[Paper Review] An analytical and experimental study of secondary atomization for vibrational and bag breakup modes

Varun Kulkarni|arXiv (Cornell University)|Jun 17, 2023

Laser-induced spectroscopy and plasma3 citations

TL;DR

This study presents a combined analytical and experimental investigation of secondary atomization in vibrational and bag breakup modes of liquid drops. It derives a theoretical We boundary for bag breakup, validates exponential growth of bag and drop deformation with Weber number, and reports Sauter mean diameter (D32) lower than prior estimates using PDA measurements, revealing a shift toward larger drops in viscous fluids.

ABSTRACT

Bag breakup of drops has been a subject of interest for almost over a century. Several issues such as theoretical estimation of the regime boundary marking the onset of such breakup, bag growth rates, drop size distribution, and the effect of Weber number, $We$, and Ohnesorge number, $Oh$, on these quantities remains unaddressed. The current study aims to clarify aspects of the atomization process through experiments and theory. We examine bag breakup of a single drop of various inviscid and low viscosity fluids as it deforms in the presence of a continuous horizontal air jet. The We boundary at which bag breakup begins is theoretically determined and the expression obtained, $We = 12(1 + \frac{2}{3} Oh^2)$, is found to match well with existing experimental data. An exponential growth in the radial extent of the deformed drop and the streamline dimension of the bag is predicted by the theoretical model and confirmed by experimental findings. These quantities are observed to strongly depend on $We$. However, their dependence on $Oh$ is weak for the range of $Oh$ considered in this study. Subsequent to drop deformation, bag formation and expansion is the bursting process. This is marked by the disintegration of the bag owing to instability of the Rayleigh-Taylor type, followed by collapse of the liquid rim bounding this bag by Plateau-Rayleigh instability. The sizes of the drops thus produced are measured using Phase Doppler Anemometry (PDA) which is in contrast to shadowgraphs used in earlier studies. A discernible shift in the peak of the drop size distribution for viscous drops is seen which indicates a preponderance of drops of higher diameters vis-à-vis fragment size distribution for inviscid drops. Furthermore, an estimate of the Sauter mean diameter ($D_{32}$) is presented which is somewhat lower than earlier predictions.

Motivation & Objective

• To clarify the theoretical and experimental basis for the onset of bag breakup in liquid drops.
• To quantify the dependence of bag and drop deformation on Weber (We) and Ohnesorge (Oh) numbers.
• To investigate secondary atomization mechanisms, including Rayleigh-Taylor and Plateau-Rayleigh instabilities.
• To measure drop size distributions using Phase Doppler Anemometry (PDA), improving on shadowgraph-based methods.
• To estimate Sauter mean diameter (D32) and compare it with prior theoretical predictions.

Proposed method

• Theoretical derivation of the Weber number boundary for bag breakup using fluid dynamic principles: We = 12(1 + (2/3)Oh²).
• Experimental setup involving single drops deformed by a horizontal air jet to induce bag breakup.
• Use of Phase Doppler Anemometry (PDA) to measure drop size distributions post-bursting.
• Analysis of radial drop deformation and bag streamline dimension growth over time.
• Application of Rayleigh-Taylor and Plateau-Rayleigh instability models to explain bag bursting and rim collapse.
• Comparison of theoretical predictions with experimental data across a range of We and Oh values.

Experimental results

Research questions

• RQ1 What is the theoretical Weber number threshold for the onset of bag breakup, and how well does it match experimental observations?
• RQ2 How do the radial extent of the deformed drop and the bag's streamline dimension evolve over time, and what is their dependence on We and Oh?
• RQ3 How does viscosity (Oh) influence the drop size distribution in secondary atomization following bag breakup?
• RQ4 What is the Sauter mean diameter (D32) of the resulting droplets, and how does it compare to previous theoretical estimates?
• RQ5 How does PDA-based measurement of drop size distribution differ from traditional shadowgraph methods in capturing post-bursting droplet characteristics?

Key findings

• The theoretical We boundary for bag breakup, We = 12(1 + (2/3)Oh²), shows strong agreement with existing experimental data.
• The radial extent of the deformed drop and the streamline dimension of the bag exhibit exponential growth, primarily dependent on Weber number.
• Dependence on Ohnesorge number is weak within the range studied, indicating minimal influence of viscosity on deformation dynamics.
• PDA measurements reveal a discernible shift in the peak of the drop size distribution toward larger diameters for viscous drops compared to inviscid ones.
• The estimated Sauter mean diameter (D32) is lower than earlier theoretical predictions, suggesting finer atomization than previously assumed.
• The bursting of the bag is driven by Rayleigh-Taylor instability, followed by collapse of the liquid rim via Plateau-Rayleigh instability, consistent with observed droplet formation.