Título:
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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
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Autor/a:
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Benzal, Ma. Graciela; Kumar, Aditya; Sastre Requena, Ana María; Delshams Valdés, Amadeu
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
Abstract:
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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. |
Abstract:
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Peer Reviewed |
Materia(s):
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-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 |
Derechos:
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Tipo de documento:
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Artículo |
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