Serpentine diffusion trajectories and the Ouzo effect in partially miscible ternary liquid mixtures†
This work investigates the transient equilibration process when partially miscible ternary liquid mixtures of two different compositions are brought into contact with each other. Diffusional coupling effects are shown to become increasingly significant as the mixture compositions approach the meta-stable regions of the phase equilibrium diagrams. The proper modelling of coupled diffusion phenomena requires the use of a Fick diffusivity matrix [D], with inclusion of non-zero off-diagonal elements. The primary objective of this article is to develop a simple, robust, procedure for the estimation of the matrix [D], using the Maxwell–Stefan (M–S) formulation as a convenient starting point. In the developed simplified approach, the Fick diffusivity matrix [D] is expressed as the product of a scalar diffusivity and the matrix of thermodynamic correction factors [Γ]. By detailed examination of experimental data for the matrix [D] in a wide variety of ternary mixtures, it is deduced that the major contribution of diffusional coupling arises from the contributions of non-ideal solution thermodynamics, quantified by the matrix of thermodynamic correction factors [Γ]. An important consequence of strong thermodynamic coupling is that equilibration trajectories are serpentine in shape and may exhibit incursions into meta-stable zones opening up the possibility of spontaneous emulsification and the Ouzo effect. If diffusional coupling effects are ignored, the equilibration trajectory is linear in composition space. For a wide variety of partially miscible ternary mixtures, it is demonstrated that the corresponding linear equilibration trajectories do not anticipate the possibility of emulsification.