properties with the use of analytical calculation of bridge profile, based on solution of Young–Laplace equation. Using the measurements of some parameters as the contact angle, half-filling angle and the neck radius of the capillary bridge between two spherical particles of radius r, the shape of the bridge is estimated using theoretical solutions of Young–Laplace equation. The corresponding analytical solution is superposed and compared with image data.

Exact calculation of axisymmetric capillary bridge properties between two unequal-sized spherical particles

A calculation method for the meridional profile of axisymmetric bridges between two spheres of different size is introduced in this manuscript. From geometrical data of the capillary bridge, such as the neck radius and boundary conditions (filling and contact angle), the shape of the capillary bridge is calculated analytically as a solution of the Young–Laplace equation. Its free surfaces, of constant mean curvature, may be classified into portions of nodoid, unduloid, and other limit cases. Moreover, other properties of the liquid bridge can be computed analytically, such as the associated capillary force exerted on the solid surfaces, liquid volume, mean curvature, and free surface area.

A model for capillary hysteresis loops in unsaturated porous media theory

In this paper, we show how very relevant mathematical works of P.I. Plotnikov, publicized by L.C. Evans and M. Portilheiro, can be used to model the effects of cyclic hysteresis phenomena for flows in unsaturated porous media. We draw particular attention to the example of a model for water–air flows, simplified for purposes of illustration. First, an unstable “spinodal” interval is artificially introduced. Then S.L. Sobolev’s method of dynamic regularization allows associating with the continuity equations additional information in the form of entropy type inequalities. The asymptotic limits of viscous approximate solutions generate effects of irreversibility and the expected clockwise hysteresis loop.