Is Unidirectional Drying in a Round Capillary Always Diffusive?

Abstract

The unidirectional drying of water in cylindrical capillaries has been described since the discovery of Stefan's solution as a vapor diffusion-controlled process with a square root of time kinetics. Here we show that this well-known process actually depends on the way the capillary is closed. Experiments are performed on the evaporation of water in capillaries closed at one end with a solid material or connected to a fluid reservoir. While we recover Stefan's solution in the first case, we show that in the second situation the water plug evaporates at a constant rate with the water-air meniscus remaining pinned at the exit where evaporation proceeds. The presence of the liquid reservoir closing the capillary combined with a capillary pumping effect induces a flow of the water plug toward the evaporation front leading to a constant-rate drying, substantially faster than the prediction of Stefan's equation. Our results show that a transition from a constant-rate evaporation regime at short times to a diffusion-driven evaporation regime at long times can be observed by increasing the viscosity of the fluid in the reservoir blocking the other end of the capillary. Such transition can also be observed by connecting the capillary end to a solidifying fluid like epoxy glue.