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, = 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)