2134/27286
Gyula Toth
Gyula
Toth
Bjorn Kvamme
Bjorn
Kvamme
Analysis of Ginzburg-Landau-type models of surfactant-assisted liquid phase separation
Loughborough University
2017
untagged
Mathematical Sciences not elsewhere classified
2017-11-03 16:21:58
Journal contribution
https://repository.lboro.ac.uk/articles/journal_contribution/Analysis_of_Ginzburg-Landau-type_models_of_surfactant-assisted_liquid_phase_separation/9387008
In this paper 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 results. 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
present in previous models. In order to make the model suitable for describing real systems, we determine the
interfacial tension analytically more precisely and analyze it over 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.