Spinodal decomposition of chemically reactive binary mixtures

Abstract

We simulate the influence of a reversible isomerization reaction on the phase segregation process occurring after spinodal decomposition of a deeply quenched regular binary mixture, restricting attention to systems wherein material transport occurs solely by diffusion. Our theoretical approach follows a diffuse-interface model of partially miscible binary mixtures wherein the coupling between reaction and diffusion is addressed within the frame of nonequilibrium thermodynamics, leading to a linear dependence of the reaction rate on the chemical affinity. Ultimately, the rate for an elementary reaction depends on the local part of the chemical potential difference since reaction is an inherently local phenomenon. Based on two-dimensional simulation results, we express the competition between segregation and reaction as a function of the Damköhler number. For a phase-separating mixture with components having different physical properties, a skewed phase diagram leads, at large times, to a system converging to a single-phase equilibrium state, corresponding to the absolute minimum of the Gibbs free energy. This conclusion continues to hold for the critical phase separation of an ideally perfectly symmetric binary mixture, where the choice of final equilibrium state at large times depends on the initial mean concentration being slightly larger or less than the critical concentration.

Thermodynamic stability of driven open systems and control of phase separation by electro-autocatalysis

“…Allen-Cahn which is the ratio of the diffusion and reaction time scales, only here diffusion is backward (D < 0) [18], and the characteristic reaction time is…”

“…Due to critical slowing down of diffusion, the Allen-Cahn-like instability dominates near the spinodal limits (Da → 0), while the Cahn-Hilliard-like instability may arise only deep into the spinodal region. Such phenomena were recently studied by Lamorgese and Mauri [18] for a non-autocatalytic reaction with linear Allen-Cahn kinetics [4], in which case the spinodal limits of phase separation cannot be altered.…”

Triphase Separation of a Ternary Symmetric Highly Viscous Mixture

“…Clearly, this definition is the same as that employed for studying phase separation in a binary system [ 38 , 39 , 41 , 49 , 52 , 54 , 55 , 56 ]; in fact, the reason that the same definition can be brought to bear on a ternary system is that, based on the mixture phase diagram in Figure 1 , both phases in any one pair of coexisting phases at equilibrium possess the same (with i denoting the component at the opposite vertex in the phase diagram). As can be seen ( Figure 4 ), phase separation for component 3 is faster than that for the remaining two components, thus confirming the (qualitative) conclusions that were reached by observing Figure 2 .…”

“…These relations, together with the equalities and , define all chemical potential differences for a ternary system. Finally, it is worth reiterating that Equations ( 4 ) and ( 5 ) constitute a system of fourth-order equations, which represents a generalization (specifically, a ternary version of Model B in the taxonomy of Hohenberg and Halperin [ 51 ]) of the classical Cahn–Hilliard equation to describe phase separation in binary mixtures [ 33 , 34 , 37 , 38 , 39 , 41 , 52 , 53 , 54 ].…”

Dissolution or Growth of a Liquid Drop via Phase-Field Ternary Mixture Model Based on the Non-Random, Two-Liquid Equation

“…In conclusion, it is worth reiterating that Equations ( 7 ) and ( 8 ) constitute a system of fourth-order equations, which represents a generalization of the classical Cahn-Hilliard equation to describe phase separation in binary mixtures [ 11 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ].…”