Modeling phase behavior for quantifying micro-pervaporation experiments

A theoretical model will be presented for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally by Jacques Leng and coworkers. The described device makes use of the pervaporation of water through a thin PDMS membrane to build up a solute concentration profile inside a long microfluidic channel. We simplify the evolution of this profile in binary mixtures to a one-dimensional model which comprises two concentration-dependent coefficients. The model then provides a link between directly accessible experimental observations, such as the widths of dense phases or their growth velocity, and the underlying chemical potentials and phenomenological coefficients. It shall thus be useful for quantifying the thermodynamic and dynamic properties of dilute and dense binary mixtures.
The model is formulated using the framework of the linear non-equilibrium thermodynamics. At the example of micro-pervaporation, we will go through the assumptions of this theory. This rather pedagogical procedure will clarify the implications of the mathematical assumptions on the description of a real experiment. At the same time, it opens the possibility to ask more fundamental questions on the formulation of near-equilibrium systems.