Net flow and tracer flow in lattice and carrier models

Solute flux in the absence of active transport is analyzed in systems with discontinuity of chemical potential. Permeability coefficients for net flow ω and self-diffusion (ω^χ) are expressed in terms of kinetic coefficients for adsorption (α), desorption (β), and transfer between sites (k). For a 1-row lattice, a composite lattice-liquid membrane, and an n-row lattice without constraints, w = w^x, both decreasing with increase of concentration. Restriction to "single file" movement, while not affecting net flow, induces positive coupling of isotopic flows (w > w^x), disappearing at low concentrations. Switch (γ) between sites of a unit permits concentration-dependent conversion to negative coupling ("counter-transport"), as predicted previously for a divalent carrier. A simple univalent carrier shows negative coupling, which disappears (1) at low concentrations; (2) when transport of free carrier is much faster than that of loaded carrier (k_c ≫ k); or (3) for k ≫ β. Near equilibrium, both for continuous and discontinuous systems, w w^x and the ratio of the logarithm of the flux ratio to the force are, equivalently, indices of coupling of isotopic flows ("isotope interaction"). Discontinuity of chemical potential per se does not produce isotope interaction or abnormality of the flux ratio.