Page 246 - Modelling in Transport Phenomena A Conceptual Approach

226 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

7.9 Suspended particles in agitated vessels are frequently encountered in the
chemical process industries. Some examples are mixer-settler extractors, catalytic
slurry reactors and crystallizators. The design of such equipment requires the mass
transfer coefficient to be known. For this purpose, solid particles (species A) with
a known external surface area, A,, and total mass, M,, are added to an agitated
liquid of volume V and the concentration of species A is recorded as a function of
time.
a) Consider the liquid as a system and show that the unsteady-state macroscopic
mass balance for species A is

where M is the total mass of solid particles at any instant and cyt is the equilibrium
solubility. Rearrange Eq. (1) in the form

and show how one can obtain the average mass transfer coefficient from the exper-
imental data.
b) Another way of calculating the mass transfer coefficient is to choose experimental
conditions so that only a small fraction of the initial solids is dissolved during a
run. Under these circumstances, show that the average mass transfer coefficient
can be calculated from the following expression:

(a,) = - (e'- CA) (3)
pat
V
(A)t
In
where (A) is the average surface area of the particles. Indicate the assumptions
involved in the derivation of Eq. (3).

7.10 Consider Problem 7.9 in which the average mass transfer coefficient of sus-
pended particles is known. Estimate the time required for the dissolution of solid
particles as follows:
a) Write down the total mass balance for species A and relate the mass of the
particles, M, to concentration of species A, CA, as

b) Substitute Eq. (1) into Eq. (1) in Problem 7.9 to get
de
dt = (I!
(1
[I - (1 + p3) o]~/~ - 0)