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

Klinteberg, Ludvig af; Lindbo, Dag; Tornberg, Anna‐Karin

doi:10.1016/j.compfluid.2014.05.029

Cited by 12 publications

(7 citation statements)

References 73 publications

(113 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A contact angle condition, which relates the unbalanced Young force to the slip velocity at the contact line, was introduced to account for the effect of surfactants on the surface wettability. Based on the domain decomposition for representing the interface, af Klinteberg et al 13 developed an explicit Eulerian method to simulate two-phase flows with insoluble surfactants and contact line dynamics in 2D. To drive the movement of the contact line, they defined the tangential velocity in the vicinity of the contact line and used the Navier slip condition on the walls away from the contact line.…”

Section: ■ Introductionmentioning

confidence: 99%

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Zhang

Liu

2019

Langmuir

View full text Add to dashboard Cite

Surfactants are widely used in many industrial processes, where the presence of surfactants not only reduces the interfacial tension between fluids but also alters the wetting properties of solid surfaces. To understand how the surfactants influence the droplet motion on a solid surface, a hybrid method for interfacial flows with insoluble surfactants and contact-line dynamics is developed. This method solves immiscible two-phase flows through a lattice Boltzmann colorgradient model and simultaneously solves the convection− diffusion equation for surfactant concentration through a finite difference method. In addition, a dynamic contact angle formulation that describes the dependence of the local contact angle on the surfactant concentration is derived, and the resulting contact angle is enforced by a geometrical wetting condition. Our method is first used to simulate static contact angles for a droplet resting on a solid surface, and the results show that the presence of surfactants can significantly modify surface wettability, especially when the surface is more hydrophilic or more hydrophobic. This is then applied to simulate a surfactantladen droplet moving on a substrate subject to a linear shear flow for varying effective capillary number (Ca e ), Reynolds number (Re), and surface wettability, where the results are often compared with those of a clean droplet. For varying Ca e , the simulations are conducted by considering a neutral surface. At low values of Ca e , the droplet eventually reaches a steady deformation and moves at a constant velocity. In either a clean or surfactant-laden case, the moving velocity of the droplet linearly increases with the moving wall velocity, but the slope is always higher (i.e., the droplet moves faster) in the surfactantladen case where the droplet exhibits a bigger deformation. When Ca e is increased beyond a critical value (Ca e,c ), the droplet breakup would happen. The presence of surfactants is found to decrease the value of Ca e,c , but it shows a non-monotonic effect on the droplet breakup. An increase in Re is able to increase not only droplet deformation but also surfactant dilution. The role of surfactants in the droplet behavior is found to greatly depend upon the surface wettability. For a hydrophilic surface, the presence of surfactants can decrease the wetting length and enables the droplet to reach a steady state faster; while for a hydrophobic surface, it increases the wetting length and delays the departure of the droplet from the solid surface.

show abstract

Section: ■ Introductionmentioning

confidence: 99%

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Zhang

Liu

2019

Langmuir

View full text Add to dashboard Cite

show abstract

“…Since of the various effects of surfactants and their high nonlinearity, nonuniform interfacial tension problems involving a mobile interface remain very challenging analytically. , This difficulty is alleviated for numerical simulations, and a wealth of models of single droplets or bubbles covered with an insoluble ,− or soluble surfactant ,− are available. Nevertheless, the effects of surfactant nonuniform coverage on the droplet formation in microfluidic channels have yet to be investigated.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Surfactant Dynamics during Emulsification in a T-Junction Microchannel

et al. 2018

View full text Add to dashboard Cite

Microchannel emulsification requires large amounts of surfactant to prevent coalescence and improve emulsions lifetime. However, most numerical studies have considered surfactant-free mixtures as models for droplet formation in microchannels, without taking into account the distribution of surfactant on the droplet surface. In this paper, we investigate the effects of nonuniform surfactant coverage on the microfluidic flow pattern using an extended lattice-Boltzmann model. This numerical study, supported by micro-particle image velocimetry experiments, reveals the likelihood of uneven distribution of surfactant during the droplet formation and the appearance of a stagnant cap. The Marangoni effect affects the droplet breakup by increasing the shear rate. According to our results, surfactant-free and surfactant-rich droplet formation processes are qualitatively different, such that both the capillary number and the Damköhler number should be considered when modeling the droplet generation in microfluidic devices. The limitations of traditional volume and pressure estimation methods for determining the dynamic interfacial tension are also discussed on the basis of the simulation results.

show abstract

“…These procedures include using Dirichlet boundary conditions on equations describing the interface or fitting the interface so that is takes a given curvature [19]. Due to the ad-hoc regularization techniques to implement velocity boundary conditions, and/or due to the manipulation of the interface, common problems with contact line models are inaccuracies and grid effects [15,24].…”

Section: Introductionmentioning

confidence: 99%

Towards Accurate Modeling of Moving Contact Lines

Holmgren¹,

Kreiss²

2015

Preprint

View full text Add to dashboard Cite

A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in developing the macroscopic part of an accurate multiscale model for a moving contact line problem in two space dimensions. We assume that a micro model has been used to determine a relation between the contact angle and the contact line velocity. An intermediate region is introduced where an analytical expression for the velocity exists. This expression is used to implement boundary conditions for the moving contact line at a macroscopic scale, along a fictitious boundary located a small distance away from the physical boundary.Model problems where the shape of the interface is constant thought the simulation are introduced. For these problems, experiments show that the errors in the resulting contact line velocities converge with the grid size h at a rate of convergence p ≈ 2.

show abstract

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

Cited by 12 publications

References 73 publications

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Numerical Study of Droplet Dynamics on a Solid Surface with Insoluble Surfactants

Numerical Study of Surfactant Dynamics during Emulsification in a T-Junction Microchannel

Towards Accurate Modeling of Moving Contact Lines

Contact Info

Product

Resources

About