Nonequilibrium Thermodynamic Model of Water-in-Water Emulsions

The dynamic behavior of highly permeable interfaces in phase-separated biopolymer solutions, liposomes, polymersomes, and colloidosomes is investigated. Using nonequilibrium thermodynamics, an expression for the correlation function of the height of a flat interface is derived for a multicomponent system, incorporating the effects of mass transfer across the interface. In addition, an expression is derived for the relaxation time of the height correlation function. This relaxation time is calculated for a phase-separated gelatin-dextran-water system. Comparing our expression with the expression for an impermeable interface shows that mass transfer has a significant impact on the fluctuations of the interface. At small values for the amplitude, the relaxation of fluctuations is completely dominated by the permeability of the interface. At high values for the amplitude, the relaxation is dominated by the viscosities and densities of the bulk phases. In this regime, the long-time limit of the height correlation function shows multiexponential decay. The existence of such a multiexponential response was confirmed by recent experiments (Biomacomolecules 2006, 7, 2224). The crossover length between permeability- and viscosity-dominated relaxation is in the range of 0.1-50 µm.