Kinetics of Surfactant Adsorption at Fluid−Fluid Interfaces

Diamant, Haim; Andelman, David

doi:10.1021/jp960377k

Cited by 170 publications

(207 citation statements)

References 29 publications

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“…These instantaneous conditions yield an algebraic relationship between ψ and φ ± on Γ(t), namely 16) where θ ± ∈ R >0 . In this case the identity G − (φ − ) = G + (φ + ) in (2.15) leads to Henry's law 17) with the Henry constant K H = θ − /θ + . In order to make (2.13) well-defined, we assume from now on, and throughout this paper, that…”

Section: Governing Equationsmentioning

confidence: 99%

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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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Section: Governing Equationsmentioning

confidence: 99%

“…Generalizing the work in [17] the model (2.3a-e), (2.4), (2.5), (2.8a-c) was supplemented with (2.13) in [26]. The important feature of (2.13) is that it allows for an energy inequality, see [26] and (3.17) below.…”

Section: Governing Equationsmentioning

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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“…The first analysis of surfactant layers dates back to the 18th century with Franklin's experiments (1) and the first comprehensive studies on adsorption kinetics by Ward and Tordai (18) and Langmuir (19). From this point, a wide variety of models describe the adsorption dynamics, accounting for all kinds of molecular effects at interfaces (20)(21)(22)(23)(24)(25)(26). We expect two limiting cases: (i) the adsorption is limited by the bulk transport toward the interface, leading to a local equilibrium between the surfactant interfacial concentration and the bulk concentration in the vicinity of the interface at all times; and (ii) the adsorption is limited by the adsorption/desorption rate constants at the interface, and the bulk concentration is homogeneous at all time.…”

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confidence: 99%

Surfactant adsorption kinetics in microfluidics

Riechers

Maes

Akoury

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Emulsions are metastable dispersions. Their lifetimes are directly related to the dynamics of surfactants. We design a microfluidic method to measure the kinetics of adsorption of surfactants to the droplet interface, a key process involved in foaming, emulsification, and droplet coarsening. The method is based on the pH decay in the droplet as a direct measurement of the adsorption of a carboxylic acid surfactant to the interface. From the kinetic measurement of the bulk equilibration of the pH, we fully determine the adsorption process of the surfactant. The small droplet size and the convection during the droplet flow ensure that the transport of surfactant through the bulk is not limiting the kinetics of adsorption. To validate our measurements, we show that the adsorption process determines the timescale required to stabilize droplets against coalescence, and we show that the interface should be covered at more than 90% to prevent coalescence. We therefore quantitatively link the process of adsorption/desorption, the stabilization of emulsions, and the kinetics of solute partitioning-here through ion exchange-unraveling the timescales governing these processes. Our method can be further generalized to other surfactants, including nonionic surfactants, by making use of fluorophore-surfactant interactions.droplet | interfaces | surfactant | emulsion | microfluidics S urface active compounds are ubiquitous in our daily life, be it in living systems or in industrial and technological products (1-3). The compounds are used widely for the stabilization of foams and emulsions for food and cosmetic products, painting materials, and industrial coatings (3). Emulsions are nowadays also used in combination with microfluidic systems for applications in biotechnology (3-11). An emulsion is a dispersion of one liquid phase into another, stabilized by surfactants in a metastable state. The kinetic stabilization of emulsions occurs through several mechanisms, involving electrostatic or steric repulsion and the buildup of Marangoni stresses to improve the lifetime of emulsions against coalescence (12, 13). On the other hand, surfactants are involved in transport processes such as Ostwald ripening or solute transport, which mediates the chemical equilibration of the system (14-17): in general, all processes affecting the lifetime of emulsions (coalescence, rupture, exchange, and loss of molecules) are directly related to the physics and dynamics of the surfactant molecules at interfaces (3,4,6,10,11,15,16). The first analysis of surfactant layers dates back to the 18th century with Franklin's experiments (1) and the first comprehensive studies on adsorption kinetics by Ward and Tordai (18) and Langmuir (19). From this point, a wide variety of models describe the adsorption dynamics, accounting for all kinds of molecular effects at interfaces (20-26). We expect two limiting cases: (i) the adsorption is limited by the bulk transport toward the interface, leading to a local equilibrium between the surfactant interfacial concen...

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“…Diffusion of such molecules to solid surface is embarrassing. The mechanism of diffusion limited adsorption is realized (Syunyaev et al, 2009;Diamant & Andelman, 1996). Gibbs energy values are more or less the same for surfaces of all investigated materials: quartz, dolomite, and mica.…”

Section: Kinetic Parameters Of Adsorptionmentioning

confidence: 88%