Page 425 - Modelling in Transport Phenomena A Conceptual Approach

9.5. MASS TRANSFER WITH CONVECTION 405

The use of Eq. (9.5135) in Eq. (9.5-134) gives

The average mass transfer coefficient can be calculated from Eqs. (9.5133) and
(9.5136) as
I
(9.5137)

Therefore, the Sherwood number is

Equation (9.5138) is recommended when
4riz
46(w,)p
1200 > RR = - -
=
P PW ' loo
It should be kept in mind that the calculated mass of species A absorbed by the
liquid based on Eq. (9.5133) usually underestimates the actual amount. This is
due to the increase in the mass transfer area as a result of ripple formation even
at a very small values of Re, i.e., Re > 20.
In the literature, Eq. (9.5137) is also expressed in the form

(9.5- 139)

where the exposure time, or, gas-liquid contact time, is defined by

L
t,, = - (9.5140)
vmax
Equation (9.5139) is also applicable to gas absorption to laminar liquid jets and
mass transfer from ascending bubbles, if the penetration distance of the solute is
small.
Example 9.13 A laminar liquid jet issuing at a volumetric flow rate of Q is
used for absorption of gas A. If the jet has a diameter D and a length L, derive
an expression for the rate of absorption of species A.
Solution

The time of exposure can be defined by