A level-set method for interfacial flows with surfactant

Xu, Jianjun; Li, Zhilin; Lowengrub, John; Zhao, Hongkai

doi:10.1016/j.jcp.2005.07.016

Cited by 175 publications

(164 citation statements)

References 62 publications

(85 reference statements)

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“…Implicit interface tracking methods have been extended to include surfactants on the interface, such as the level-set method by Xu et al [69,70] and various VOF methods [52,28,19]. The main concern in such methods is conservation of surfactant; [69] is largely concerned with modifications that deal with this.…”

Section: Surfactantsmentioning

confidence: 99%

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An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

2014

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The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the Immersed Boundary Method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.

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Section: Surfactantsmentioning

confidence: 99%

“…The main concern in such methods is conservation of surfactant; [69] is largely concerned with modifications that deal with this. Other implicit methods recently proposed include phase-field (Cahn-Hilliard) methods by Liu & Zhang [41] and Teigen et al [62], as well as a "smoothed particle hydrodynamics" method by Adami et al [1].…”

Section: Surfactantsmentioning

confidence: 99%

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

2014

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“…Note these are the same advantages that signed distance functions have for representing interfaces. In fluids, the values of the function may refer to the amount of surfactants at a fluid-fluid interface [22]. In level set methods, the values may refer to calculated velocities on the interface [2,3].…”

Section: Extension Of Valuesmentioning

confidence: 99%

Redistancing by flow of time dependent eikonal equation

Cheng

Tsai

2008

Journal of Computational Physics

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Construction of signed distance to a given inteface is a topic of special interest to level set methods. There are currently, however, few algorithms that can efficiently produce highly accurate solutions. We introduce an algorithm for constructing an approximate signed distance function through manipulation of values calculated from flow of time dependent eikonal equations. We provide operation counts and experimental results to show that this algorithm can efficiently generate solutions with a high order of accuracy. Comparison with the standard level set reinitialization algorithm shows ours is superior in terms of predictability and local construction, critical, for example, in local level set methods. We further apply the same ideas to extension of values off interfaces. Together, our proposed approaches can be used to advance the level set method for fast and accurate computations of the latest scientific problems.In a level set method [11], an interface is represented as the zero level set of a continuous realvalued function, called a level set function. Let φ denote this function. Then φ embeds the interface Γ as its zero level set: Γ = {x ∈ R m |φ(x) = 0}. This representation retains geometric information of the interface, which can be extracted using formulas involving derivatives and integrals of φ. Furthermore, by adding a time variable, the level set function can be used to capture a given dynamics of the interface using a time dependent PDE in φ. The location of the interface at time t in this case is the zero level set of φ at that time: Γ(t) = {x ∈ R m |φ(x, t) = 0}.The level set function φ is certainly not unique; for example αφ, α = 0, is also a level set function for the same interface. Thus one can ask for the best level set function according to some chosen criterion. In applications, even when a physically relevant level set function exists, that function may not satisfy that choice and so should not be used. Instead, the commonly desired criterion for the form of the level set function is one that leads to small errors when numerically solving the time dependent PDE for the dynamics of the interface, or when extracting the interface location. This form is most important to a level set method near the interface of interest.Analytic solutions to the time dependent PDE for φ do not exist in all but the most trivial cases. Thus, one needs to turn to numerical approximations and solutions. The errors of a large class of popular numerical methods that operate on a discretization of the function over a grid, called finite differencing schemes, are typically calculated from Taylor expansions. This implies the derivatives of φ have a bearing on the error, with large magnitudes correlated to large errors. In addition to smoothness in φ, one would thus desire that φ avoid derivatives with large magnitudes, most notably at or near the zero level set of interest.

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“…58 For the computationally more challenging flows with soluble surfactants, a diffuse interface method was presented by Van der Smaan and Van der Graaf 47 for surfactant adsorption onto liquid interfaces. A diffuse-interface implementation including the effects of advection, diffusion and bulk-surface exchange of soluble surfactants was introduced by Teigen et al 49 together with a finite difference technique to model two-phase flows.…”

Section: Soluble Surfactant I Introductionmentioning

confidence: 99%

Soluble surfactant spreading on spatially confined thin liquid films

2012

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We studied the spreading of soluble surfactants on spatially confined thin liquid films by means of comprehensive experiments and numerical simulations. We determined the time evolution of the liquid film thickness both from interference microscopy measurements and finite element calculations. A characteristic rim develops ahead of the spreading surfactant front. Within certain time intervals, the rim position can be well represented by a power-law relation x rim $ t a . The corresponding spreading exponent a depends on the method of surfactant deposition and the numerical values deduced from experiments and simulations quantitatively agree. Depth-resolved simulations that account for domain deformability using the Arbitrary Lagrangian-Eulerian method show that shear-induced concentration non-uniformities across the rim film thickness tend to reduce the rim height. Fingering instabilities that are frequently observed in experiments were qualitatively reproduced in the simulations.

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A level-set method for interfacial flows with surfactant

Cited by 175 publications

References 62 publications

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

Redistancing by flow of time dependent eikonal equation

Soluble surfactant spreading on spatially confined thin liquid films

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