Bridging transitions for spheres and cylinders

We study bridging transitions between spherically and cylindrically shaped particles (colloids) of radius $R$ separated by a distance $H$ that are dissolved in a bulk fluid (solvent). Using macroscopics, microscopic density functional theory and finite-size scaling theory we study the location and order of the bridging transition and also the stability of the liquid bridges which determines spinodal lines. The location of the bridging transitions is similar for cylinders and spheres, so that for example, at bulk coexistence the distance $H_b$ at which a transition between bridged and unbridged configurations occurs, is proportional to the colloid radius $R$. However all other aspects, and, in particular, the stability of liquid bridges, are very different in the two systems. Thus, for cylinders the bridging transition is typically strongly first-order, while for spheres it may be first-order, critical or rounded as determined by a critical radius $R_c$. The influence of thick wetting films and fluctuation effects beyond mean-field are also discussed in depth

Stability of Liquid Bridges between Unequal Disks under Zero-Gravity Conditions

The stability, of axisymmetric equilibrium shapes of a liquid bridge between two coaxial disks of different radii under zero-gravity conditions is investigated. The stability regions have been evaluated for different values of the ratio of the disk radii in terms of the dimensionless parameters which characterize the length and the volume of the bridge. It has been found that disk radii unequality radically changes the upper boundary of the stability region. The analysis of the shape of marginally stable equilibrium surfaces has been carried out. Relationships between the critical values of the parameters have been deduced for some particular cases, which are of special interest for the materials purification processes and growing of single crystals by the floating zone method: for typical values of the growing angle for semiconductor materials and for liquid volumes close to that of the cylinder having a radius equal to the mean radius of the disk

Collapse of a hemicatenoid bounded by a solid wall:Instability and dynamics driven by surface Plateau border friction

The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air, with film viscosity playing only a minor role. Recently [Goldstein, et al., Phys. Rev. E 104, 035105 (2021)], we introduced a variant of this problem in which the catenoid is bisected by a glass plate located in a plane of symmetry perpendicular to the rings, producing two identical hemicatenoids, each with a surface Plateau border (SPB) on the glass plate. Beyond the critical ring separation, the hemicatenoids collapse in a manner qualitatively similar to the bulk problem, but their motion is governed by the frictional forces arising from viscous dissipation in the SPBs. Here we present numerical studies of a model that includes classical friction laws for SPB motion on wet surfaces and show consistency with our experimental measurements of the temporal evolution of this process. This study can help explain the fragmentation of bubbles inside very confined geometries such as porous materials or microfluidic devices.Comment: 9 pages, 9 figures, supplementary videos available at website of RE

Instability of a Möbius strip minimal surface and a link with systolic geometry

We describe the first analytically tractable example of an instability of a nonorientable minimal surface under parametric variation of its boundary. A one-parameter family of incomplete Meeks Möbius surfaces is defined and shown to exhibit an instability threshold as the bounding curve is opened up from a double-covering of the circle. Numerical and analytical methods are used to determine the instability threshold by solution of the Jacobi equation on the double covering of the surface. The unstable eigenmode shows excellent qualitative agreement with that found experimentally for a closely related surface. A connection is proposed between systolic geometry and the instability by showing that the shortest noncontractable closed geodesic on the surface (the systolic curve) passes near the maximum of the unstable eigenmode