Linear instability theory is used to predict the lateral diffusivity K for eddy buoyancy fluxes in an idealized channel model, following a suggestion by Killworth (1997). The vertical structure and magnitude of K agree approximately with the non-linear model results. The lateral structure of K from linear theory lacks minima within eddy-driven zonal jets, pointing towards a non-linear mechanism for mixing barriers in the channel model. This effect can be accounted for by a modification of K from linear theory by the kinematic effect of the background flow following a recent suggestion by Ferrari and Nikurashin (2010). Implementation of this closure for K in an eddy mixing framework based on potential vorticity mixing in a zonally averaged model version yields approximate agreement with the zonally resolved version over a certain range of external parameters, in particular with respect to the reproduction of eddy-driven zonal jets. (C) 2011 Elsevier Ltd. All rights reserved.