Page 692 - Bird R.B. Transport phenomena

672 Chapter 22 Interphase Transport in Nonisothermal Mixtures

Schmidt numbers for a number of relatively simple systems. We emphasize the different
behavior of systems with fluid-fluid and solid-fluid interfaces.
In §22.3 we show how dimensional analysis leads to predictions involving the Sher-
wood number (Sh) and the Schmidt number (Sc), which are the analogs of the Nusselt
number (Nu) and the Prandtl number (Pr) defined in Chapter 14. Here the emphasis is
on the analogies between heat transfer in pure fluids and mass transfer in binary mix-
tures. Then in §22.4 we proceed to the definition of mass transfer coefficients for systems
with diffusion in two adjoining phases. We show there how to apply the information
about mass transfer in single phases to the understanding of mass transfer between two
phases.
Finally, in the last five sections of the chapter, we take up some effects that are pecu-
liar to mass transfer systems: mass transfer with chemical reactions (§22.5), the interac-
tion of heat and mass transfer processes in free convection (§22.6), the complicating
factors of interfacial tension forces and Marangoni effects (§22.7), the distortions of tem-
perature and concentration profiles that arise in systems with large net mass transfer
rates across the interface (§22.8); and finally the matrix analysis of mass transport in mul-
ticomponent systems. In this chapter the emphasis is on the non-analogous behavior of
heat and mass transfer systems.
In this chapter we have limited the discussion to a few key topics on mass transfer
and transfer coefficient correlations. Further information is available in specialized text-
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books on these and related topics. "

§22.1 DEFINITION OF TRANSFER COEFFICIENTS IN ONE PHASE
In this chapter we relate the rates of mass transfer across phase boundaries to the rele-
vant concentration differences, mainly for binary systems. These relations are analogous
to the heat transfer correlations of Chapter 14 and contain mass transfer coefficients in
place of the heat transfer coefficients of that chapter. The system may have a true phase
boundary, as in Fig. 22.1-1, 2, or 4, or an abrupt change in hydrodynamic properties, as
in the system of Fig. 22.1-3, containing a porous solid. Figure 22.1-1 shows the evapora-
tion of a volatile liquid, often used in experiments to develop mass transfer correlations.
Figure 22.1-2 shows a permselective membrane, in which a selectively permeable sur-
face permits more effective transport of solvent than of a solute that is to be retained, as
in ultrafiltration of protein solutions and the desalting of sea water. Figure 22.1-3 shows
a macroscopically porous solid, which can serve as a mass transfer surface or can pro-
vide sites for adsorption or reaction. Figure 22.1-4 shows an idealized liquid-vapor con-
tactor where the mass transfer interface may be distorted by viscous or surface-tension
forces.

Stream of gas В
Vapor A moving
/ into gas stream Fig. 22.1-1. Example of
Interface j l l l l l l l l l l ^ l mass transfer across a
mass transrer across a
Slab wet with liquid A I P l a n e boundary: drying of
1 a saturated slab.

T. K. Sherwood, R. L. Pigford, and С R. Wilke, Mass Transfer, McGraw-Hill, New York (1975).
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2
R. E. Treybal, Mass Transfer Operations, 3rd edition, McGraw-Hill, New York (1980).
3
E. L. Cussler, Diffusion: Mass Transfer in Fluid Systems, 2nd edition, Cambridge University Press
(1997).
D. E. Rosner, Transport Processes in Chemically Reacting Flow Systems (Unabridged), Dover, New
4
York (2000).