Instabilities of capillary forces in the evaporating granular medium

Tomasz Hueckel, Duke University, Durham, NC, USA

 Dynamic variables characterizing evolution during evaporation of capillary bridge between two, three and an assembly of several grains are analyzed. The variables include: average Laplace pressure, pressure resulting force, surface tension force and total capillary force calculated based on the previously reported geometrical variables using Young-Laplace law. This is the first time to our knowledge that Laplace pressure is calculated from the measured bridge curvatures along the process of evaporation and compared to experimental measurement data. A comparison with the experimental data from analogous capillary bridge extension tests is also shown and discussed. The behavior of evaporating liquid bridges is seen as strongly dependent on the grain separation. Initial negative Laplace pressure at small separations is seen to significantly augment during an advanced stage of evaporation, but to turn into positive pressure, after an instability toward the end of the process, and prior to rupture. At larger separations the pressure is positive all the time, changing a little, but rupturing early. Rupture in all cases occurs at positive pressure (not suction!!). However, because of the evolution of the surface area of contact, the resultant total capillary forces are always tensile, and decreasing toward zero in all cases. Comparison between measured total resultant capillary forces and those calculated from the Young-Laplace law is very good, except for some discrepancies at very small separations (below50 μm). Up to four consecutive instabilities of capillary bridge are seen developing at some sphere separations. They are: re-pinning-induced suction (pressure) instability; Rayleigh nodoid/catenoid/unduloid unstable transition, associated with zero-pressure; Rayleigh unduloid/cylinder unstable transition, associated with the formation of a liquid-wire; and lastly, a pinching instability of the liquid-wire, associated with the bridge rupture. Rupture of the bridges is seen at large separations to occur quite early, at only 1/4–1/3 of the initial water volume evaporated. At smallest separations, rupture occurs in a seemingly unstable way when water evaporates from the bridge.

Consequences of the liquid instabilities to the stability of the whole medium are discussed, especially in terms of tensile cracking during “the air entry”.