Analysis of Ginzburg-Landau-type models of surfactant-assisted liquid phase separation

Abstract

Citation: TOTH, G. and KVAMME, B., 2015 In this paper the diffuse interface models of surfactant assisted liquid-liquid phase separation are addressed. We start from the generalized version of the Ginzburg-Landau free energy functional based model of van der Sman and van der Graaf. First we analyze the model in the constant surfactant approximation and show the presence of a critical point, at which the interfacial tension vanishes. Then we determine the adsorption isotherms and investigate the validity range of previous result. As a key point of the work, we propose a new model of the van der Sman / van der Graaf type designed for avoiding both unwanted unphysical effects and numerical difficulties being present in previous models. In oder to make the model suitable to describe real systems, we determine the interfacial tension analytically more precisely, and analyze it on the entire accessible surfactant load range. Emerging formulas are then validated by calculating the interfacial tension from the numerical solution of the Euler-Lagrange equations. Time dependent simulations are also performed to illustrate the slowdown of the phase separation near the critical point, and to prove that the dynamics of the phase separation is driven by the interfacial tension.

Phenomenological Continuum Theory of Asphaltene-Stabilized Oil/Water Emulsions

“…26 Theoretical analyses and consistent formulation of the generalized van der Sman / van der Graaf model for two qualitatively different systems, as well as numerical simulations of spinodal decomposition in diffusion driven systems have recently been published by Tóth and Kvamme. 9,10 All the aforementioned works addressed thermodynamics driven emulsion formation in liquid systems, i.e. a situation, in which the phase separation stops because of the vanishing interfacial tension.…”

Phase field modelling of spinodal decomposition in the oil/water/asphaltene system

“…The Helmholtz free energy of the inhomogeneous system is given in a functional form: [17][18][19][20][22][23][24]27 The Helmholtz free energy of the inhomogeneous system is given in a functional form: [17][18][19][20][22][23][24]27 …”

“…27 Furthermore, F c is the free energy associated with the presence of the surfactant: 27 Furthermore, F c is the free energy associated with the presence of the surfactant:…”

“…We mention that there are different ways of regularizing the surfacedelta function. It has been revealed that the squaregradient coupling results in unphysical behaviour, namely, shrinking interface width and accelerating phase separation with increasing surfactant load, 27 and, moreover, the dynamic equations have no stable solution under physically relevant circumstances. It has been revealed that the squaregradient coupling results in unphysical behaviour, namely, shrinking interface width and accelerating phase separation with increasing surfactant load, 27 and, moreover, the dynamic equations have no stable solution under physically relevant circumstances.…”

“…It has been revealed that the squaregradient coupling results in unphysical behaviour, namely, shrinking interface width and accelerating phase separation with increasing surfactant load, 27 and, moreover, the dynamic equations have no stable solution under physically relevant circumstances. 27 Although our findings regarding the critical behaviour of the model are valid in general, this coupling also leads to unstable interfaces for high interface loads (i.e. 27 Although our findings regarding the critical behaviour of the model are valid in general, this coupling also leads to unstable interfaces for high interface loads (i.e.…”