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100 3. Heterogeneous Processes and Reactor Analysis

3.3.6 External mass transfer in liquid–solid systems

The slip-velocity theories are based on the correlations of steady state transfer to
v
ix
particles fed in space, with the aerage slip velocity used to calculate the Reynolds
v
. numberWhen natural conection effects are absent and when the Reynolds number is
v
greater than 1, the transfer rate for single spheres is gien by the semitheoretical
equation (Harriot, 1962)
2
Sh 0.6 Re Sc 0.5 p 0.33 (3.117)
Here, the particle Reynolds number is based on the slip v. If terminal velocity is elocity
es the minimum v used, then the abo alue for the mass transfer coefficient. e correlation gi v v
f
Minimum mass transfer coeficients further depend on the density difference between
solid particles and solvent. For the typical case of water, the approximate v alues presented
in Table 3.7 can be used (Harriot, 1962).
These values hold for particle diameters of 100 – 10,000 m or 0.1 –10 mm, co ering v
all practical applications. Furthermore, the typical density dif since par- ference is about 1,
ticle densities are around 2 g/cm 3 .
fled tanks, icients in baf Harriot (1962) measured the mass transfer coef using six-blade f
turbines and seeral liquids such as water and glycerine. According to that study v ,

• Mass transfer coefficients are probably the same for any stirrer location if the particles
are completely suspended.
• For small ion-exchange particles in w the mass transfer coef , ater icient decreases with f
increasing particle size, b ger than about ut is almost independent of size for particles lar
200 m.
• Viscosity has only a small effect on the mass transfer coef f icient.
• The effect of particle shape was not determined, but is expected to be of minor impor-
tance.
f
• The coeficients in unbaffled tanks increased with only the 0.3 power of the stirrer
speed. At the speed needed for complete suspension in a baffled tank, the coef icients f
are about the same with or without bafAt higher speeds, the more uniform disper- fles.
sion of the particles and the greater velocity fluctuations make the coeficients lar f ger
with baffles present.

Table 3.7
f Mass transfer coeficient range (approximate v alues).

Density difference icient range Minimum mass transfer coef f
(g/cm 3 ) (cm/s)
3 0.008–0.01
1 0.005–0.007
0.3 0.003–0.005
0.1 0.0025–0.003