A two-dimensional model of the flow and mixing of particulate solids has been developed on the basis of the Markov chain theory for an alternately revolving static mixer of Sysmix (R) type. In such a system, mixing occurs in both vertical and horizontal directions. Simulations are presented here to investigate the effect of the initial loading of the components, as well as the effect of the values of the transition probabilities that constitute the main parameters of the model. It is shown that a horizontal arrangement of the components always leads to better mixture quality and improved mixing kinetics. This research is presented for non-segregating mixtures, as well as potentially segregating mixtures. for which the empirically well-known oscillations in variance are represented by the model. Results suggest that there is a rational way of approaching a static-mixing problem with regard to the initial loading of the component and the optimal number of revolutions. Comparison of model results with experimental data published previously for a Sysmix (R) apparatus contributes to validating the viability of the model. (C) 2009 Elsevier B.V. All rights reserved.