Page 305 - Modelling in Transport Phenomena A Conceptual Approach

8.4. MASS TRANSPORT WITHOUT CONVECTION 285

The rate of mass of A entering and leaving the system is determined from the
mass (or, molar) flux. As stated in Chapter 2, the total flux is the sum of the
- (8.42)
molecular and convective fluxes. For a one-dimensional transfer of species A in the
z-direction in rectangular coordinates, the total molar flux is expressed as

Molecular flux Convective
flux
where vz is the molar average velocity defined by Eq. (2.3-2). For a binary system
composed of species A and B, the molar average velocity is given by

(8.43)

As we did for heat transfer, we will first consider the case of mass transfer without
convection. For the transport of heat without convection, we focused our attention
on conduction in solids and stationary liquids simply because energy is transferred
by collisions of adjacent molecules and the migration of free electrons. In the case
of mass transport, however, since species have individual velocities6, the neglect
of the convection term is not straightforward. It is customary in the literature
to neglect the convective flux in comparison with the molecular flux when mass
transfer takes place in solids and stationary liquids. The reason for this can be
explained as follows. Substitution of Eq. (8.43) into Eq. (8.42) gives

(8.44)

Since ZA is usually very small in solids and liquids, the convective term is considered
negligible. It should be kept in mind, however, that if XA is small, this does not
imply that its gradient, Le., dxA/dz, is also small.
Another point of interest is the equimolar counterdiffusion in gases. The term
“equimolar counterdiffusion” implies that for every mole of species A diffusing
in the positive z-direction, one mole of species I3 diffuses back in the negative
z-direction, i.e.,
NA, = - NB, + CAVA, = - CBVB, (8.45)

Under these circumstances the molar average velocity, Eq. (8.43), becomes

(8.46)

and the convective flux automatically drops out in Eq. (8.42).
‘Transport of mass by diffusion as a result of random molecular motion is called a Brownian
motion.