A multi-stage model for drop breakage in stirred vessels

Abstract

Existing models for d_max predict that, in the limit of μ_d → ∞, d_max increases with μ power of μ_d. Further, at low values of interfacial tension, d_max becomes independent of σ even at moderate values of μ_d. However, experiments contradict both the predictions show that d_max dependence on μ_d is much weaker, and that, even at very low values of σ, d_max does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. d_max is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μ_d and σ. The model successfully predicts the reduced dependence of d_max on μ_d at high values of μ_d as well as the dependence of d_max on σ at low values of σ. The data available in literature on d_max could be predicted to a greater accuracy by the model in comparison with existing models and correlations.