On interdependence of instabilities and average drop sizes in bag breakup

TL;DR

This paper investigates the breakup of liquid drops in cross flow, revealing new scaling laws for instability wavelengths and drop sizes related to the Weber number, enhancing understanding of disintegration mechanisms.

Contribution

It introduces a novel parabolic dependence of instability wavelengths on the Weber number and derives size scaling laws for rim and bag film in drop breakup.

Findings

Instability wavelengths scale as We^2.

Drop rim size decreases as We^{-1}.

Bag film size decreases as We^{-2}.

Abstract

A drop exposed to cross flow of air experiences sudden accelerations which deform it rapidly ultimately proceeding to disintegrate it into smaller fragments. In this work, we examine the breakup of a drop as a bag film with a bounding rim resulting from acceleration induced Rayleigh-Taylor instabilities and characterized through the Weber number, \textit{We}, representative of the competition between the disruptive aerodynamic force imparting acceleration and the restorative surface tension force. Our analysis reveals a previously overlooked parabolic dependence ($\sim We^2$) of the combination of dimensionless instability wavelengths $({\bar{\lambda}}_{bag}^2/ {\bar{\lambda}}_{rim}^4 {\bar{\lambda}}_{film})$ developing on different segments of the deforming drop. Further, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, $\langle{\bar{D}}_{rim}\rangle$ and bag film, $\langle{\bar{D}}_{film}\rangle$ individually, on $We$ and see them to decrease linearly for the rim ($\sim We^{-1}$) and quadratically for the bag film ($\sim We^{-2}$). The reported work is expected to have far-reaching implications as it provides unique insights on destabilization and disintegration mechanisms based on theoretical scaling arguments involving the commonly encountered canonical geometries of a toroidal rim and a curved liquid film.