Abstract
Network and numerical analysis of permeation through a membrane under non-stationary, stationary, and pseudo-stationary conditions is described. A compartmentalized membrane system (feed solution|membrane|stripping solution) was represented by a linear network of capacitances, diffusion, and sorption/desorption graphs. Reticulation degree of diffusion layers sufficient for quantitative modeling of the diffusion through a homogeneous membrane was estimated. It was found that for membranes of the thickness from 0.001 cm to 0.1 cm and the diffusion coefficients from 1 × 10−7 cm2 s−1 to 1 × 10−5 cm2 s−1, the membrane (or other diffusion layer) partition into ten slices leads to simulated time lags and stationary fluxes differing from the theoretical ones by less than 0.5 % and 1 %, respectively. Extended model with two unstirred interfacial layers and the feed and stripping solution of finite volumes was applied to characterize the effects caused by possible membrane heterogeneity.
[1] Baird, J. K., & Frieden, R. W. (1987). Rigorous theory of the diaphragm cell when the diffusion coefficient depends upon concentration. Journal of Physical Chemistry, 91, 3920–3923. DOI: 10.1021/j100298a038. http://dx.doi.org/10.1021/j100298a03810.1021/j100298a038Search in Google Scholar
[2] Castilla, J., García-Hernández, M. T., Hayas, A., & Horno, J. (1996). Simulation of non-stationary electrodiffusion processes in charged membranes by the network approach. Journal of Membrane Science, 116, 107–116. DOI: 10.1016/0376-7388(96)00031-2. http://dx.doi.org/10.1016/0376-7388(96)00031-210.1016/0376-7388(96)00031-2Search in Google Scholar
[3] Castilla, J., García-Hernández, M. T., Hayas, A., & Horno, J. (1997a). A network approach to analysis of nonsteady-state facilitated ionic diffusion processes. Journal of Membrane Science, 136, 101–109. DOI: 10.1016/s0376-7388(97)00157-9. http://dx.doi.org/10.1016/S0376-7388(97)00157-910.1016/S0376-7388(97)00157-9Search in Google Scholar
[4] Castilla, J., García-Hernández, M. T., Moya, A. A., Hayas, A., & Horno, J. (1997b). A study of the transport of ions against their concentration gradient across ion-exchange membranes using the network method. Journal of Membrane Science, 130, 183–192. DOI: 10.1016/s0376-7388(97)00022-7. http://dx.doi.org/10.1016/S0376-7388(97)00022-710.1016/S0376-7388(97)00022-7Search in Google Scholar
[5] Ceynowa, J., & Adamczak, P. (2001). Analysis of the bond graph network model of membrane reactor for olive oil hydrolysis. Separation and Purification Technology, 22–23, 443–449. DOI: 10.1016/s1383-5866(00)00173-8. http://dx.doi.org/10.1016/S1383-5866(00)00173-810.1016/S1383-5866(00)00173-8Search in Google Scholar
[6] Couenne, F., Jallut, C., Maschke, B., Tayakout, M., & Breedveld, P. (2008). Structured modeling for processes: A thermodynamical network theory. Computers & Chemical Engineering, 32, 1120–1134. DOI: 1016/j.compchemeng.2007.04.012. http://dx.doi.org/10.1016/j.compchemeng.2007.04.01210.1016/j.compchemeng.2007.04.012Search in Google Scholar
[7] Crank, J. (1956). The mathematics of diffusion. Oxford, UK: Clarendon Press. Search in Google Scholar
[8] González-Caballero, F., González-Fernández, C. F., Horno Montijano, J., & Barrú, A. H. (1988). On the simulation of nonstationary diffusion through homogeneous membranes using network thermodynamics. Zeitschrift fur Physikalische Chemie-Leipzig, 269, 1137–1146. 10.1515/zpch-1988-269126Search in Google Scholar
[9] Horno, J., González-Fernández, C. F., Hayas, A., & González-Caballero, F. (1989). Application of network thermodynamics to the computer modelling of nonstationary diffusion through heterogeneous membranes. Journal of Membrane Science, 42, 1–12. DOI: 10.1016/s0376-7388(00)82361-3. http://dx.doi.org/10.1016/S0376-7388(00)82361-310.1016/S0376-7388(00)82361-3Search in Google Scholar
[10] Horno, J., González-Caballero, F., Hayas, A., & González-Fernández, C. F. (1990). The effect of previous convective flux on the nonstationary diffusion through membranes. Network simulation. Journal of Membrane Science, 48, 67–77. DOI: 10.1016/s0376-7388(00)80796-6. http://dx.doi.org/10.1016/S0376-7388(00)80796-610.1016/S0376-7388(00)80796-6Search in Google Scholar
[11] Horno, J., & Castilla, J. (1994). Application of network thermodynamics to the computer simulation of non-stationary ionic transport in membranes. Journal of Membrane Science, 90, 173–181. DOI: 10.1016/0376-7388(94)80044-8. http://dx.doi.org/10.1016/0376-7388(94)80044-810.1016/0376-7388(94)80044-8Search in Google Scholar
[12] Horno, J., González-Fernández, C. F., & Hayas, A. (1995). The network method for solutions of oscillating reaction-diffusion systems. Journal of Computational Physics, 118, 310–319. DOI: 1006/jcph.1995.1101. http://dx.doi.org/10.1006/jcph.1995.110110.1006/jcph.1995.1101Search in Google Scholar
[13] Imai, Y. (1996). Network thermodynamics: analysis and synthesis of membrane transport system. Japanese Journal of Physiology, 46, 187–199. DOI: 10.2170/jjphysiol.46.187. http://dx.doi.org/10.2170/jjphysiol.46.18710.2170/jjphysiol.46.187Search in Google Scholar
[14] Kislik, V. S. (2010). Bulk hybrid liquid membrane with organic water-immiscible carriers: Application to chemical, biochemical, pharmaceutical, and gas separations. In V. S. Kislik (Ed.), Liquid membranes. Principles and applications in chemical separations and wastewater treatment (Chapter 5, pp. 201–275). Amsterdam, The Netherlands: Elsevier. DOI: 10.1016/b978-0-444-53218-3.00005-2. 10.1016/B978-0-444-53218-3.00005-2Search in Google Scholar
[15] Leo, A., Hansch, C., & Elkins, D. (1971). Partition coefficients and their uses. Chemical Reviews, 71, 525–616. DOI:10.1021/cr60274a001. http://dx.doi.org/10.1021/cr60274a00110.1021/cr60274a001Search in Google Scholar
[16] Macey, R., & Oster, G. (2001). Berkeley Madonna: Modeling and analysis of dynamic systems (v.8.0.3) [computer software]. Berkeley, CA, USA: University of California. http://www.berkeleymadonna.com/ Search in Google Scholar
[17] Mikulecky, D. C. (2001). Network thermodynamics and complexity: A transition to relational systems theory. Computers & Chemistry, 25, 369–392. DOI: 10.1016/s0097-8485(01)00072-9. http://dx.doi.org/10.1016/S0097-8485(01)00072-910.1016/S0097-8485(01)00072-9Search in Google Scholar
[18] Moya, A. A., & Horno, J. (1999). Application of the network simulation method to ionic transport in ion-exchange membranes including diffuse double-layer effects. Journal of Physical Chemistry B, 103, 10791–10799. DOI: 10.1021/jp992701s. http://dx.doi.org/10.1021/jp992701s10.1021/jp992701sSearch in Google Scholar
[19] Moya, A. A., & Horno, J. (2001). Stationary electrodiffusion-adsorption processes in membranes including diffuse double layer effects: A network approach. Journal of Membrane Science, 194, 103–115. DOI: 10.1016/s0376-7388(01)00528-2. http://dx.doi.org/10.1016/S0376-7388(01)00528-210.1016/S0376-7388(01)00528-2Search in Google Scholar
[20] Oster, G., Perelson, A., & Katchalsky, A. (1971). Network thermodynamics. Nature, 234, 393–399. DOI: 10.1038/234393a0. http://dx.doi.org/10.1038/234393a010.1038/234393a0Search in Google Scholar
[21] Oster, G. F., Perelson, A. S., & Katchalsky, A. (1973). Network thermodynamics: dynamic modelling of biophysical systems. Quarterly Reviews of Biophysics, 6, 1–134. DOI: 10.1017/s0033583500000081. http://dx.doi.org/10.1017/S003358350000008110.1017/S0033583500000081Search in Google Scholar
[22] Pabby, A. K., Rizvi, S. S. H., & Sastre Requena, A. M. (Eds.) (2009). Handbook of membrane separations: Chemical, pharmaceutical, food, and biotechnological applications. Boca Raton, FL, USA: CRC Press. Search in Google Scholar
[23] Paterson, R. (1988). Practical application of network thermodynamics and bond graph methods to the simulation of membrane processes. Swiss Chemistry, 10, 17–20. Search in Google Scholar
[24] Paterson, R. (1989). Simulation and design of membrane processes using network thermodynamics. In A. M. Mika, & T. Z. Winnicki (Eds.), Advances in membrane phenomena and processes (pp. 94–109). Wrocław, Poland: Wrocław Technical University Press. Search in Google Scholar
[25] Paterson, R., & Lutfullah (1985). Simulation of transport processes using bond graph methods: I. Gas diffusion through planar membranes and systems obeying Fick’s laws. Journal of Membrane Science, 23, 59–70. DOI: 10.1016/s0376-7388(00)83134-8. http://dx.doi.org/10.1016/S0376-7388(00)83134-810.1016/S0376-7388(00)83134-8Search in Google Scholar
[26] Peacocke, A. R. (1989). An introduction to the physical chemistry of biological organisation. Oxford, UK: Clarendon Press. Search in Google Scholar
[27] Peusner, L. (1986). Studies in network thermodynamics. Amsterdam, The Netherlands: Elsevier. Search in Google Scholar
[28] Schnakenberg, J. (1977). Thermodynamic network analysis of biological systems. Berlin, Germany: Springer. http://dx.doi.org/10.1007/978-3-642-96394-010.1007/978-3-642-96394-0Search in Google Scholar
[29] Simon, A. M., Doran, P., & Paterson, R. (1996). Assessment of diffusion coupling effects in membrane separation. Part I. Network thermodynamics modelling. Journal of Membrane Science, 109, 231–246. DOI: 10.1016/0376-7388(95)00192-1. http://dx.doi.org/10.1016/0376-7388(95)00192-110.1016/0376-7388(95)00192-1Search in Google Scholar
[30] Srivastava, R. C., & Mehta, A. (1980). Network thermodynamic modelling of anisotropic membranes. Journal of Non-Equilibrium Thermodynamics, 5, 255–258. DOI: 10.1515/jnet.1980.5.4.255. http://dx.doi.org/10.1515/jnet.1980.5.4.25510.1515/jnet.1980.5.4.255Search in Google Scholar
[31] Wódzki, R. (1994). Dyfuzyjno-wymienny transport jonów w modelach ścian komórkowych (Exchange-diffusion of ions in cell wall mimicking synthetic membranes). Toruń, Poland: Nicolaus Copernicus University Press. Search in Google Scholar
[32] Wódzki, R., & Sionkowski, G. (1995). Exchange diffusion transport of ions in liquid membranes. Part IV. Thermodynamic network analysis of nonstationary transport of divalent ions. Polish Journal of Chemistry, 69, 407–422. Search in Google Scholar
[33] Wódzki, R., & Szczepański, P. (2001). Integrated process of Donnan dialysis and pertraction in a multimembrane hybrid system. Separation and Purification Technology, 22–23, 697–706. DOI: 10.1016/s1383-5866(00)00186-6. http://dx.doi.org/10.1016/S1383-5866(00)00186-610.1016/S1383-5866(00)00186-6Search in Google Scholar
[34] Wódzki, R., & Szczepański, P. (2002). Integrated hybrid membrane systems—membrane extraction and pertraction coupled to a pervaporation process. Journal of Membrane Science, 197, 297–308. DOI: 10.1016/s0376-7388(01)00640-8. http://dx.doi.org/10.1016/S0376-7388(01)00640-810.1016/S0376-7388(01)00640-8Search in Google Scholar
[35] Wódzki, R., Szczepańska, G., & Szczepański, P. (2004). Unsteady state pertraction and separation of cations in a liquid membrane system: Simple network and numerical model of competitive M2+ /H+ counter-transport. Separation and Purification Technology, 36, 1–16 DOI: 10.1016/s1383-5866(03)00146-1. http://dx.doi.org/10.1016/S1383-5866(03)00146-110.1016/S1383-5866(03)00146-1Search in Google Scholar
© 2012 Institute of Chemistry, Slovak Academy of Sciences
Articles in the same Issue
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Articles in the same Issue
- Immobilization in biotechnology and biorecognition: from macro- to nanoscale systems
- Bond-graph description and simulation of membrane processes: Permeation in a compartmental membrane system
- Design simulations for a biogas purification process using aqueous amine solutions
- Experimental and numerical investigation of pressure drop coefficient and static pressure difference in a tangential inlet cyclone separator
- Trace elements in Variegated Bolete (Suillus variegatus) fungi
- N,N′-methylenedipyridinium Pt(II) and Pt(IV) hybrid salts: synthesis, crystal and molecular structures of [(C5H5N)2CH2] · [PtCl4] and [(C5H5N)2CH2] · [PtCl6]
- Formation of membranes based on polyacrylonitrile and butadiene-acrylonitrile elastomer in the presence of copper ions
- One-step synthesis of solid sulfonic acid catalyst and its application in the acetalization of glycerol: crystal structure of cis-5-hydroxy-2-phenyl-1,3-dioxane trimer
- Mechanistic insights into the reaction of CF3CCl3 with SO3: Theory and experiment
- Near-infrared imaging for quantitative analysis of active component in counterfeit dimethomorph using partial least squares regression
- Corrosion of titanium diboride in molten FLiNaK(eut)
- Domino synthesis of novel series of 4-substituted 5-thioxo-1,2,4-triazolidin-3-one derivatives
- Erratum to: “Nguyen Hoang Loc, Nguyen Thanh Giang: Effects of elicitors on the enhancement of asiaticoside biosynthesis in cell cultures of centella (Centella asiatica L. Urban)”, Chemical Papers 66 (7) 642–648 (2012)