Vapor–Liquid Equilibrium
For a vapor and liquid system, thermodynamic equilibrium is reached when the fugacities are the equal in both phases (for each species i)
(3-191)
Here, fiV denotes the vapor phase fugacity, and fiL is the liquid phase fugacity. The fugacity is a measure of the chemical potential and relates to the tendency of a substance to prefer one of the phases over the other. In general, the fugacity in each phase depends on the temperature, T, the absolute pressure, P, as well as composition. The composition is usually expressed by the molar fractions in each phase, yi and xi, respectively. When accounting for nonideal behavior, the fugacity equality in Equation 3-191 can be formulated as (see Ref. 1)
(3-192)
Here the fugacity coefficient accounts for nonideality in the gas, while the activity coefficient γi, accounts for nonideality in the liquid phase. Both these coefficients are functions of the temperature, pressure, and fraction of species i in the respective solutions. For the liquid, and denote the fugacity coefficient and the vapor pressure, both for a pure species i. The superscript ‘sat’ indicates saturation conditions. The exponential term on the right hand side is the Poynting correction factor, including the molar liquid volume. Here, Mi is the molar mass of species i, and ρL is the liquid density. The correction factor describes the effect of pressure on the liquid fugacity. For low pressures, the Poynting correction factor is close to one, and two simplified relations can be formulated.
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In the case of an ideal gas mixture and an ideal liquid solution, the fugacity coefficient and the activity coefficient are both one, and Equation 3-192 reduces to Raoult’s law:
(3-193)
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For an ideal gas mixture, but a nonideal liquid solution, Equation 3-192 reduces to the modified Raoult’s law:
(3-194)
Assuming that the thermodynamic equilibrium prevails at the vapor–liquid interface, the molar fraction to prescribe on the vapor side of the interface is in general (from Equation 3-192)
(3-195)
The Vapor–Liquid-Solution Interface feature uses separate composition variables for the two phases along the droplet surface. To enforce a thermodynamic equilibrium, the composition on the vapor side is prescribed from Equation 3-195 using the liquid composition, the temperature, and the pressure at the surface. When the feature is coupled to a thermodynamics system, functions for both the liquid phase fugacity, and the vapor phase fugacity are available. It is also possible to prescribe a vapor pressure for each species. In this case, the system is assumed ideal and the vapor molar fraction is
(3-196)
The Vapor–Liquid Interface uses the same formulation for the vapor–liquid equilibrium, but the composition in the liquid phase is user-specified. It can be used to model vapor transport to or from a liquid where the composition changes are assumed small.
The The Transport of Concentrated Species in Vapor Interface interface solves for the mass fractions denote ω. For a species i, the boundary condition applied on the vapor side of the droplet surface is
(3-197)
where MVn is the mean molar mass of the vapor.
Using the ideal gas law of the form
(3-198)
the vapor side concentration corresponds to
(3-199)