On Diffuse Interface Modeling and Simulation of Surfactants in Two-Phase Fluid Flow

Engblom, Stefan; Do-Quang, Minh; Amberg, Gustav; Tornberg, Anna‐Karin

doi:10.4208/cicp.120712.281212a

Cited by 59 publications

(106 citation statements)

References 51 publications

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“…The enthalpic contribution f e (φ) = φ 2 /2 expresses that presence of the surfactant is energetically penalized in the bulk liquids, while the surface delta function δ S (φ) can be regularized on several fashions for continuum models. 26 In agreement with the results of our previous works 9 we choose δ S (φ) = g(φ) resulting in broadening interface with increasing surfactant composition. In the surfactant-free case (i.e.…”

Section: Theorysupporting

confidence: 81%

Phenomenological Continuum Theory of Asphaltene-Stabilized Oil/Water Emulsions

2017

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In this paper we use a phenomenological continuum theory of the Ginzburg-Landau type to address emulsion formation in water/light hydrocarbon/asphaltene systems.Based on the results of recent molecular dynamics simulations, we first calibrate the model parameters and show, that the theory produces a reasonable equation of state.Next, the coalescence of oil droplets is studied by a convection-diffusion dynamics as a function of both the surface coverage and the viscosity contrast between the asphaltene and the bulk liquids. We show, that, besides the traditional thermodynamic interpretation of emulsion formation, the timescale of drop coalescence can be controlled independently from the interfacial tension drop, which offers an alternative, solely kinetic driven mechanism of emulsion formation.

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Section: Theorysupporting

confidence: 81%

Phenomenological Continuum Theory of Asphaltene-Stabilized Oil/Water Emulsions

2017

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“…The logarithmic term in F ψ is the ideal part of the entropy of mixing, while the term −w(c/2)ψ 2 represents the energy associated with the lateral interaction between adjacent surfactant layers [17]. F 1 is a general linear coupling between the liquid-liquid interface and the surfactant field, emerging from the regularization of the surface Diracdelta function [20]. Finally, F ex accounts for the extra energy due to the presence of the surfactant in the bulk phases [17].…”

Section: A Free Energy Functionalmentioning

confidence: 99%

“…Finally, F ex accounts for the extra energy due to the presence of the surfactant in the bulk phases [17]. Contrary to the work of Engblom et al [20], we do not consider a coupling term ∝ ψ[φ(1 − φ)] in F 1 , since it is equivalent to ∝ ψ φ 2 in F ex . Note that the only asymmetric term of the free energy functional is −w e φ ψ, being responsible for different equilibrium mole fractions of the surfactant in the bulk phases.…”

Section: A Free Energy Functionalmentioning

confidence: 99%

“…Nevertheless, they have also succesfully addressed the Marangoni effect on droplet dynamics. A different fashion of fixing interface related problems has been proposed by S. Engblom and co-workers [20]. Besides the unphysical behavior of the interface width, the authors gave strong evidences of that the PDE problem has no solution at all under physically relevant circumstances.…”

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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“…The level set method, which describes the interface as the level set of a function, was considered in [43]. Numerical computations based on diffuse interface models have been presented in [35,42,24,26]. The immersed boundary method has been used in [34,15].…”

Section: Introductionmentioning

confidence: 99%

Stable finite element approximations of two-phase flow with soluble surfactant

Barrett

Garcke

Nürnberg

2015

Journal of Computational Physics

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Please cite this article in press as: J.W. Barrett et al., Stable finite element approximations of two-phase flow with soluble surfactant, J. Comput. Phys. (2015), http://dx.doi.org/10. 1016/j.jcp.2015.05.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractA parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

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On Diffuse Interface Modeling and Simulation of Surfactants in Two-Phase Fluid Flow

Cited by 59 publications

References 51 publications

Phenomenological Continuum Theory of Asphaltene-Stabilized Oil/Water Emulsions

Phenomenological Continuum Theory of Asphaltene-Stabilized Oil/Water Emulsions

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

Stable finite element approximations of two-phase flow with soluble surfactant

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