Mass Transfer
459
i.e., first order in the bulk substrate concentration and with rate constant kj. Here the kinetics is totally
independent of the intrinsic kinetic parameters M
-ma.v
and Ks._______________________________
Note 10.6. Finding values of the mass transfer coefficient
ks
The same basic principles as previously described for finding mass transfer correlations for bubbles apply
also for the mass transfer between a solid particle and a liquid. The difference is primarily that the
assumption of a rigid particle surface is more credible. In Table 10.7 only the correlations for immobile
interfaces are thus of interest. For suspended pellets the linear velocity of the pellets relative to the
continuous phase, i.e. the surrounding medium, derives from the density difference. The velocity can
therefore be described by Stokes law
« è
g (p P- p M l
18
77
(
1
)
Inserting the expression for
ub
Eq. (1) into the definition of the Reynolds number, we get:
I
8 7
17
18
'
The Grashof number can thus be applied in the correlations instead of the Reynolds number. However, the
coefficients multiplying the Reynolds number will be different. For e.g. the third correlation in Table 10.7,
valid for Re < 1, Pe < 10
4
we get:
Sh =
4 + 1.211
~
T S c
3
2
2
1
V
f
1 7 V
4 + 0.18GHSC3
7
(3)
For a pellet with a diameter of 2 mm suspended in water, with a density difference of 20 kg m
'3
between the
liquid and the pellet, we find
Gr
=
(2 *10
-3) 3
9.81 -997 -20
(
1 0
J)2
= 1564
(4)
The viscosity of water has been used in the calculation above. We see that
Gr
18
>1
(5)
i.e. the validity range of correlation (3) is exceeded and another correlation should be used. The top
correlation from Table 10.7 appears applicable since the validity range should be 36 < Gr < 23400. We get