Emulsion liquid membrane (ELM) systems are an important technique for wastewater cleanup. For this purpose, emulsion globules are dispersed in wastewater (external phase), each emulsion globule consisting of many tiny aqueous droplets (internal phase) enclosed in oil (membrane phase). Hazardous chemicals in the wastewater are transported into the internal droplets by mass transfer mechanisms.

Since Li first invented an ELM system in the 1960s, much research effort has been devoted to experimentally finding the optimal conditions for ELM recovery of various chemicals. Such studies would have benefited greatly from the guidance of mathematical models, especially those that provide analytical predictions. However, mathematical modeling of ELM systems is highly challenging due to the interplay of transport phenomena and chemical reactions.

In carrier mediated mass transfer in an ELM system, the hazardous chemical in the external phase are extracted by reactions at the external membrane interface to form a complex with the carrier compound in the membrane phase. The complex then diffuses to the internal-membrane interface, where the hazardous chemical is stripped from t1le complex and the carrier freed.

This thesis establishes a mathematical model of carrier mediated mass transfer in ELM systems. This model yields analytical solution that accurately predicts experimental results. This solution provides theoretical guidance to optimal recovery conditions and maximum achievable recovery efficiency.

Using metal recovery as an example, this thesis conducts a first-principle study of the extraction chemical reactions at the external-membrane and the stripping chemical reactions at the internal-membrane interfaces and derives the extraction and stripping distribution coefficients. This thesis also finds chemical reactions in the internal phase greatly improve equilibrium recovery efficiency but also greatly lengthen the time to reach equilibrium.

The analytical concentration profiles consist of converging series of infinite terms each involving an eigenvalue of a certain eigenvalue equation. When external resistance exceeds internal resistance, this eigenvalue equation exhibits a remarkable singular behavior with significant impact on the concentration profiles. Also remarkable is the metal accumulation phenomenon at the external-membrane interface when internal resistance is big relative to external resistance.