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A Linear Diffusion Model of Adsorption Kinetics at Fluid/Fluid Interfaces.

Staszak M - J Surfactants Deterg (2016)

Bottom Line: The proposed approach assumes the near interface, adsorptive layer which is described based on Fick's transient diffusion law.The solution to the model contains the estimation of effective diffusivities with adsorptive layer thickness as well.The experimental results of toluene/water + sodium dodecyl sulfate are presented and used for model verification.

View Article: PubMed Central - PubMed

Affiliation: Institute of Chemical Technology and Engineering, Poznan University of Technology, Pl. Skłodowskiej-Curie 2, 60-965 Poznan, Poland.

ABSTRACT

The paper presents a new model for kinetically controlled adsorption at the fluid/fluid interface. The main purpose of the presented approach is to relate easy to estimate bulk surfactant concentration with Gibbs surface excess. Two adsorption isotherms are involved in the new model development: Frumkin and Szyszkowski isotherms. Additionally the Johannsen time profile of concentration in the adsorption layer is assumed and estimated in the model derivation. The proposed approach assumes the near interface, adsorptive layer which is described based on Fick's transient diffusion law. The solution to the model contains the estimation of effective diffusivities with adsorptive layer thickness as well. The experimental results of toluene/water + sodium dodecyl sulfate are presented and used for model verification.

No MeSH data available.


Sketch of modeling steps
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Fig2: Sketch of modeling steps

Mentions: Modeling of the experimental measurements requires estimation of the experimental (designated by subscript e) dynamic Gibbs surface excess values Γe and equivalent bulk phase concentrations ce. The procedure consists of several steps which are presented in Fig. 2. In the first step, the Szyszkowski or Frumkin isotherm parameters (ASz, BSz or AFr, A′, BFr) are estimated because they are needed for further calculations. In the sense of the proposed method, this is an initial approximation of their values that will be improved in the next steps. The calculation is based on the equilibrium surface tension data γ(cbulk). Estimation of isotherms parameters is easily done by the typical least squares method which is used to adjust the fitting line to the experimental data. For that purpose several numerical tools can be used. The author used genfit from Mathcad [34] and also NonlinearFit from Maple [35] software. In most cases a relatively accurate estimation to the initial values is required. Tools exist for estimating the isotherm parameters [36] which simplifies the numerical minimization process under altering initial values for a given interval. This approach guarantees finding the global minimum of the objective function determined by minimization of the least squares error.Fig. 2


A Linear Diffusion Model of Adsorption Kinetics at Fluid/Fluid Interfaces.

Staszak M - J Surfactants Deterg (2016)

Sketch of modeling steps
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4764644&req=5

Fig2: Sketch of modeling steps
Mentions: Modeling of the experimental measurements requires estimation of the experimental (designated by subscript e) dynamic Gibbs surface excess values Γe and equivalent bulk phase concentrations ce. The procedure consists of several steps which are presented in Fig. 2. In the first step, the Szyszkowski or Frumkin isotherm parameters (ASz, BSz or AFr, A′, BFr) are estimated because they are needed for further calculations. In the sense of the proposed method, this is an initial approximation of their values that will be improved in the next steps. The calculation is based on the equilibrium surface tension data γ(cbulk). Estimation of isotherms parameters is easily done by the typical least squares method which is used to adjust the fitting line to the experimental data. For that purpose several numerical tools can be used. The author used genfit from Mathcad [34] and also NonlinearFit from Maple [35] software. In most cases a relatively accurate estimation to the initial values is required. Tools exist for estimating the isotherm parameters [36] which simplifies the numerical minimization process under altering initial values for a given interval. This approach guarantees finding the global minimum of the objective function determined by minimization of the least squares error.Fig. 2

Bottom Line: The proposed approach assumes the near interface, adsorptive layer which is described based on Fick's transient diffusion law.The solution to the model contains the estimation of effective diffusivities with adsorptive layer thickness as well.The experimental results of toluene/water + sodium dodecyl sulfate are presented and used for model verification.

View Article: PubMed Central - PubMed

Affiliation: Institute of Chemical Technology and Engineering, Poznan University of Technology, Pl. Skłodowskiej-Curie 2, 60-965 Poznan, Poland.

ABSTRACT

The paper presents a new model for kinetically controlled adsorption at the fluid/fluid interface. The main purpose of the presented approach is to relate easy to estimate bulk surfactant concentration with Gibbs surface excess. Two adsorption isotherms are involved in the new model development: Frumkin and Szyszkowski isotherms. Additionally the Johannsen time profile of concentration in the adsorption layer is assumed and estimated in the model derivation. The proposed approach assumes the near interface, adsorptive layer which is described based on Fick's transient diffusion law. The solution to the model contains the estimation of effective diffusivities with adsorptive layer thickness as well. The experimental results of toluene/water + sodium dodecyl sulfate are presented and used for model verification.

No MeSH data available.