Interfacial Mass Transfer During Gas–Liquid Phase Change in Deformable Porous Media with Heat Transfer

Transitions between liquid and gaseous phases of a fluid material are characterised by a jump in density and the coexistence of both phases during the phase change process. The jump occurs at the interface between the fluid phases and can be handled numerically by the introduction of a singular surface. This allows for a thermodynamically consistent description of mass transfer across the interface and the transition of the interfacial term towards the mass production term included in the mass balance equations. In the present article, a multicomponent and multiphasic porous aggregate is treated in a non-isothermal environment, while accounting for the thermodynamics of the fluid-phase transitions. Based on the Theory of Porous Media, this approach provides a well-founded continuum mechanical basis for the description of deformable, fluid-saturated porous solid aggregates. In particular, a bicomponent, triphasic model is proposed consisting of a thermoelastic porous solid, which is percolated by compressible gaseous and liquid fluid phases. The thermodynamical behaviour, i.e. the dependency of the fluid densities on temperature and pressure, is governed by the van der Waals equation of state and the Antoine equation for the vaporisation–condensation line. Moreover, the interface between the fluid phases is represented by a singular surface and results in jump conditions included in the balance relations of the components of the overall aggregate. The evaluation of the jump conditions leads to a formulation of the interfacial mass transfer, which basically relates the energy added to the system to the latent heat needed for the phase change in a certain amount of a substance. The mass transfer itself or the mass production, respectively, furthermore depends on interfacial areas introduced as a function of porosity and saturation. Thus, geometrical and fluid-flow-dependent parameters are included into the phase change process. Finally, this allows for the numerical simulation of evaporation or condensation of, for example, $${\hbox {CO}}_2$$ in a deformable porous solid with heat transfer.