Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes

The splitting of globules is an important phenomenon during the final stages of disintegration processes. Three basic types of deformation of globules and six types of flow patterns causing them are distinguished.

The forces controlling deformation and breakup comprise two dimensionless groups: a Weber group N_We and a viscosity group N_Vi. Breakup occurs when N_We exceeds a critical value (N_We)_crit. Three cases are studied in greater detail: (a) Taylor's experiments on the breakup of a drop in simple types of viscous flow, (b) breakup of a drop in an air stream, (c) emulsification in a turbulent flow.

It is shown that (N_We)_crit depends on the type of deformation and on the flow pattern around the globule. For case (a) (N_We)_crit shows a minimum value ∼ 0.5 at a certain value of (N_Vi) and seems to increase indefinitely with either decreasing or increasing ratio between the viscosites of the two phases. For case (b) (N_We)_crit varies between 13 and ∞, depending on N_Vi and on the way in which the relative air velocity varies with time, the lowest value refers to the true shock case and N_vi→0. For case (c) (N_We)_crit, which determines the maximum drop size in the emulsion, amounts to ∼1, and the corresponding values of N_Vi appear to be small. A formula is derived for the maximum drop size.