A simple numerical solution to the Ward–Tordai equation for the adsorption of non-ionic surfactants

Li, Xueliang; Shaw, Ryan; Evans, Geoffrey M.; Stevenson, Paul

doi:10.1016/j.compchemeng.2009.08.004

Cited by 55 publications

(39 citation statements)

References 18 publications

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“…(40) is the analytical solution of the classical Ward and Tordai problem with the governing equation (18) in the sharp interface model, and it can be numerically solved with a given adsorption isotherm which relates the interface excess w 0 to w s [47].…”

Section: Adsorption Dynamicsmentioning

confidence: 99%

Phase-field modeling droplet dynamics with soluble surfactants

Liu

Zhang

2010

Journal of Computational Physics

125

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Section: Adsorption Dynamicsmentioning

confidence: 99%

Phase-field modeling droplet dynamics with soluble surfactants

Liu

Zhang

2010

Journal of Computational Physics

125

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“…The Ward-Tordai diffusion model [9], subsequently developed as asymptotic solutions by Fainerman et al [40], and presented as a numerical solution by Li et al [41], describes how the adsorption kinetics of a non-ionic soluble surfactant is governed by a twostep process: (1) the diffusion of molecules from the bulk solution to the subsurface (i.e., the layer immediately below the surface layer, at a thickness of only a few molecular diameters); (2) the molecular diffusion and adsorption from the subsurface layer to the interface [4,5]. Thus, when, as in the ''interfacial areaexpansion method", a new clean surface is created and presented to a surfactant solution, a finite time is required for the excess surface concentration C(t) to reach equilibrium with the bulk concentration, C 0 , and attain its equilibrium value, C eq .…”

Section: Dynamic Behavior: the Ward-tordai Diffusion Modelmentioning

confidence: 99%

New sensitive micro-measurements of dynamic surface tension and diffusion coefficients: Validated and tested for the adsorption of 1-Octanol at a microscopic air-water interface and its dissolution into water

Kinoshita

Parra

2017

Journal of Colloid and Interface Science

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Currently available dynamic surface tension (DST) measurement methods, such as Wilhelmy plate, droplet- or bubble-based methods, still have various experimental limitations such as the large size of the interface, convection in the solution, or a certain "dead time" at initial measurement. These limitations create inconsistencies for the kinetic analysis of surfactant adsorption/desorption, especially significant for ionic surfactants. Here, the "micropipette interfacial area-expansion method" was introduced and validated as a new DST measurement having a high enough sensitivity to detect diffusion controlled molecular adsorption at the air-water interfaces. To validate the new technique, the diffusion coefficient of 1-Octanol in water was investigated with existing models: the Ward Tordai model for the long time adsorption regime (1-100s), and the Langmuir and Frumkin adsorption isotherm models for surface excess concentration. We found that the measured diffusion coefficient of 1-Octanol, 7.2±0.8×10cm/s, showed excellent agreement with the result from an alternative method, "single microdroplet catching method", to measure the diffusion coefficient from diffusion-controlled microdroplet dissolution, 7.3±0.1×10cm/s. These new techniques for determining adsorption and diffusion coefficients can apply for a range of surface active molecules, especially the less-characterized ionic surfactants, and biological compounds such as lipids, peptides, and proteins.

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“…15,20 Tensiometry is widely used for both equilibrium and dynamic measurements but provides limited information on adsorption-desorption processes due to the predominance of diffusion at large scales. 13,[21][22][23] Deviations of the experimental data from the minimal diffusive-limited model introduced by Ward and Tordai are almost systematically observed, and attributed to curvature effects, [24][25][26][27] convective currents, 23,28,29 or adsorption barriers. 14,17 These adsorption barriers are revealed in the transfer-limited regimes which dominate at small dimensions 21,30 and in convective systems, 29,31 namely under the conditions relevant to emulsication or foaming.…”

Section: Introductionmentioning

confidence: 96%

Microfluidic Dynamic Interfacial Tensiometry (μDIT)

2014

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We designed, developed and characterized a microfluidic method for the measurement of surfactant adsorption kinetics via interfacial tensiometry on a microfluidic chip. The principle of the measurement is based on the deformability of droplets as a response to hydrodynamic forcing through a series of microfluidic expansions. We focus our analysis on one perfluoro surfactant molecule of practical interest for droplet-based microfluidic applications. We show that although the adsorption kinetics is much faster than the kinetics of the corresponding pendant drop experiment, our droplet-based microfluidic system has a sufficient time resolution to obtain quantitative measurement at the sub-second time-scale on nanoliter droplet volumes, leading to both a gain by a factor of ∼10 in time resolution and a downscaling of the measurement volumes by a factor of ∼1000 compared to standard techniques. Our approach provides new insight into the adsorption of surfactant molecules at liquid-liquid interfaces in a confined environment, relevant to emulsification, encapsulation and foaming, and the ability to measure adsorption and desorption rate constants.

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A simple numerical solution to the Ward–Tordai equation for the adsorption of non-ionic surfactants

Cited by 55 publications

References 18 publications

Phase-field modeling droplet dynamics with soluble surfactants

Phase-field modeling droplet dynamics with soluble surfactants

New sensitive micro-measurements of dynamic surface tension and diffusion coefficients: Validated and tested for the adsorption of 1-Octanol at a microscopic air-water interface and its dissolution into water

Microfluidic Dynamic Interfacial Tensiometry (μDIT)

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