Abstract
A fluid in a pore can form diverse heterogeneous structures. 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. The analysis presented in this work is a step towards developing a thermodynamic framework to map the rich heterogeneous phase diagrams of porous media and other confined systems.
Highlights
Some phenomena occur exclusively in pores or under strong confinement
We show that the thermodynamic stability of the simplest type of film, the thick film, is very different for closed and open systems
We have studied the thermodynamic stability of free and adsorbed droplets, bubbles and gas and liquid films in open and closed pores by use of capillary models coupled to an equation of state
Summary
Some phenomena occur exclusively in pores or under strong confinement. In porous materials, a liquid phase can form at pressures below the saturation pressure during capillary condensation [1,2,3,4], liquid water can be stretched to negative pressures exceeding 140 MPa in quartz inclusions [5, 6] and giant charge reversal has been observed in confined systems filled with electrolytes [7]. While the thermodynamics of homogeneous systems is well understood [11], this is not the case for heterogeneous systems, as evident e.g. from the large deviations between experiments, theory and simulations for the formation of drops [12, 13] Both in bulk systems and in systems under confinement, equilibrium is characterized by a minimum of an energy state function whose nature is determined by the boundary conditions. A complicating factor in pores, is that multiple heterogeneous structures such as films, adsorbed or free droplets and bubbles, and combinations of these, could all be stationary states of the same energy state function [14] Such states are typically characterized by uniform temperature, equality of chemical potentials and mechanical equilibrium [11, 15].
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