Simulation of non-linear flow density in transition state from the mathematical model of the diffusion of metal anions through a flat sheet supported liquid membrane
A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick’s second law. From this model, and from Fick’s first law, the flow density is derived as a non-linear concentration gradient. Both...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/924 |
| Acceso en línea: | https://hdl.handle.net/2117/924 |
| Access Level: | acceso abierto |
| Palabra clave: | Parabolic partial differential equations Fluid mechanics Natural sciences Diffusion of metal anions Non-linear flow density Equacions en derivades parcials Difusió Convecció (Física) Fluxos (Sistemes dinàmics diferenciables) Fisiologia Medicina Classificació AMS::76 Fluid mechanics::76R Diffusion and convection Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems Classificació AMS::76 Fluid mechanics::76S05 Flows in porous media filtration seepage Classificació AMS::92 Biology and other natural sciences::92C Physiological, cellular and medical topics |
| Sumario: | A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick’s second law. From this model, and from Fick’s first law, the flow density is derived as a non-linear concentration gradient. Both expressions, concentration and flow density, depend on the thickness of the membrane and on time. Since the rate constant plays an important role in the model, it is considered as the parameter that controls the system and an equation for it is obtained. This equation explains the velocity of the co-transport process. The proposed model takes into account the species co-transported together with the metal ions. An equation for the number of moles of this species is obtained as a function of the metal species. The concentration gradient of this species explains the behaviour of pH in the feed phase during the process. The model is tested against experimental data corresponding to the transport of metal anions in acidic solution and it is shown that the co-transport process is reproduced with high accuracy. |
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