Page 602 - Bird R.B. Transport phenomena

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Chapter I

tions of Change for

Multicomponent Systems

§19.1 The equations of continuity for a multicomponent mixture
§19.2 Summary of the multicomponent equations of change
§19.3 Summary of the multicomponent fluxes
§19.4 Use of the equations of change for mixtures
§19.5 Dimensional analysis of the equations of change for binary mixtures

In Chapter 18, problems in diffusion were formulated by making shell mass balances
on one or more of the diffusing species. In this chapter we start by making a mass bal-
ance over an arbitrary differential fluid element to establish the equation of continuity
for the various species in a multicomponent mixture. Then insertion of mass flux ex-
pressions gives the diffusion equations in a variety of forms. These diffusion equations
can be used to set up any of the problems in Chapter 18 and more complicated ones as
well.
Then we summarize all of the equations of change for mixtures: the equations of
continuity, the equation of motion, and the equation of energy. These include the equa-
tions of change that were given in Chapters 3 and 11. Next we summarize the flux ex-
pressions for mixtures. All these equations are given in general form, although for
problem solving we generally use simplified versions of them.
The remainder of the chapter is devoted to analytical solutions and dimensional
analyses of mass transfer systems.

§19.1 THE EQUATIONS OF CONTINUITY FOR A
MULTICOMPONENT MIXTURE
In this section we apply the law of conservation of mass to each species a in a mixture,
where a = 1, 2, , . . . , IV. The system we consider is a volume element Ax Ay Az fixed in
3
space, through which the fluid mixture is flowing (see Fig. 3.1-1). Within this mixture, re-
actions among the various chemical species may be occurring, and we use the symbol r a
to indicate the rate at which species a is being produced, with dimensions of mass/vol-
ume • time.
The various contributions to the mass balance are
rate of increase of mass of {dp a/dt)kx Ay Az (19.1-1)
a in the volume element
rate of addition of mass of n ax\ x Ay Az (19.1-2)
a across face at x

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