Capillary rise in a circular tube with interfacial condensation process

In this work, we develop a theoretical model for the spontaneous imbibition process of a non-isothermal liquid body in a capillary tube. The imbibition front is in contact with a saturated vapor originating a direct condensation at the interface. In the mathematical model, the liquid phase has been coupled with the saturated vapor through the interfacial heat flux condition. The model predicts the evolution for the imbibition front being present the phase change occurring in the imbibition front at a constant rate, which is driven by a temperature difference at the interface between the liquid and the saturated vapor. The results shown a deviation from the Lucas-Washburn solution for the imbibition front, as a function of the dimensionless parameter involved in the analysis: the Jakob number, Ja; β representing the ratio of a characteristic equilibrium height to the characteristic thermal penetration, and ε, which depends on the physical properties of the liquid that penetrates the capillary tube.