Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

Abstract

In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component incompressible liquid mixtures. First, a thermodynamically consistent convectiondiffusion type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free energy functional is presented for arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and demonstrate, that the energy penalization for multi-component states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (4-component) systems. Simulations addressing liquid flow assisted spinodal decomposition in these systems are also presented.

Phase-field modeling of isothermal quasi-incompressible multicomponent liquids

“…Eq. (36) can also be expressed in terms of the absolute densities, yield- To solve the dynamic equations we apply an operatorsplitting based, pseudo-spectral semi-implicit method, yielding [8,35]:…”

“…The free energy density of a general multicomponent liquid undergoing liquid-liquid phase separation can be defined as [8,33]:…”

“…Although the theory of multicomponent liquid diffusion is well developed and in use in chemical engineering and materials science [1][2][3][4], the generalization of theory describing the time evolution of liquid systems being out of mechanical equilibrium is still lacking. Nevertheless, even results of simple continuum theories indicate that the hydrodynamic mode might influence pattern formation significantly even on small length scales [5][6][7][8], which indeed comes into play in microfluidics [9][10][11][12], or even in oil industry related research: CO 2 /water/hydrocarbon emulsions may offer a novel and ultimate solution for the global CO 2 storage problem with combined Enhanced Oil Recovery, however, the continuum description of kinetic processes in these molecularly complex liquids is nontrivial [7]. Besides, significant volume changes occur in case of formation/dissociation of CO 2 /CH 4 hydrates (clathrates), also necessitating thus a hydrodynamic description.…”

Accuracy Evaluation of Phase-field Models for Grain Growth Simulation with Anisotropic Grain Boundary Properties

“…Furthermore, within the framework of the MPF model, a recent work by Tóth et al 59) proposed a generalized MPF (XMPF) model based on a unique formulation. All of these phase-field models are reportedly capable of accurate simulation of grain growth under isotropic or weakly anisotropic grain boundary properties (e.g., the ratio of the maximum and minimum boundary energies is less than two [60][61][62][63] ). However, for cases with strong anisotropy in grain boundary properties, the accuracy of the models has not yet been tested in detail.…”

Моделирование Распада Бинарных Сплавов На Основе Метода Функционала Плотности Свободной Энергии

“…Одним из основных уравнений для моделей такого типа яв-ляется уравнение Кана-Хилларда [5][6][7], которое, как правило, применяется (с учетом различных модифи-каций) для описания процесса формирования фаз в области спинодального распада (см., например, [8][9][10]). Использование данного уравнения для описания про-цесса нуклеации также является весьма эффективным (см., например, [11,12]), поскольку позволяет рассмат-ривать кластеры, имеющие переменный состав и ха-рактеризующиеся протяженной областью сопряжения фаз и переменным поверхностным натяжением.…”