Page 52 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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According to them this power is equal to 1/2 for the liquid side control mass
transfer, and about 2/3 for the gas side controlled process.
1.5,2,2.2. Penetration model
The penetration model, proposed by Higbie [18] is oriented first of all
to the liquid side mass transfer. It is accepted that in industrial apparatuses the
period of exposure of the gas and liquid at the interface is very short. The
second assumption is that the liquid can be considered consisting of many
identical small liquid elements and that at the interface there is no action of
shear forces upon them. That is why it is possible to consider these elements as
solid particles. Before and after the contact at the interface these elements are
mixed with the liquid in the bulk and have the same concentration. The same
situation is assumed also for the gas phase.
The time of exposure 0 O, for example, for bubbles is:

e o=d b/u b. (148)

where <4 is the diameter of the bubble, and ttj,- its velocity.
In case of absorption in a packing

0 o=dJu L. (149)

where d p is the packing size, and ife-the liquid velocity.
For a steady state mass transfer process in immovable liquid the second
Fick's low (equation (79)) can be written as follows

8x 2 80 '
T

where 0 T is the time from the moment of appearance of the element on the
surface.
The boundary conditions are:

(151)