Vergleich einer gemessenen Abhängigkeit mit der Lösung der entsprechenden Integralgleichung durch Abschätzung der maximalen Abweichung ohne numerische Berechnung der Lösung

Vogel, J. J.

doi:10.1135/cccc19730979

Cited by 3 publications

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“…The numerical solution for the diffusion-controlled Langmuirian adsorption on the planar surface has been given by Miller and Lunkenheimer . The solvability of the integral equations stemming from the diffusion-controlled adsorption to the planar and spherical surfaces has been treated by Vogel in the case of Langmuirian and Temkin isotherms. The effect of Langmuirian adsorption on the electrode reactions has been thoroughly treated by Guidelli and Reinmuth and Balasubramanian. − A general method for treating the problems of diffusion-controlled adsorption kinetics was reported by Mysels and further elaborated by Frisch and Mysels .…”

Section: Introductionmentioning

confidence: 99%

Kinetics of Langmuirian Adsorption onto Planar, Spherical, and Cylindrical Surfaces

Kankare

Vinokurov

1999

Langmuir

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The kinetics of adsorption processes in solution onto adsorbents having different geometric shapes have been explored theoretically. The basic assumptions were (i) the diffusion of adsorbate in quiescent homogeneous solution with no convection, (ii) simple Langmuir-type adsorption kinetics and isotherm, (iii) the bulk concentration of the adsorbate in solution being sufficiently high to stay constant during the adsorption process, and (iv) the geometric shape of the adsorption surface being planar, spherical, or cylindrical. The diffusion equation with the time-dependent boundary conditions implied by the adsorption process was shown to lead to a nonlinear Volterra-type integral equation which is common for the three adsorbent geometries with a single definitive parameter, geometric factor, varying between 0 and 1. A numerical method was developed for solving this equation, and approximate analytical solutions were derived for the very beginning and the very end of the adsorption process. Implications of the results for the analytical methods based on the use of microparticles, such as various immunoassays, are discussed.

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