  Wetting of surfaces with porous coating is relevant for a wide variety of
technical applications, such as printing technologies and heat transfer
enhancement. Imbibition and evaporation of liquids on surfaces covered with
porous layers are responsible for significant improvement of cooling efficiency
during drop impact cooling and flow boiling on such surfaces. Up to now, no
reliable model exists which is able to predict the kinetics of imbibition
coupled with evaporation on surfaces with porous coatings. In this work we
consider one of possible mechanisms of imbibition on a substrate covered by a
nanofiber mat. This is the capillary pressure-driven flow in a corner formed
between a flat substrate and a fiber attached to it. The shape and the area of
the cross-section occupied by the liquid as well as the capillary pressure
change along the flow direction. A theoretical/numerical model of simultaneous
imbibition and evaporation is developed, in which viscosity, surface tension
and evaporation are taken into account. At the beginning of the process the
imbibition length is proportional to the square root of time, in agreement with
the Lucas-Washburn law. As the influence of evaporation becomes significant,
the imbibition rate decreases. The model predictions are compared with
experimental data for imbibition of water-ethanol mixtures into nanofiber mat
coatings.
