A geometric approach for predicting vertical stationary profiles of weakly inertial advecting-diffusing particles in closed incompressible flows

Mixing of weakly inertial particles in closed flows is often addressed by considering individual particles as passive advecting-diffusing tracers, subjected to an additional settling velocity resulting from body forces (e.g. gravity). We show that the qualitative and quantitative features of the vertical particle distribution (i.e. the horizontal cross-sectional averages of particle concentration) can be predicted from the structure of the flow resulting from the superposition of the stirring field and the settling velocity. The prediction is based upon the observation that the resulting flow can be divided into two nonoverlapping regions, namely trajectories that are confined within the mixing space (recirculation loops), and trajectories that cross the mixing space. The spatial extent of these regions is exploited to define an effective vertical convective velocity entering the one-dimensional lumped model. Model two-dimensional flows possessing different flow patterns are used to illustrate the proposed estimate for effective velocity. A CFD-computed threedimensional turbulent flow inside a baffled stirred vessel is used as a benchmark test to assess the model performance in typical industrial flows.