The effects of viscous and inertial forces on drop breakup in an agitated tank

The well-known equation for the maximum stable drop size in a mixing vessel, d_max/L∞ (ρ_cn_r ²L³/σ)^−0.6, is in good accord with the data of various investigators. It has been commonly believed that inertial force is the only external force controlling drop breakup. Although the applicable regime of this equation should be limited to the inertial subrange, the data of drop sizes correlated with the above equation do not always lie in the inertial subrange, and some of the data are in the region near the Kolmogoroff length scale. It should also be noted that viscous force acting on such a small drop cannot be ignored in comparison with inertial force, and that the maximum stable drop size is thus controlled not only by Weber number but also by Reynolds number. By introducing the Reynolds number for the drop breakup mechanism, it is explained that small drops are successfully correlated by the above equation.