Abstract
An optimization of facilitated transport in liquid membranes is accomplished to determine the maximum facilitation factor and corresponding dimensionless equilibrium constant for a given inverse Damkohler number, ϵ, and a parameter, α, which is directly proportional to the initial carrier concentration. The analysis covers the entire range of diffusion-limited to reaction-limited mass transport. A wide range of downstream permeate concentrations are also considered. The existence of the maximum is demonstrated. The optimal facilitation factor and optimal dimensionless equilibrium constant are plotted for a range 0.001 ≤ ϵ ≤ 10.0 and 0.01 ≤ α ≤ 100.0 For this range the optimal dimensionless equilibrium constant lies between 1.5 and 10. The optimal facilitation factor increases with decreasing ϵ and is strongly dependent on α. As the downstream permeate concentration increases, the optimal facilitation factor and dimensionless equilibrium constant both decrease. The results can be used to select optimal operating conditions and/or carriers, or to compare actual to optimal results.
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