Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach
A mathematical model of the anomalous diffusion of surfactant and the process of adsorption–desorption on an interface is analyzed using a fractional calculus approach. The model is based on time-fractional partial differential equations in the bulk phases and the corresponding time-fractional descr...
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MDPI AG
2025-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/7/408 |
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| author | Ivan Bazhlekov Emilia Bazhlekova |
| author_facet | Ivan Bazhlekov Emilia Bazhlekova |
| author_sort | Ivan Bazhlekov |
| collection | DOAJ |
| description | A mathematical model of the anomalous diffusion of surfactant and the process of adsorption–desorption on an interface is analyzed using a fractional calculus approach. The model is based on time-fractional partial differential equations in the bulk phases and the corresponding time-fractional description of the flux bulk–interface. The general case, when the surfactant is soluble in both phases, is considered under the assumption that the adsorption–desorption process is diffusion-controlled. Some of the most popular kinetic models of Henry, Langmuir, and Volmer are considered. Applying the Laplace transform, the partial differential model is transformed into a single multi-term time-fractional nonlinear ordinary differential equation for the surfactant concentration on the interface. Based on existing analytical solutions of linear time-fractional differential equations, the exact solution in the case of the Henry model is derived in terms of multinomial Mittag–Leffler functions, and its asymptotic behavior is studied. Further, the fractional differential model in the general nonlinear case is rewritten as an integral equation, which is a generalization of the well-known Ward–Tordai equation. For computer simulations, based on the obtained integral equation, a predictor–corrector numerical technique is developed. Numerical results are presented and analyzed. |
| format | Article |
| id | doaj-art-6172f2b8c73b40178bb655b9f89fc192 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-6172f2b8c73b40178bb655b9f89fc1922025-08-20T03:58:26ZengMDPI AGFractal and Fractional2504-31102025-06-019740810.3390/fractalfract9070408Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus ApproachIvan Bazhlekov0Emilia Bazhlekova1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl.8, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl.8, 1113 Sofia, BulgariaA mathematical model of the anomalous diffusion of surfactant and the process of adsorption–desorption on an interface is analyzed using a fractional calculus approach. The model is based on time-fractional partial differential equations in the bulk phases and the corresponding time-fractional description of the flux bulk–interface. The general case, when the surfactant is soluble in both phases, is considered under the assumption that the adsorption–desorption process is diffusion-controlled. Some of the most popular kinetic models of Henry, Langmuir, and Volmer are considered. Applying the Laplace transform, the partial differential model is transformed into a single multi-term time-fractional nonlinear ordinary differential equation for the surfactant concentration on the interface. Based on existing analytical solutions of linear time-fractional differential equations, the exact solution in the case of the Henry model is derived in terms of multinomial Mittag–Leffler functions, and its asymptotic behavior is studied. Further, the fractional differential model in the general nonlinear case is rewritten as an integral equation, which is a generalization of the well-known Ward–Tordai equation. For computer simulations, based on the obtained integral equation, a predictor–corrector numerical technique is developed. Numerical results are presented and analyzed.https://www.mdpi.com/2504-3110/9/7/408fractional calculusanomalous diffusioninterfacesurfactantadsorption–desorptionmultinomial Mittag–Leffler functions |
| spellingShingle | Ivan Bazhlekov Emilia Bazhlekova Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach Fractal and Fractional fractional calculus anomalous diffusion interface surfactant adsorption–desorption multinomial Mittag–Leffler functions |
| title | Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach |
| title_full | Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach |
| title_fullStr | Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach |
| title_full_unstemmed | Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach |
| title_short | Adsorption–Desorption at Anomalous Diffusion: Fractional Calculus Approach |
| title_sort | adsorption desorption at anomalous diffusion fractional calculus approach |
| topic | fractional calculus anomalous diffusion interface surfactant adsorption–desorption multinomial Mittag–Leffler functions |
| url | https://www.mdpi.com/2504-3110/9/7/408 |
| work_keys_str_mv | AT ivanbazhlekov adsorptiondesorptionatanomalousdiffusionfractionalcalculusapproach AT emiliabazhlekova adsorptiondesorptionatanomalousdiffusionfractionalcalculusapproach |