Adsorption from a well-stirred solution of finite volume: I. Linear adsorption kinetics through a stagnant boundary layer

Abstract

A macroscopic transport model of adsorption kinetics in well-stirred systems has been developed. The resistance to interfacial mass transfer is accounted for by assuming a stagnant boundary layer—in which transport is by diffusion—separates the adsorbing surface from a well-stirred solution of changing concentration. To generalize the analysis, we consider (i) an adsorbing surface of spherical geometry, (ii) batch and constant-flow operating conditions, (iii) uniform and segregated starting conditions, and (iv) nonequilibrium surface mass action. Explicit series solutions as well as short- and long-time asymptotic solutions of the mass balance equations are given for the important case of linear adsorption kinetics. As illustrated here, the series expressions provide physical insight into the coupling which can occur among transport, adsorption, and constant-flow processes; while the asymptotic solutions provide information on the operating conditions which can lead to rate-limiting behavior. In addition, we show that under certain conditions the stagnant boundary layer model presented here reduces to previously reported linear adsorption models.