Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes
Nanoporous membranes are heterogeneous structures, with heterogeneity manifesting at the microscale. In examining particle transport through such media, it has been observed that this transport deviates from classical diffusion, as described by Fick’s second law. Moreover, the classical model is phy...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Membranes |
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| Online Access: | https://www.mdpi.com/2077-0375/15/1/11 |
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| author | Slobodanka Galovic Milena Čukić Dalibor Chevizovich |
| author_facet | Slobodanka Galovic Milena Čukić Dalibor Chevizovich |
| author_sort | Slobodanka Galovic |
| collection | DOAJ |
| description | Nanoporous membranes are heterogeneous structures, with heterogeneity manifesting at the microscale. In examining particle transport through such media, it has been observed that this transport deviates from classical diffusion, as described by Fick’s second law. Moreover, the classical model is physically unsustainable, as it is non-causal and predicts an infinite speed of concentration perturbation propagation through a substantial medium. In this work, we have derived two causal models as extensions of Fick’s second law, where causality is linked to the effects of inertial memory in the nanoporous membrane. The results of the derived models have been compared with each other and with those obtained from the classical model. It has been demonstrated that both causal models, one with exponentially fading inertial memory and the other with power-law fading memory, predict that the concentration perturbation propagates as a damped wave, leading to an increased time required for the cumulative amount of molecules passing through the membrane to reach a steady state compared to the classical model. The power-law fading memory model predicts a longer time required to achieve a stationary state. These findings have significant implications for understanding cell physiology, developing drug delivery systems, and designing nanoporous membranes for various applications. |
| format | Article |
| id | doaj-art-3038468849904ef78de687114a15a55d |
| institution | Kabale University |
| issn | 2077-0375 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Membranes |
| spelling | doaj-art-3038468849904ef78de687114a15a55d2025-01-24T13:41:00ZengMDPI AGMembranes2077-03752025-01-011511110.3390/membranes15010011Inertial Memory Effects in Molecular Transport Across Nanoporous MembranesSlobodanka Galovic0Milena Čukić1Dalibor Chevizovich2Vinca Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovica Alasa 12-14, P.O. Box 522, 11001 Belgrade, SerbiaEmpa, Swiss Federal Institute for Materials Science and Technology, Laboratory for Biomimetic Membranes and Textiles, Lerchenfeldstrasse 5, 9014 St. Gallen, SwitzerlandVinca Institute of Nuclear Sciences-National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovica Alasa 12-14, P.O. Box 522, 11001 Belgrade, SerbiaNanoporous membranes are heterogeneous structures, with heterogeneity manifesting at the microscale. In examining particle transport through such media, it has been observed that this transport deviates from classical diffusion, as described by Fick’s second law. Moreover, the classical model is physically unsustainable, as it is non-causal and predicts an infinite speed of concentration perturbation propagation through a substantial medium. In this work, we have derived two causal models as extensions of Fick’s second law, where causality is linked to the effects of inertial memory in the nanoporous membrane. The results of the derived models have been compared with each other and with those obtained from the classical model. It has been demonstrated that both causal models, one with exponentially fading inertial memory and the other with power-law fading memory, predict that the concentration perturbation propagates as a damped wave, leading to an increased time required for the cumulative amount of molecules passing through the membrane to reach a steady state compared to the classical model. The power-law fading memory model predicts a longer time required to achieve a stationary state. These findings have significant implications for understanding cell physiology, developing drug delivery systems, and designing nanoporous membranes for various applications.https://www.mdpi.com/2077-0375/15/1/11nanoporous membranesparticle transportnon-Fickian’s modelsinertial memoryfractional modelhyperbolic model |
| spellingShingle | Slobodanka Galovic Milena Čukić Dalibor Chevizovich Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes Membranes nanoporous membranes particle transport non-Fickian’s models inertial memory fractional model hyperbolic model |
| title | Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes |
| title_full | Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes |
| title_fullStr | Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes |
| title_full_unstemmed | Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes |
| title_short | Inertial Memory Effects in Molecular Transport Across Nanoporous Membranes |
| title_sort | inertial memory effects in molecular transport across nanoporous membranes |
| topic | nanoporous membranes particle transport non-Fickian’s models inertial memory fractional model hyperbolic model |
| url | https://www.mdpi.com/2077-0375/15/1/11 |
| work_keys_str_mv | AT slobodankagalovic inertialmemoryeffectsinmoleculartransportacrossnanoporousmembranes AT milenacukic inertialmemoryeffectsinmoleculartransportacrossnanoporousmembranes AT daliborchevizovich inertialmemoryeffectsinmoleculartransportacrossnanoporousmembranes |