Despite very low Reynolds numbers in the bronchial ducts, acinar flow associated with wall motion can exhibit irreversibility and chaoticity, two efficient features of convective mixing contributing to alveolar dispersion. This paper describes a new computational fluid dynamics (CFD) approach in which an Eulerian continuous scalar field transported by fluid flow is used as a numerical tracer to quantify convective mixing in an incompressible flow of non-diffusive fluid. This flow cyclically enters into and exits from an elementary alveolar model made of a single beating alveolus connected to a deformable bronchiole. A non-dimensional parameter defined as the residual mass of marked fluid normalized by the initial alveolar mass of fluid, m(res), is used to study the efficiency of convective mixing in different conditions of alveolar ventilation. This parameter is dependent on the alveolar-to-bronchial flow ratio, Q(A)/Q(D), which reveals that a relative maximum efficiency for convective mixing is expected to occur in the mid acinar region in quasi-normal conditions of breathing. (C) 2014 Elsevier Ltd. All rights reserved.