On interdependence of instabilities and average drop sizes in bag breakup

Abstract

A drop exposed to cross flow of air experiences sudden accelerations, which deform it rapidly, ultimately proceeding to disintegrate 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, 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 (∼We2) of the combination of dimensionless instability wavelengths (λ¯bag2/λ¯rim4λ¯film) developing on different segments of the deforming drop. Furthermore, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, ⟨D¯rim⟩, and bag film, ⟨D¯film⟩, individually, on We and see them decreasing linearly for the rim (∼We−1) and quadratically for the bag film (∼We−2). The reported work is expected to have far-reaching implications as it provides unique insight 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.