A semi-empirical conjugate model for droplet size distribution in the breakup of a Newtonian liquid sheet
Year: 2026
Type: article
Abstract: This paper investigates the atomization of Newtonian liquid sheets and the resulting droplet size distributions in the primary breakup. A conjugate model is proposed that combines Kelvin–Helmholtz instability (KHI) with a sheet perforation mechanism. In this framework, the KHI governs the large-scale structures, while sheet perforation controls the small-scale features, enabling the development of a comprehensive size distribution for sheet atomization. The KHI model incorporates the gas-phase boundary layer, demonstrating that the wavelength of the dominant waves increases along the liquid sheet. As a result, the predicted wavelength at the sheet breakup location becomes larger and scales with the sheet velocity U as U − 16 / 15 for inviscid liquid sheets and as U − 37 / 30 for viscous liquid sheets. The growth of surface waves produces alternating thick and thin regions within the sheet. The thin regions progressively decrease in thickness and eventually perforate when their thicknesses reach the order of 1 μ m , approximated by the Rayleigh–Plateau wavelength on the receding rim. These perforations expand rapidly, forming rims that subsequently break into filaments, which further disintegrate into droplets. Based on these observation, the proposed model predicts two characteristic filaments with semi-empirically correlated breakup length and approximated mean film thickness. These two characteristic sizes can be used to fit a mixture of two Gamma distributions to the droplet size distribution in the experiments using two fitting parameters.
Authors: Siyu Chen, Nasser Ashgriz
Institution: University of Toronto
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,900
OpenAlex ID: W7213766351