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Keywords = Maxwell–Stefan theory

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15 pages, 1897 KiB  
Article
A Maxwell–Stefan Approach to Ion and Water Transport in a Reverse Electrodialysis Stack
by Joost Veerman
Processes 2024, 12(7), 1407; https://doi.org/10.3390/pr12071407 - 5 Jul 2024
Cited by 1 | Viewed by 2006
Abstract
Reverse electrodialysis (RED) is one of the methods able to generate energy from the salinity gradient between sea- and river water. The technique is based on the diffusion of ions through membranes that specifically allow either cations or anions to pass through. This [...] Read more.
Reverse electrodialysis (RED) is one of the methods able to generate energy from the salinity gradient between sea- and river water. The technique is based on the diffusion of ions through membranes that specifically allow either cations or anions to pass through. This ion current is converted into an external electric current at electrodes via suitable redox reactions. Seawater contains mainly eight different ions and the description of transport phenomena in membranes in classical terms of isolated species is not sufficient because the different particles have different velocities—in the same direction or opposite—in the same membrane. More realistic is the Maxwell–Stefan (MS) theory that takes all interactions between the different particles in account; however, such a model is complex and validation is difficult. Therefore, a simplified system is used with solely NaCl in solution, using only 9 diffusivities in the calculation. These values are estimated from the literature and are applied to an MS model of the RED process. Using experimental data of NaCl and water transport as well as power density, these diffusivities are adapted in the MS model. Reliable values for the diffusivities were obtained for the following three interactions: H2O–Na+, H2O–Cl and Na+–Cl. Full article
(This article belongs to the Section Chemical Processes and Systems)
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15 pages, 1901 KiB  
Article
Predicting the Water Sorption in ASDs
by Dominik Borrmann, Andreas Danzer and Gabriele Sadowski
Pharmaceutics 2022, 14(6), 1181; https://doi.org/10.3390/pharmaceutics14061181 - 31 May 2022
Cited by 7 | Viewed by 2773
Abstract
Water decreases the stability of amorphous solid dispersions (ASDs) and water sorption is, therefore, unwanted during ASD storage. This work suggests a methodology to predict the water-sorption isotherms and the water-sorption kinetics in amorphous pharmaceutical formulations like ASDs. We verified the validity of [...] Read more.
Water decreases the stability of amorphous solid dispersions (ASDs) and water sorption is, therefore, unwanted during ASD storage. This work suggests a methodology to predict the water-sorption isotherms and the water-sorption kinetics in amorphous pharmaceutical formulations like ASDs. We verified the validity of the proposed methodology by measuring and predicting the water-sorption curves in ASD films of polyvinylpyrrolidone-based polymers and of indomethacin. This way, the extent and the rate of water sorption in ASDs were predicted for drug loads of 0.2 and 0.5 as well as in the humidity range from 0 to 0.9 RH at 25 °C. The water-sorption isotherms and the water-sorption kinetics in the ASDs were predicted only based on the water-sorption isotherms and water-sorption kinetics in the neat polymer on the one hand and in the neat active pharmaceutical ingredient (API) on the other hand. The accurate prediction of water-sorption isotherms was ensured by combining the Perturbed-Chain Statistical Association Theory (PC-SAFT) with the Non-Equilibrium Thermodynamics of Glassy Polymers (NET-GP) approach. Water-sorption kinetics were predicted using Maxwell–Stefan diffusion coefficients of water in the ASDs. Full article
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18 pages, 1868 KiB  
Article
Water Sorption in Glassy Polyvinylpyrrolidone-Based Polymers
by Dominik Borrmann, Andreas Danzer and Gabriele Sadowski
Membranes 2022, 12(4), 434; https://doi.org/10.3390/membranes12040434 - 17 Apr 2022
Cited by 21 | Viewed by 4681
Abstract
Polyvinylpyrrolidone (PVP)-based polymers are excellent stabilizers for food supplements and pharmaceutical ingredients. However, they are highly hygroscopic. This study measured and modeled the water-sorption isotherms and water-sorption kinetics in thin PVP and PVP-co-vinyl acetate (PVPVA) films. The water sorption was measured at 25 [...] Read more.
Polyvinylpyrrolidone (PVP)-based polymers are excellent stabilizers for food supplements and pharmaceutical ingredients. However, they are highly hygroscopic. This study measured and modeled the water-sorption isotherms and water-sorption kinetics in thin PVP and PVP-co-vinyl acetate (PVPVA) films. The water sorption was measured at 25 °C from 0 to 0.9 RH, which comprised glassy and rubbery states of the polymer-water system. The sorption behavior of glassy polymers differs from that in the rubbery state. The perturbed-chain statistical associating fluid theory (PC-SAFT) accurately describes the water-sorption isotherms for rubbery polymers, whereas it was combined with the non-equilibrium thermodynamics of glassy polymers (NET-GP) approach to describe the water-sorption in the glassy polymers. Combined NET-GP and PC-SAFT modeling showed excellent agreement with the experimental data. Furthermore, the transitions between the PC-SAFT modeling with and without NET-GP were in reasonable agreement with the glass transition of the polymer-water systems. Furthermore, we obtained Fickian water diffusion coefficients in PVP and in PVPVA from the measured water-sorption kinetics over a broad range of humidities. Maxwell-Stefan and Fickian water diffusion coefficients yielded a non-monotonous water concentration dependency that could be described using the free-volume theory combined with PC-SAFT and NET-GP for calculating the free volume. Full article
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