Flux expressions in multicomponent systems

Chemical separation problems can involve a binary or a multicomponent mixture. The flux expressions commonly used for multicomponent mixtures are considered here. 

The MaxweU-Stefan equations for describing the diffusion of gases in a multicomponent gas mixture have been developed from the kinetic theory of gases. A highly simplified illustration may be pursued as follows. Consider a system of a gas mixture of n species at constant T and P. Focus first on molecules of species i. The net force exerted on species i in the absence of any external forces is - Vpig / gmol of i. The net force exerted on species i per unit volume of the mixture is —(V/tjg) xig Ctg, where C,g is the total molar density of the gas mixture from equation (3.1.40) and an ideal gas mixture, the net force on species i per unit mixture volume is —xjg Ctg Rr V tn Pxtg), which is equivalent to 

these molecules of species i collide with molecules of species k, and momentum is transferred/lost by molecules of species i, resulting essentially in a frictional force on molecules of species i this loss of momentum is proportional to the difference in velocities between the two types of molecules. Further, the number of such collisions per unit time per unit volume of the gas mixture is proportional to Xig Xgg. At steady state, the force on molecules of species i per unit volume of the mixmre, RT VXjg, should be equal to the frictional force on molecules of species i created by the loss of momentum of species i via collisions with species k molecules, namely fikmkigkkg vig — Vkg), whereis a frictional coefficient of sorts of species i due to species k in the unit volume  

Configuration Experimentai correlation/anaiytical soiution Variabie range Reference Equation number(s) 

Spiral-wound membrane channel in reverse osmosis Hollow fiber membrane module Laminar tube-side flow Sh = = 0.065 Be Da Re = vdh/o) Schock and Miquel (1987) (3.1.170) 

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