A free-standing liquid membrane can be composed of various different components, and different formulations may have different properties. For example, one composition may typically have a longer lifetime than others. In an effort to create a long-lasting liquid membrane and to demonstrate how liquid membranes might be tailored to meet the needs of various applications, we used a genetic algorithm called differential evolution (23), an algorithm that has been successfully implemented in other experimental studies (25). For our experiments, we used deionized water, glycerol, tannic acid (22), PEO, and SDS as components of the liquid membranes and selected for average liquid membrane longevity. These additives were chosen because of their hygroscopic or stabilizing properties. Our component concentration search ranges (min/step size/max) were as follows: deionized water (0 ml/5 ml/40 ml), SDS (0 mM/1.7 mM/15.6 mM), tannic acid (0 mM/0.3 mM/2.9 mM), PEO (0 g/.09 g/1.0 g in 40 ml of solution), and glycerol (40 ml minus the volume of deionized water for the given formulation).

The search for the composition with the longest average longevity had five compositions per generation (NP = 5), with four components (D = 4; glycerol not considered, as its volume is dependent on the water volume). The first generation of compositions was determined by random number generation for each component. To determine the next generation, we used the equations outlined by Storn and Price (23), using a crossover constant of 0.5 (CR = 0.5) and a step size of 0.5 (F = 0.5) to generate a set of test compositions. We then compared the average longevity of each composition Xi,G (i = 1, 2, … D; G denotes the generation) to that of the respective test composition Ui,G. Composition Xi,G + 1 was determined to be either composition Xi,G or composition Ui,G: The composition with the higher average longevity was chosen to be Xi,G + 1. Note that it is possible to select for other properties to achieve a liquid membrane of interest. For example, instead of selecting for average longevity, it is possible to select for maximum longevity, number of perturbations before rupture, bactericidal effectiveness, or other properties desired for the liquid membrane. We measured the longevity of 72 different compositions. For each of those compositions, we formed up to 59 membranes in parallel for statistical purposes and measured their longevity. The total volume of the solutions was kept constant (40 ml).

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