Abstract

In this presentation, we explore the disintegration of thin fluid sheets, a topic of interest specifically with regards to the modelling of aerosol transmission of disease. We begin by discussing the configuration of Savart sheets, where a liquid jet impinges a small disc and forms a film that spreads radially until it disintegrates at a certain critical radius. Several methods have been used to determine this radius, including a force balance analysis by Taylor, which predicts the thickness of the sheet to decrease with increasing radius and leads to a non-zero film curvature. However, Taylor’s analysis does not provide an explicit model for the disintegration. Lin’s perturbative instability analysis involves Fourier transforms and normal modes to determine criticality conditions, while Villermaux focuses on the dimensionless parameter β, representing the thickness of the boundary layer formed on the disc. Our study focuses on the Navier-Stokes equation and establishes a criticality condition on the Weber number, without assuming a self-similar velocity profile. We apply a thin film approximation for the velocity profile and isolate the curvature of the film to derive this condition. Our analysis provides a theoretical prediction for the disintegration of thin fluid sheets based on momentum balance and surface tension considerations and demonstrates the importance of considering the velocity profile within the film.