By Endre Nagy
With an in depth research of the mass delivery via membrane layers and its impact on varied separation techniques, this publication offers a accomplished examine the theoretical and useful facets of membrane delivery houses and features. simple equations for each membrane are supplied to foretell the mass move cost, the focus distribution, the convective pace, the separation potency, and the impact of chemical or biochemical response considering the heterogeneity of the membrane layer to assist higher comprehend the mechanisms of the separation techniques. The reader should be capable of describe membrane separation strategies and the membrane reactors in addition to pick out the main compatible membrane constitution for separation and for membrane reactor. Containing distinct dialogue of the newest ends up in shipping tactics and separation procedures, this publication is key for chemistry scholars and practitioners of chemical engineering and method engineering.
- Detailed survey of the theoretical and sensible facets of each membrane method with particular equations
- Practical examples mentioned intimately with transparent steps
- Will help in making plans and instruction of extra effective membrane constitution separation
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Extra resources for Basic equations of the mass transport through a membrane layer
89, 143À151. , and Stephan, W. (1994b) A generalized solution-diffusion model of the pervaporation process through composite membrane, Part II. Concentration polarization, coupled diffusion and the influence of the porous layer. J. Membr. Sci. 89, 153À169. L. (2005) Kinetic modeling of partial oxidation of methane in an oxygen permeable membrane reactor. Chem. Eng. Res. Design 82, 177À186. , and Uchytil, P. (2003) Description of binary liquid mixtures transport through non-porous membrane by modified MaxwellÀStefan equations.
Stokes’ law was used to describe the drag on the moving solute molecule. Accordingly, the diffusion coefficient (DAB, m2/s) can be estimated by DAB 5 kT 6πrs η ð2:14Þ where k is Boltzmann’s constant; rs is the radius of solute (m); and η is the solute dynamic viscosity (cP). The equation is a good approximation for large solutes with radii greater than ˚ (Baker, 2004). But, as the solute becomes smaller, the approximation of 5À10 A the solvent as a continuous fluid becomes less valid. Thus, the above equation was modified by assuming that all molecules are alike and arranged in a cubic lattice, and by expressing the molecular radius in therms of molar volume (Geankoplis, 2003): DAB 5 9:96 3 10216 T ð2:15Þ 1=3 ηVA where T is temperature (K); η is viscosity of solution (Pa s); and VA is the solute molar volume at its normal boiling point (m3 kg mol).
Besides these special cases, the mass transport through a membrane layer through plate-and-frame, tubular, and spiral-wound modules should be regarded as that through a plane interface. Basic Equations of the Mass Transport through a Membrane Layer. 00003-X © 2012 Elsevier Inc. All rights reserved. 1). When the value of cÃ . CδÃ ; then the diffusion process occurs from one side of the membrane to the other side due to the driving force existing in the membrane layer. For a longer time, a steady state is reached in which the concentration in the membrane remains constant.