What determines the drop size in sprays of polymer solutions?

TL;DR

This study experimentally examines how viscoelasticity influences droplet size in agricultural spray nozzles, revealing that polymer solutions produce larger droplets with broader distributions, and identifying key parameters affecting droplet formation.

Contribution

It provides a quantitative relationship between viscoelastic properties and droplet size, introducing a master curve and detailed distribution modeling for polymer solutions in sprays.

Findings

Droplet size increases linearly with the liquid's extensional relaxation time.

Rescaling data reveals a universal curve when plotted against Weber and Deborah numbers.

Droplet size distributions follow a compound gamma distribution with parameters saturating at high polymer concentrations.

Abstract

The effect of viscoelasticity on sprays produced from agricultural flat fan nozzles is investigated experimentally using dilute aqueous solutions of polyethylene oxide (PEO). Measurements of the droplet size distribution using laser diffraction reveal that polymer addition to water results in the formation of overall bigger droplets with a broader size distribution. The median droplet size $D_{50}$ is found to increase linearly with the extensional relaxation time of the liquid. The non-dimensional median droplet sizes of different polymer solutions, sprayed at different operating pressures from nozzles of different sizes, rescale on a single master curve when plotted against an empirical function of the Weber and Deborah numbers. Using high-speed photography of the spraying process, we show that the increase in droplet size with viscoelasticity can be partly attributed to an increase of the wavelength of the flapping motion responsible for the sheet breakup. We also show that droplet size distributions, rescaled by the average drop size, are well described by a compound gamma distribution with parameters $n$ and $m$ encoding for the ligament corrugation and the width of the ligament size distribution, respectively. These parameters are found to saturate to values $n=4$ and $m=4$ at high polymer concentrations.