Calculating leakage in emulsion liquid membrane systems from pH measurements

Leakage of the internal phase droplets reduces the extraction efficiency of emulsion liquid membrane systems by spilling the stripping agent and previously extracted solute into the bulk phase. When the stripping agent is acid or base, internal phase leakage can be determined from bulk phase pH measurements. New equations for calculating leakage from these pH measurements are presented, which account for bulk phase chemistry and volume changes due to leakage and emulsion swell. We show that equations used in several studies published over more than 30 years include unidentified assumptions that can cause erroneous leakage estimates for systems with weak acid or base stripping agents or bulk phase solutions that are not initially neutral. Guidelines identifying when these approximate equations will underestimate leakage by 10% or more are presented. Based on these guidelines and calculations quantifying errors in examples from the literature, we expect that many results calculated from pH underestimate the actual leakage. The new equations use the same experimental data as the approximate equations with minimal increased complexity and are recommended whenever leakage is calculated from pH measurements in systems without solute extraction. Methods for extending the equations to systems with simultaneous solute extraction are described.