Hollow Fiber Passes and Ethanol Rejection Coefficient
Continuous ILDF was explored using the arrangement shown in Figure 1D to
mimic the arrangement in Figure 1C, but with the ability to analyze the
output of each pass/stage. The entirety of the bulk of the liposome
formation mixture was fed through the hollow fiber as a single pass into
the second vessel. The retentate and permeate were analyzed, buffer
added to replace the permeate, then the entirety of the adjusted bulk
returned to the first vessel in preparation for another pass. This was
repeated until the target ethanol removal was achieved. The intent was
to simulate the arrangement in Figure 1C with the ability to assess the
output of each pass/stage discretely.
The assessment of the continuous ILDF arrangement involved processing
the post-liposome formation bulk mixture with various levels of
pre-dilution from undiluted (36% EtOH) to significantly diluted (5%
EtOH). The ethanol concentration was assessed after each pass/stage and
the process repeated.
Figures 3A and B show the results of the various initial ethanol
concentrations and the ethanol removal curves over the repeated passes.
As expected, ethanol concentration was reduced with each pass and the
number of passes needed to remove the ethanol decreased with decreased
initial ethanol concentrations. For example, an initial concentration of
24% EtOH required 36 passes for target removal while starting at 5%
EtOH required 9 passes. The behavior of the curves followed the pattern
of the diafiltration model (Equation 1) with passes in place of
diavolumes, but with a notable exception. Unexpectedly, the fitted
curves for the simulated ILDF results showed a variable exponent. The
exponent, where the rejection coefficient is contained in the
traditional diafiltration equation (Equation 1), was expected to be
constant, but instead, decreased as the initial ethanol concentration
decreased. This supports the previous notion of an ethanol concentration
dependent rejection coefficient.
From this, a continuous ILDF equation (Equation 2) was derived where\(c_{0}\)= initial EtOH concentration, c = final EtOH
concentration, \(P\) = simulated ILDF passes and α = ethanol rejection
coefficient. The ethanol rejection coefficient is dependent on the
initial ethanol concentration, α = \(f(c_{0})\). This function was
derived from the results in Figures 3A and B as shown in Figure 3C and
represented with Equation 3.
\(c=c_{0}e^{-\left(1-\alpha\right)P}\) (Equation 2)\(\alpha=f\left(c_{0}\right)=0.059\ln\left(c_{0}\right)+0.99\)(Equation 3)