Our article entitled Thermodynamic stability of droplets, bubbles and thick films in open and closed pores has been published in Fluid Phase Equilibria.
A fluid in a pore can form diverse heterogeneous structures. In our latest work on thermodynamic stability analysis, we combine a capillary description with the cubic-plus-association equation of state to study the thermodynamic stability of droplets, bubbles and films of water at 358 K in a cylindrically symmetric pore. The equilibrium structure depends strongly on the size of the pore and whether the pore is closed (canonical ensemble) or connected to a particle reservoir (grand canonical ensemble). A new methodology is presented to analyze the thermodynamic stability of films, where the integral that describes the total energy of the system is approximated by a quadrature rule. We show that, for large pores, the thermodynamic stability limit of adsorbed droplets and bubbles in both open and closed pores is governed by their mechanical stability, which is closely linked to the pore shape. This is also the case for a film in a closed pore. In open pores, the film is chemically unstable except for very low film-phase contact angles and for a limited range in external pressure. This result emphasizes the need to invoke a complete thermodynamic stability analysis, and not restrict the discussion to mechanical stability. A common feature for most of the heterogeneous structures examined is the appearance of regions where the structure is metastable with respect to a pore filled with a homogeneous fluid. In the closed pores, these regions grow considerably in size when the pores become smaller. This can be understood from the larger energy cost of the interfaces relative to the energy gained from having two phases. Complete phase diagrams are presented that compare all the investigated structures. In open pores at equilibrium, the most stable structure is either the homogeneous phase or adsorbed droplets and bubbles, depending on the type of phase in the external reservoir. Smaller pores allow for droplets and bubbles to adsorb for a larger span in pressure. In closed pores, most of the investigated configurations can occur depending on the total density, the contact angle, the pore shape and the pore size. Phase diagrams for closed pores of different sizes are shown below.
The analysis presented in the work is a step towards developing a thermodynamic framework to map the rich heterogeneous phase diagrams of porous media and other confined systems. The work was done in collaboration with Magnus Aa. Gjennestad from the Department of Physics at NTNU.