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Mafi A.,Amirkabir University of Technology | Raisi A.,Amirkabir University of Technology | Hatam M.,Amirkabir University of Technology | Hatam M.,Research Institute of Mechanics | Aroujalian A.,Amirkabir University of Technology
Desalination and Water Treatment | Year: 2014

Abstract: This work focuses on the modeling of mass transfer in the pure compound pervaporation through hydrophobic membranes. For this purpose, a mathematical predictive model was established based on the solution-diffusion mechanism. In the sorption step, the Flory–Huggins theory was applied to predict the amount of component absorbed into the membrane. In the diffusion step, the generalized Fick’s law with a constant diffusion coefficient and a concentration/temperature-dependent diffusion coefficient was employed to describe the component diffusion across the polydimethylsiloxane (PDMS) membrane. The concentration/temperature-dependent diffusion coefficient was determined using Duda’s free volume theory. In order to solve the resulting nonlinear transport equations, both finite difference (FD) and finite element (FE) methods were employed. The proposed model enables to predict the permeation flux as well as the concentration, temperature, and diffusion coefficient profiles inside the membrane. The model was then validated using the experimental data obtained from the pervaporative process of pure substance with the PDMS membrane. The results showed that although both FD and FE approaches were able to solve the dominant equations with appropriate accuracy. The modeling case II was capable of predicting the permeation flux for systems of pure ethanol and isobutanol, respectively. Finally, the effect of feed temperature on the permeation flux was investigated. © 2013, Balaban Desalination Publications. All rights reserved.


Mafi A.,Amirkabir University of Technology | Raisi A.,Amirkabir University of Technology | Hatam M.,Amirkabir University of Technology | Hatam M.,Research Institute of Mechanics | Aroujalian A.,Amirkabir University of Technology
Journal of Applied Polymer Science | Year: 2014

In this work, free volume theories are coupled with a thermodynamic model and generalized Fick's law to develop a mass transfer model based on solution-diffusion mechanism for pervaporation process with a hydrophobic polymeric membrane. The Wesselingh, Fujita and Vrentas-Duda's theories are used to calculate concentration-dependent diffusion coefficient of permeants inside polydimethylsiloxane membrane. The sorption and pervaporation experiments on aqueous ethanol solutions are performed to validate the sorption and pervaporation models. The results reveal that the proposed models are able to predict influences of feed concentration and temperature as well as permeate-side pressure on partial fluxes through the membrane. The comparative investigation indicated that Wesselingh's free volume theory underestimated the diffusion coefficients inside the membrane and the accuracy of the model used this theory is very low for prediction of the permeation flux. Generally, Fujita and Vrentas-Duda's theories are found to be much more accurate especially for dilute aqueous feed solutions. © 2014 Wiley Periodicals, Inc.


Afanas'eva D.A.,Moscow State University | Tsaturyan A.K.,Research Institute of Mechanics
Biophysics | Year: 2010

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. Muscle is modeled as an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. There are two types of shear waves in an infinite medium. Waves of the second type (transverse) propagate without decay even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer was investigated numerically. The values of the problem parameters are found for which one can easily estimate the active tension (or muscle tone) from the characteristics of standing waves. This value is informative for diagnostics of the muscle state. © 2010 Pleiades Publishing, Ltd.

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