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Journal ArticleDOI

On membrane diffusion with near-equilibrium reaction

01 Apr 1970-Chemical Engineering Science (Pergamon)-Vol. 25, Iss: 4, pp 665-683
TL;DR: In this paper, an analysis of the facilitated transport problem with steady diffusion through a finite membrane, accompanied by rapid and reversible, homogeneous chemical reaction is presented, where matched asymptotic expansions are used to analyze the structure of the diffusion field, which is shown to consist of an equilibrium core, together with boundary-layer reaction zones at the membrane boundaries.
About: This article is published in Chemical Engineering Science.The article was published on 1970-04-01 and is currently open access. It has received 62 citations till now. The article focuses on the topics: Molecular diffusion & Method of matched asymptotic expansions.
Citations
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Book ChapterDOI
01 Jan 2002
TL;DR: In this paper, the authors consider the problem of finding an analytical solution to the governing equations of a series of apparently unrelated problems, such as the plug flow reactor with diffusion, the stefan problem, and the shock wave in gases.
Abstract: This chapter explores various apparently unrelated problems and formulating them in the simplest form such that in most cases an analytical solution to the governing equations can be obtained. Lessons of general applicability are extracted from the solutions of the problems considered. The concept that the subjects of transport phenomena and of thermodynamics are strongly intertwined is strictly emphasized. All problems in engineering science are formulated on the basis of two types of equations: balance and constitutive. A balance equation can be written either for a quantity for which a general principle of conservation exists, or for a quantity for which no such principle exists provided its rate of generation is included in the balance equation. A constitutive equation is one that assigns the value of F ( X , t )—the flux of the quantity considered—in terms of C ( X , t )—the amount of the quantity considered per unit volume—so that the problem becomes a mathematically well posed one. The two types of equations are discussed by illustrating several classic problems such as the plug flow reactor with diffusion, shock waves in gases, and stefan problem.

240 citations

Journal ArticleDOI
TL;DR: In this article, the authors compare the theoretical predictions of a closed-and an open-system model for the evolution of pH and calcite-saturation state during the sequential oxidation of organic matter by O2, NO3−, and SO4=.

109 citations

Journal ArticleDOI
TL;DR: In this paper, the stagnant film model for the transport of CO2 across the air-sea interface has been re-examined, by incorporating the constraint of electroneutrality, equations are derived that govern the flux of the carbon containing species within the film.
Abstract: The stagnant film model for the transport of CO2 across the air-sea interface has been reexamined. By incorporating the constraint of electroneutrality, equations are derived that govern the flux of the carbon containing species within the film. Electroneutrality obviates the incorrect assumption of constant pH that is implicit in previous exchange calculations. Numerical results for typical ocean conditions indicate that for film thicknesses less than, say, 400μ. oceanic exchange is not influenced by the hydration/dehydration reactions of dissolved carbon dioxide. This conclusion is in substantial agreement with the approximate analysis of Bolin [1960]. However, if suitable catalysts are present in the ocean (there is recent evidence to suggest that this may be true [Berger and Libby, 1969]), the accelerated reactions are capable of augmenting the exchange rate by a considerable amount. The extent of this enhancement can be predicted by the model presented here.

92 citations

Journal ArticleDOI
TL;DR: In this article, an open-system diagenetic (transport) model is presented which accounts for the concurrent behavior of all the dissolved carbonate species (i.e., CO2(aq), HCO3−, and CO3=) as well as hydrogen and hydroxyl ions in the porewaters of marine sediments during the oxic and suboxic decay of organic-matter.

92 citations

References
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Book
01 Jan 1962

6,437 citations

Book
01 Jan 1975

2,966 citations

Journal ArticleDOI
TL;DR: In this article, it is shown that if the motion is to be exactly steady there is an integral condition, arising from the existence of viscous forces, which must be satisfied by the vorticity distribution no matter how small the viscosity may be.
Abstract: Frictionless flows with finite voticity are usually made determinate by the imposition of boundary conditions specifying the distribution of vorticity ‘at infinity’. No such boundary conditions are available in the case of flows with closed streamlines, and the velocity distributions in regions where viscous forces are small (the Reynolds number of the flow being assumed large) cannot be made determinate by considerations of the fluid as inviscid. It is shown that if the motion is to be exactly steady there is an integral condition, arising from the existence of viscous forces, which must be satisfied by the vorticity distribution no matter how small the viscosity may be. This condition states that the contribution from viscous forces to the rate of change of circulation round any streamline must be identically zero. (In cases in which the vortex lines are also closed, there is a similar condition concerning the circulation round vortex lines.)The inviscid flow equations are then combined with this integral condition in cases for which typical streamlines lie entirely in the region of small viscous forces. In two-dimensional closed flows, the vorticity is found to be uniform in a connected region of small viscous forces, with a value which remains to be determined—as is done explicitly in one simple case—by the condition that the viscous boundary layer surrounding this region must also be in steady motion. Analogous results are obtained for rotationally symmetric flows without azimuthal swirl, and for a certain class of flows with swirl having no interior boundary to the streamlines in an axial plane, the latter case requiring use of the fact that the vortex lines are also closed. In all these cases, the results are such that the Bernoulli constant, or ‘total head’, varies linearly with the appropriate stream function, and the effect of viscosity on the rate of change of vorticity at any point vanishes identically.

626 citations

Journal ArticleDOI
16 Jun 1967-Science
TL;DR: An immobilized film of an aqueous bicarbonate-carbonate solution was developed which was 4100 times more permeable to carbon dioxide than to oxygen and could be increased by addition to the film of catalysts for the hydrolysis of carbon dioxide.
Abstract: An immobilized film of an aqueous bicarbonate-carbonate solution was developed which was 4100 times more permeable to carbon dioxide than to oxygen. The carbon dioxide transport was reaction-rate limited, and thus it could be increased by addition to the film of catalysts for the hydrolysis of carbon dioxide.

236 citations