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Mass transfer across a nonequilibrium interface
Author(s) -
Dang ViDuong,
Gill William N.
Publication year - 1970
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690160518
Subject(s) - non equilibrium thermodynamics , mass transfer , thermodynamics , function (biology) , chemistry , intersection (aeronautics) , steady state (chemistry) , transfer (computing) , physics , convection , evolutionary biology , parallel computing , computer science , engineering , biology , aerospace engineering
The problem of mass transfer with nonequilibrium at, and significant convection across, the interface has been studied by the method of matched asymptotic expansions. The inner solution for small values of t or z / U m was found in terms of f k functions which were obtained in closed analytical form. The outer solution for large values of t or z / U m was found in terms of g k functions which had to be determined numerically. With these solutions, calculation of concentratration distributions or instantaneous rates of mass transfer is straightforward, but determination of the total amount of mass transfer as a function of time is complicated by the lack of an intersection wherein the inner and outer solutions overlap and converge. To avoid the need for graphical interpolation and integration of the interfacial concentration as a function of time to obtain the total mass transferred, the constant of integration M 1 is found to be (−kγ \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt \pi $\end{document} /2 h ) by assuming that the ratio of mass transferred with an equilibrium interface to that with a nonequilibrium interface is independent of whether or not V y convection is negligible in the system as t → ∞. The effect of a nonequilibrium interface is greatest for small t in unsteady systems and z / U m in steady state systems. This occurs because the departure from their equilibrium values of the interfacial concentrations of the phases in contact is greatest when they are first brought into contact. The larger the interfacial mass transfer coefficient α, the smaller is the time required for the interfacial concentrations to achieve their equilibrium values. Other things being equal, the rate of mass transfer is greatest when the driving force x A *‐ x A 0is greatest. Since the departure from equilibrium at the interface is greatest for small values of time, it follows that nonequilibrium interfacial phenomena can be observed most easily in systems where the rate of mass transfer is high. This is also the case when one cannot neglect the effect of finite velocity at the interface which is shown in the present work to be a significant effect. The method of analysis can be used to study a variety of problems in addition to the specific system considered here. In particular, both batch and flow reverse osmosis problems can be attacked by the present approach.