Mixing of Macroscopically Quiescent Liquid Mixtures

We simulate the mixing process of a quiescent binary mixture that is instantaneously brought from the two- to the one-phase region of its phase diagram. Our theoretical approach follows the diffuse interface model, where convection and diffusion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. In liquid systems, as this driving force induces a material flux which is much larger than that due to pure molecular diffusion, drops tend to coalesce and form larger domains, therefore accelerating all phase separation processes. On the other hand, convection induced by phase transition effectively slows down mixing, since such larger domains, eventually, must dissolve by diffusion. Therefore, whenever all other convective fluxes can be neglected and the mixture can be considered to be macroscopically quiescent, mixing is faster for very viscous mixtures, unlike phase separation which is faster for very fluid mixtures. In addition, the mixing rate is also influenced by the Margules parameter, which describes the relative weight of enthalpic versus entropic forces. In the late stage of the process, this influence can approximately be described assuming that mixing is purely diffusive, with a given effective diffusivity. That shows that mixing at late stages is characterized by a self-similar solution of the governing equations, which leads to a t^-1 power-law decay for the degree of mixing, i.e. the mean square value of the composition fluctuations.