Forced and natural convective mass transfer in multicomponent gaseous mixtures

Abstract

The use of the Chilton-Colburn analogy to obtain an effective film thickness over which the Stefan-Maxwell equations can be integrated was confirmed for binary mixtures and found opplicoble for ternary, quaternary, and presumably higher order mixtures under conditions of nonequimolal counterdiffusion in a differential convective flow system. A method of averaging binary diffusivities was developed for use in computing the Schmidt number in these multicomponent systems. It was also found necessary to modify the usual Shenvood number, if there was a large molecular weight c h n g e across the diffusion barrier when the Chilton-Colburn analogy was employed.One of the most dacult current problems in chemical engineering involves mass transfer in multicomponent gaseous mixtures under conditions of convective flow. For many years the concept of a film resistance to diffusion, originally proposed by Noyes and Whitney ( 1 ) and subsequently extended by Nernst ( 2 ) , was sufficient for most applications involving systems with two components or one diffusing component in a mixture of nondiffusing components ( 3 ) . Whitman ( 4 ) proposed the additive resistances of these films, and Fischbeck (5) and Tu et al. (6) extended their utility to interfaces at which a chemical reaction is occurrin However, Bischoff and Froment (7) reaction and kinetic resistances for real systems without the use of computational equipment. In recent years the penetration theory of Higbie ( 8 ) , with suitable modifications, has been gaining in popularity (9 to 1 2 ) , and Sherwood et al. have recently suggested turbulent film (13, 1 4 ) and parallel eddy and molecular diffusion ( 1 5 ) models. However, the film concept is still widely used industrially and is quite satisfactory for many applications.The use of analogies between momentum, heat, and mass transfer is especially he1 ful in defining a resistance ject is by Sherwood ( 1 6 ) . However, if these analogies are to be employed with the kinetic theory of gases to solve multicomponent diffusion problems, a model such,as eff ective f i l m , surface renewal, etc., must be employed. In addition, multicomponent systems present problems, because the analogies between momentum and heat transfer no longer bear a direct similarity with mass transfer. The diffusion rates of various components in a mixture are not necessarily directly related to the heat and momentum transport rates. For instance, the diffusion rates of a given component, or of the mixture as a whole, can vary in both sign and magnitude under conditions where the heat or momentum transfer is relatively invariant. Ackerman (1 7) first reported this difficult and showed how total heat ponent, as well as by the transport parameters of the bulk stream. Mickley et al.( 1 8 ) extended this concept to the case where the flow to or from an interface was essentially independent of bulk stream conditions. Such a situation can occur, for instance, in transpiration or ablative coolhave pointed out t f e difficulty of treating simultaneous to ma...

A review on the methods of preparation of elemental boron

“…This is majorly due to the significance of diffusion resistance in the parallel flow reactor. In this CVD reactor, diffusion of BCl 3 to the heated substrate surface plays an important role on the deposition rate; even at higher temperatures, a larger amount of BCl 3 is converted into BHCl 2 in the gas phase within the thermal boundary layer adjacent to the substrate, while such transport effects are minimized in the impinging jet reactors, which results in the high fractional conversion of BCl 3 to B than that of BCl 3 to BHCl 2 .…”

Gas Flow Pattern and Mass Transfer Analysis in a Horizontal Flow Reactor for Chemical Vapor Deposition

“…When combined flow is fully developed 3u/Oz = O, 3v/Oz = 0, and Ow/Oz = 0 [19] dimensionless conservation equations can be stated as [20] and [21] is known as the vorticity equation, that is [26] ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address.…”

Multicomponent mass transfer in turbulent flow

“…The determinant method of Toor (6) is used to uncouple the multicomponent time-averaged equations of convective (1) This yields a set of n -1 independent equations coupled by the cross-diffusion coefficients ( D + e ) i j where i # j.…”

“…Equation (1) has been solved by Toor for the ternary case where the eddy diffusivity is unimportant. This method is now extended to include both molecular and turbulent diffusivities.…”

“…Three models were proposed: film, modified Prandtl-Taylor, and Chilton-Colburn. The Chilton-Colburn analogy was modified by Carleton and Oxley (1) by correcting the Sherwood number to reflect the effect of a large molecular weight change across the diffusion barrier. Toor later published two methods for linearizing the diffusion equations in a multicomponent system to a set of equivalent binary equations.…”