Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes

TLDR

Splitting of globules is a key phenomenon in the final stages of disintegration processes. Deformation and breakup are governed by two dimensionless groups, the Weber number (N We) and viscosity ratio (N Vi), and are examined in three canonical settings: Taylor’s viscous flow, air‑stream breakup, and turbulent emulsification. Breakup occurs when N We exceeds a critical value that varies with deformation type and flow pattern—≈0.5 at a specific N Vi for viscous flow, 13–∞ for air streams, and ≈1 for turbulent emulsification—allowing a formula for maximum drop size to be derived.

Abstract

Abstract 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.