F. James et al., STATISTICAL THERMODYNAMICS MODELS FOR MULTICOMPONENT ISOTHERMAL DIPHASIC EQUILIBRIA, Mathematical models and methods in applied sciences, 7(1), 1997, pp. 1-29
We propose in this paper a whole family of models for isothermal dipha
sic equilibrium, which generalize the classical Langmuir isotherm. The
main tool to obtain these models is a fine modeling of each phase, wh
ich states various constraints on the equilibrium. By writing down the
Gibbs conditions of thermodynamical equilibrium for both phases, we a
re led to a constrained minimization problem, which is solved through
the Lagrange multipliers. If one of the phases is an ideal solution, w
e can solve explicitly the equations, and obtain an analytic model. In
the most general case, we have implicit formulas, and the models are
computed numerically. The models of multicomponent isotherm we obtain
in this paper are designed for chromatography, but can be adapted muta
tis mutandis to other cases.