Evaporation Limited Radial Capillary Penetration in Porous Media

The capillary penetration of fluids in thin porous layers is of fundamental interest in nature and various industrial applications. When capillary flows occur in porous media, the extent:of penetration is known to increase with the square root of time following the Lucas-Washburn law. In practice, volatile liquid evaporates at the surface of porous media, which restricts penetration to a limited region. In this Work, On the basis of Darcy's law and mass conservation, a general theoretical model is developed for the evaporation-limited radial capillary penetration in porous media. The presented model predicts that evaporation decreases the rate of fluid penetration and limits it to a critical radius. Furthermore, we construct a unified phase diagram that describes the limited penetration in an annular porous medium, in which the boundaries of outward and inward liquid are predicted quantitatively. It is expected that the proposed theoretical model will advance the understanding of penetration dynamics in porous media and facilitate the design of engineered porous architectures.