Page 322 - Modelling in Transport Phenomena A Conceptual Approach

302 CHAPTER 8. STEADY MICROSCOPIC BALANCES WITHOUT GEN.

(8.5-3)

The tricky part of the mass transfer problems is that there is no need to have
a bulk motion of the mixture as a result of external means, such as pressure drop,
to have a non-zero convective flux term in Eqs. (8.51)-(8.5-3). Even in the case of
the diffusion of species d through a stagnant film of B, non-zero convective term
arises as can be seen from the following examples.
It should also be noted that if one of the characteristic velocities is zero, this
does not necessarily imply that the other characteristic velocities are also zero. For
example, in Section 8.4, it was shown that the molar average velocity is zero for
an equimolar counterdiffusion since NA, = - NB,. The mass average velocity for
this case is given by
WA, + WB,
v, = (8.5-4)
P
The mass and molar fluxes are related by

(8.5-5)

where Mi is the molecular weight of species i. The use of Eq. (8.55) in Eq. (8.5-4)
gives
MANA, + MBNB, NA,(MA - MB)
-
v, = - (8.5-6)
P P
which is non-zero unless MA = MB.

8.5.1 Diffusion Through a Stagnant Gas

8.5.1.1 Evaporation from a tapered tank
Consider a pure liquid d in an open cylindrical tank with a slightly tapered top
as shown in Figure 8.32. The apparatus is arranged in such a manner that the
liquid-gas interface remains fixed in space as the evaporation takes place. As an
engineer, we are interested in the rate of evaporation of A from the liquid surface
into a mixture of A and 0. For this purpose, it is necessary to determine the
concentration distribution of A in the gas phase. The problem will be analyzed
with the following assumptions:

1. S teady-state conditions prevail.

2. Species d and B form an ideal gas mixture.
3. Species B has a negligible solubility in liquid A.