A 3D front-tracking approach for simulation of a two-phase fluid with insoluble surfactant

Jesus, Wellington C. de; Roma, Alexandre M.; Pivello, Márcio Ricardo; Villar, Millena Martins; Neto, Aristeu da Silveira

doi:10.1016/j.jcp.2014.10.021

Cited by 39 publications

(29 citation statements)

References 54 publications

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“…Interface tracking methods use a separate grid or mesh to track the interface. The most popular are the Front-Tracking (FT) method [6,15,42,45,87], the Boundary Integral Method (BIM) [13,41,65] and the Immersed Boundary Method (IBM) [37,38]. These methods, initially developed for insoluble surfactants, have been then extended to soluble surfactants [44,87].…”

Section: Introductionmentioning

confidence: 99%

Coalescence of surfactant-laden drops by Phase Field Method

Soligo

Roccon

Soldati

2019

Journal of Computational Physics

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In this work, we propose and test the validity of a modified Phase Field Method (PFM), which was specifically developed for large scale simulations of turbulent flows with large and deformable surfactant-laden droplets. The time evolution of the phase field, φ, and of the surfactant concentration field, ψ, are obtained from two Cahn-Hilliard-like equations together with a two-order-parameter Time-Dependent Ginzburg-Landau (TDGL) free energy functional. The modifications introduced circumvent existing limitations of current approaches based on PFM and improve the well-posedness of the model. The effect of surfactant on surface tension is modeled via an Equation Of State (EOS), further improving the flexibility of the approach. This method can efficiently handle topological changes, i.e. breakup and coalescence, and describe adsorption/desorption of surfactant. The capabilities of the proposed approach are tested in this paper against previous experimental results on the effects of surfactant on the deformation of a single droplet and on the interactions between two droplets. Finally, to appreciate the performances of the model on a large scale complex simulation, a qualitative analysis of the behavior of surfactant-laden droplets in a turbulent channel flow is presented and discussed.

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Section: Introductionmentioning

confidence: 99%

Coalescence of surfactant-laden drops by Phase Field Method

Soligo

Roccon

Soldati

2019

Journal of Computational Physics

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“…The distortion of the drop is measured by the benchmark deformation parameter for almost ellipsoidal drops proposed by Taylor [43] in a pioneering work. In fact, this is a very natural choice if we consider that most of theoretical, numerical, and experimental works on droplets undergoing shear or extensional flows until nowadays use the Taylor distortion parameter as the main geometrical measure [53][54][55]. This quantity can be written in function of the components of the Cauchy-Green distortion tensor of the droplet surface as [10]…”

Section: Automatic Time-step Control Methodsmentioning

confidence: 99%

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Siqueira

Rebouças

Oliveira

et al. 2016

Numerical Methods in Fluids

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Summary We present a numerical methodology for the simulation of a viscous drop under simple shear flows by using the boundary integral method. The present work treats only a single drop in an unbounded fluid‐flow, but the results can be directly applied to studies on the rheology of dilute emulsions, in which the hydrodynamic interactions between two or more drops can be neglected. Singular and non‐singular integral representations of the velocity field are considered. Several aspects of the method are presented, including a new mesh relaxation approach and an automatic time‐step control method. The relaxation strategy is used in order to contain the distortion of the mesh and is performed by using relaxation iterations in a virtual temporal march between each physical time step of the simulation and monitoring the standard deviation of the areas of the elements. The automatic time‐step control method uses a global quantity related to the drop deformation in order to automatically set the temporal integration time step. It is carried out in a way to keep the local integration error less than a given tolerance. This strategy reduces the computational cost of the simulation by dramatically reducing the number of time steps in the temporal integration process. Copyright © 2016 John Wiley & Sons, Ltd.

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“…Besides the external applying flow, the motion of the interface and fluids is mainly driven by the surface tension along the free interface where an insoluble surfactant is distributed and varied on the interface that changes the surface tension in a timely fashion. Using the immersed boundary (or front-tracking) formulation, the fluid variables are represented in Eulerian manner while the interface quantities are represented in Lagrangian manner so the dimensionless governing equations for the above two-phase flow with insoluble surfactant can be written as one whole fluid system as follows [9,25].…”

Section: Equations Of Motionmentioning

confidence: 99%

“…In order to take the inertia effect into account, various numerical methods were proposed to incorporate with Navier-Stokes equations. These methods are based upon volume-of-fluid (VOF) [4,11,21], front-tracking method [9,32,33], immersed boundary method [7,[25][26][27], level-set [47,48], and arbitrary Lagrangian-Eulerian (ALE) finite element method [3, 15-17, 19, 36]. Apart from the methods listed above, other numerical studies include diffuse-interface method [43], segmented projection method [22,23], lattice Boltzmann method [13], moving particle semi-implicit method [14], and smoothed particle hydrodynamics (SPH) method [1] etc.…”

Section: Introductionmentioning

confidence: 99%

An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

Seol

Hsu²,

Lai³

2018

CICP

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In this paper, an immersed boundary (IB) method for simulating the interfacial flows with insoluble surfactant in three dimensions is developed. We consider a doubly periodic interface separating two fluids where the surfactant exists only along the evolving interface. An equi-arclength parametrization is introduced in order to track the moving interface and maintain good Lagrangian meshes, so stable computations can be performed without remeshing. This surface mesh-control technique is done by adding two artificial tangential velocity components into the Lagrangian marker velocity so that the Lagrangian markers can be equi-arclength distributed during the time evolution. As a result, the surfactant equation on the interface must be modified based on the new parametrization. A conservative scheme for solving the modified surfactant equation has been developed and proved to satisfy the total surfactant mass exactly in discrete level. A series of numerical experiments consisting of the validation of Lagrangian mesh control technique, the convergence study, the study of self-healing dynamics, and the simulations of two-layer fluids under Couette flow have been conducted to test our present numerical scheme.

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A 3D front-tracking approach for simulation of a two-phase fluid with insoluble surfactant

Cited by 39 publications

References 54 publications

Coalescence of surfactant-laden drops by Phase Field Method

Coalescence of surfactant-laden drops by Phase Field Method

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

An Immersed Boundary Method for Simulating Interfacial Flows with Insoluble Surfactant in Three Dimensions

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