Biomedical Engineering Reference
In-Depth Information
Figure
6.9.
Solute transport to permeate stream as a function of passage (1 rejection coeffi-
cient) for continuous, constant volume diafiltration.
Figure 6.9 illustrates the transport of solute from the retentate to permeate as a
function of the solute rejection. This represents ideal, theoretical mass transport. In actual
operation, there exist system nonlinearities such as solute interactions and imperfect
level and feed control that hinder solute transport. To ensure solute removal, engineering
over design factor of two diavolumes is typically added to the calculated number of
diavolumes [18]. Using such a factor represents good quality design by accounting for the
system nonlinearities.
The optimal concentration at which to commence diafiltration is derived from the
equation for permeate flux in the gel layer controlled region. From this equation, the
optimal diafiltration concentration has been derived from the film theory model as [10]
C
D
¼
C
G
2
:
7
gel layer
concentration, and C
G
can be determined from a plot of permeate flux versus feed
concentration as shown in Fig. 6.10. For proteins, C
G
is generally in the range of 20-40%
(200-400 g/L), which is approximately an order of magnitude higher than typical
processing conditions. Operating at a feed concentration as close as possible to C
D
will minimize the total diafiltration volume and processing time. Note that the slope of a
plot of J versus ln(C
B
) is the mass transfer coefficient, k, which can additionally be
computed to further characterize the TFF system.
In practice, TFF systems are often operated by concentrating to the final desired
concentration and performing diafiltration at this concentration. However, this may not
be the most efficient operating mode since the flux at the final concentrationmay be quite
low resulting in excessively long operating times. Generally, the most time efficient
diafiltration operating mode is to concentrate the feed close to C
D
, perform the required
number of diafiltrations, and then concentrate or dilute to the final desired concentration.
where C
D
¼
optimal retentate concentration for diafiltration and C
G
¼
