A new phase-field model for a water–oil-surfactant system

Yun, Ana; Li, Yibao; Kim, Junseok

doi:10.1016/j.amc.2013.12.054

Cited by 34 publications

(27 citation statements)

References 32 publications

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“…in the first order, which becomes a Frumkin adsorption isotherm for lateral interaction parameters strong enough to win over (19)], as also suggested by Engblom et al [20].…”

Section: Langmuir and Frumkin Adsorption Isotherms For C =mentioning

confidence: 55%

“…no phase separation occurs. Since ψ c is only the function of λ 1 and a, but does not depend on the particular form of F ψ , the critical point exists in the models of Theissen and Gompper [12], van der Sman and van der Graaf [14], Liu and Zhang [17], Li and Kim [18], Engblom et al [20], and Yun et al [19]. Using Eq.…”

Section: A Constant Surfactant Field Approximationmentioning

confidence: 99%

“…Despite their efforts, the models still suffered from some unphysical properties, such as shrinking interface width with increasing surfactant load. To avoid the problem, Yun, Li and Kim [19] introduced a non-variatinal formalism of the dynamic equations, however, the surfactant-free solution is not present in the new model anymore. Nevertheless, they have also succesfully addressed the Marangoni effect on droplet dynamics.…”

Section: Introductionmentioning

confidence: 99%

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

Tóth

Kvamme

2015

Phys. Rev. E

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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.

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“…in the first order, which becomes a Frumkin adsorption isotherm for lateral interaction parameters strong enough to win over (19)], as also suggested by Engblom et al [20].…”

Section: Langmuir and Frumkin Adsorption Isotherms For C =mentioning

confidence: 55%

Section: A Constant Surfactant Field Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tóth

Kvamme

2015

Phys. Rev. E

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“…Subsequent efforts have been directed to extend this type of model with regards to non-matched densities [57], divergence-free mixture velocities [25], thermodynamic consistency [1,40], and flows with more than two fluids [9,15,26,27,48,49,50]. Regarding the inclusion of surfactants we refer to [30,55,56,74,76,81], all of which are restricted to two fluids. Our phase field model builds up on [33], where surfactants in two-phase flow are studied within a free energy framework.…”

Section: Introductionmentioning

confidence: 99%

Phase field modelling of surfactants in multi-phase flow

Dunbar

Lam

Stinner

2019

Interfaces Free Bound.

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A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions.

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“…Multiphase flows play an increasingly important role in many scientific and bio-medical engineering applications, such as, gas bubble trapped in water [1], oil-water mixtures [2], nanofluids [3,4], biological fluids and cells in blood [5]. Multiphase fluid motions have been extensively studied both theoretically and experimentally, yet still remain an active interdisciplinary research field.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation for multi-phase fluids considering different densities with continuous finite element method

Jiang

Yang

2018

J. Phys.: Conf. Ser.

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Abstract. In this paper, we compute a phase field model of Cahn-Hilliard type for multicomponent mixture fluids considering surface tension and buoyancy effects. We discretize Navier-Stokes and Cahn-Hilliard coupled equations with a continuous finite element scheme in space and the finite difference in time. Also, we apply a penalty formulation to the continuity equation which may increase the stability in solving the continuity condition and momentum equation. The dynamic of a rising lighter drop due to different densities between other two immiscible fluids is studied as the numerical example with a relatively coarse grid. Numerical results show that this model can be solved with a relative simple scheme and coarse grid which leads to the higher efficiency.

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A new phase-field model for a water–oil-surfactant system

Cited by 34 publications

References 32 publications

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

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

Phase field modelling of surfactants in multi-phase flow

Numerical simulation for multi-phase fluids considering different densities with continuous finite element method

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