The VLE model assumes that the characteristic time scale for the establishment of vapor-liquid equilibration is much shorter than other processes such as that of regular intra-phase chemical reactions and transport. This assumption implies that both forward and reverse rates of the phase-change process at the interface are fast compared to the intra-phase mass transfer rates in both the corresponding phases, that is, the liquid (bulk) phase and the gas phases.

The transport rate [mol/s] of the liquid species from the liquid-bulk phase to the gas-liquid interface can be expressed as

(9–16)

Where and are the molar concentration [mol/cm³] of the liquid species in the liquid bulk and at the interface, respectively. [cm/s] is the mass transfer coefficient of species in the liquid phase and [cm²] is the area of the gas-liquid interface.

Similarly, the transport rate of the corresponding vapor species from the interface to the bulk gas is

(9–17)

The mass flow rate of species must be continuous at the interface. Therefore

(9–18)

Because the phase equilibrium is always maintained at the gas-liquid interface, the liquid and the gas concentrations at the interface are correlated depending on the type of the liquid-bulk mixture.

Regular Liquid Mixture

When liquid-vapor equilibrium is established for a regular liquid species, its distribution in liquid and vapor phases is determined by Raoult's law, that is,

(9–19)

is the vapor pressure of a gaseous tar species at a given temperature. is the gas-phase mole fraction of species , and is the mole fraction (or bulk activity) of the corresponding bulk species in the liquid-bulk phase on which it resides:

(9–20)

where is the total number of liquid species in the same liquid mixture as the vaporizing species and is the molar concentration of liquid species in the liquid mixture. At the gas-liquid interface, Equation 9–19 can be rewritten as

(9–21)

Or

(9–22)

Z is the compressibility of the gas-phase mixture (for an ideal gas, Z=1), R the universal gas constant, and T the gas temperature next to the interface. The vapor pressure of a liquid species is computed from the empirical correlations. For example, measured vapor pressure of a condensable gas species is fitted to a function of temperature as

(9–23)

The fitting parameters for the liquid species are given as part of the thermodynamic data.

Combining Equation 9–16 - Equation 9–18 and Equation 9–22 the (mass transport controlled) vaporization rate of species can be found as

(9–24)

Where

(9–25)

Diluted Solution

For a diluted solution, the vapor-liquid relationship at the interface is described by Henry's law

(9–26)

is the vapor/partial pressure of species at the interface and is the Henry's law constant of species .

According to the gas law, the partial pressure of a vapor species at the interface is related to its concentration as

(9–27)

Therefore, the vapor concentration of species at the interface can be written as a function of its concentration in the liquid phase as

(9–28)

Accordingly, the transport-limited vaporization rate of species in a diluted solution becomes

(9–29)

where

(9–30)

The transformation between a liquid species and its vapor is specified by the Vapor-Liquid Equilibrium (VLE) reaction in the surface mechanism. Details of the VLE reaction format and rate parameters are given in Vapor-Liquid Phase Transfer in the Chemkin Input Manual .