Page 419 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 399

For a dilute liquid solution, the total density is almost constant and Eqs. (9.577)
and (9.5-78) become

WA, = -DAB- apA (9.579)
dX
WA, = -DAB apA +PAW% (9.580)
Dividing Eqs. (9.579) and (9.580) by the molecular weight of species A, MA,
gives

(9.581)

dCA +
NA, = -DAB - CAW, (9.582)
dz
Since there is no generation of species A, Eq. (9.4-1) simplifies to

Rate of
( species A in ) - ( species A out (9.583)

For a rectangular differential volume element of thickness Ax, length Az and width
W, as shown in Figure 9.20, Eq. (9.583) is expressed as
( NA, Is w Az+NAz 1% Ax>-( NA, Iz+& W Az+ NA. Iz+Aa WAX) = 0 (9.584)

Dividing Eq. (9.584) by WAXAZ and taking the limit as Ax + 0 and Az -+ 0
gives

(9.586)

Substitution of Eqs. (9.581) and (9.5-82) into Eq. (9.586) yields

(9.587)

Convection in Diffusion in Diffusion in
s-direction s-direction %-direction
In the z-direction, the mass of species A is transported by both convection and
diffusion. As stated by Eq. (2.48), diffusion can be considered negligible with
respect to convection when P~M >> 1. Under these circumstances, Eq. (9.587)
reduces to
(9.588)