Application of nonlinear frequency response to investigation of membrane transport

Abstract

The concept of higher order frequency response functions, used for investigation of weekly nonlinear systems by frequency response techniques, is applied to investigation of membrane systems. Isothermal permeation of single gases through non-porous and porous membranes is analysed for three transport mechanisms: solution-diffusion, pore-surface diffusion, and viscous-flow. In the course of definition of the transmembrane transport in dynamic conditions, a new concept of generalized membrane permeability, defined as an indefinite sequence of the permeabilities of the first, second, third,...order, dependent on the equilibrium and transport parameters of the membrane in steady-state, is introduced. A simple two-reservoir system, with variation of the volume of one reservoir, is defined and its first and second order frequency response functions are derived. It is shown that these functions can be used for identification of the transport mechanism, i.e., of the corresponding model and for estimation of the model parameters: permeabilities of different orders, as well as the separate values of the relevant equilibrium and transport parameters.