JOURNAL REVIEW z Facilitated Transport via Carrier-Mediated Diffusion in Membranes Part 1. Mechanistic Aspects, Regimes Experimental Systems and Characteristic z Carrier-mediated transport in membranes zyxwvut as a globally nonreactive process is distinguished from film theory with chemical reaction and other facilitated diffusion phenomena. With the concept of stoichiometric and system invariants, an approach is developed for the analysis of carrier- mediated transport with multiple permeants involving multiple reactions in the membrane. Approximate solutions of the requisite differential equa- tions according to the relative importance of diffusion and reaction rates are reviewed, as well as typical experimental studies. Criteria for evaluat- ing whether a membrane is in the diffusion or equilibrium regime are given, and, in the latter case, the effects of some system parameters are given, for example, binding constants, competitive permeants. JEROME S. SCHULTZ JOE D. GODDARD SHYAM R. SUCHDEO Department of Chemical Engineering University of Michigan Ann Arbor, Michigan 48104 Advances in membrane technology have made it possi- ble in recent years to manufacture membranes in diverse forms such as sheets, tubes, and hollow fibers. In most current applications to separations processes, the mem- brane functions as a physical diffusion barrier or simple (micro-) sieve. However, &rough recent studies on models of biological membranes, it has become evident that arti- ficial membranes, often in the form of liquid films, can be made functionally very specific in their properties by incorporating mobile or partially mobile compounds within the membrane structure which selectively react with a restricted class of permeants, for example, in ion- specific electrodes. These compounds serve effectively as carriers which not only can render the membrane very specific in its transport properties but also can enhance the relative rate at which the preferred permeants diffuse across the barrier. While various mechanistic models have been proposed to describe carrier-mediated transport in membranes, those models based on diffusion accompanied by chemical reaction have received the most theoretical and experi- mental study and are the main subject of this review. Recent studies of carriepmediated membrane transport of this type has led to a basic and more precise under- standing of the effect of the major parameters involved, including the reaction kinetics, equilibrium (binding) con- stant, membrane diffusivities, concentration gradients, membrane thickness, and solubilities of the permeants zyxwvu in the membrane phase. Currently available numerical methods, together with various asymptotic and approximate analytic methods, based on the respective concepts of weak gradients or fast and slow reactions, allow one to estimate with a good deal of confidence the response of a particular carrier- mediated membrane to a variety of operational condi- tions. Apart from their potential for direct applications to processes such as drug transport into cells, the concepts and methods developed in these studies, relating to reac- tion boundary-layer analysis, global nonreactivity, and competitive interactions with carriers, suggest similar theoretical treatments in a diversity of related phenomena, such as facilitated heat transfer, ion-selective transport, and liquid-liquid ion exchange, where diff usion-coupled chemical reaction is of paramount importance. The objective here is to review briefly some of the physico-chemical systems and conceptual models that have been studied as membrane systems; to provide a somewhat unified, theoretical framework for defining or characterizing certain invariant global aspects of carrier- mediated transport systems in general and the diffusion- reaction regimes of membranes in particular; and finally, to evaluate and extend some of the more powerful mathe- matical methods that are available for analyzing or pre- dicting the detailed behavior of such carrier-mediated membranes. CONCLUSIONS AND SIGNIFICANCE The major emphasis of this review is on the homo- geneous chemico-diffusion model for membrane transport. In this model the permeapt species enter the membrane and react with other species which are confined to the membrane. The net flux of the permeant through the membrane is the result of its ordinary (Fickian) diffusion rate and the diffusion rate in combinations with other species (carriers). AlChE Journal (Vol. 20, No. 3) May, 1974 Page 417