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Wetting of surfaces with porous coating is relevant for a wide variety oftechnical applications, such as printing technologies and heat transferenhancement. Imbibition and evaporation of liquids on surfaces covered withporous layers are responsible for significant improvement of cooling efficiencyduring drop impact cooling and flow boiling on such surfaces. Up to now, noreliable model exists which is able to predict the kinetics of imbibitioncoupled with evaporation on surfaces with porous coatings. In this work weconsider one of possible mechanisms of imbibition on a substrate covered by ananofiber mat. This is the capillary pressure-driven flow in a corner formedbetween a flat substrate and a fiber attached to it. The shape and the area ofthe cross-section occupied by the liquid as well as the capillary pressurechange along the flow direction. A theoretical/numerical model of simultaneousimbibition and evaporation is developed, in which viscosity, surface tensionand evaporation are taken into account. At the beginning of the process theimbibition length is proportional to the square root of time, in agreement withthe Lucas-Washburn law. As the influence of evaporation becomes significant,the imbibition rate decreases. The model predictions are compared withexperimental data for imbibition of water-ethanol mixtures into nanofiber matcoatings.

Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nanofiber mat coating