Evaporation in a capillary tube of square cross-section: application to ion transport

Modelling of evaporation of a pure liquid within a capillary tube of circular cross-section is a classic problem which has been the subject of many studies. Here we consider the case of tubes of polygonal cross-section. This case leads to quite different results owing to the liquid flow along the tube edges induced by the capillary forces. Various evaporation regimes can be distinguished depending on the competition between capillary, gravity and viscous forces. We concentrate on the regime dominated by the capillary forces. It is shown that the position z0 of the bulk meniscus should scale as z0∝t in this case. The prefactor depends on the liquid distribution within the entrance region of the tube. A simplified model for a tube of square cross-section is then presented and calibrated against data from three-dimensional simulations. The last part of the paper is devoted to an analysis of ion transport during evaporation in a tube of square cross-section. The results suggest that the ion transport by liquid film can be a very effective mechanism for explaining the formation of efflorescence at the surface of porous media.