Axisymmetric numerical simulations of Rayleigh-Ohnesorge Jetting Rheometer (ROJER) with FENE-P rheology*

Spray formation is an important aspect of many industrial and biological processes like inkjet printing, the dispersal of fertilizers and pesticides, and human subject sneezing. Sprays are the result of an atomization process where the liquids are destabilized and undergo breakup into several fragments, i.e. ligaments and liquid threads, and eventually droplets, where complex topological transitions of the interface which feature “pinch-off singularities” emerge. Here, we perform axisymmetric simulations of an impulsively-started viscoelastic jet exiting a nozzle and entering a stagnant gas phase using the open-source code Basilisk. This code allows for efficient computations through an adaptively-refined volume-of-fluid technique to capture the interface. We use the FENE-P constitutive equation to describe the viscoelasticity of the fluid and employ the log-conformation transformation, which provides a stable solution for the conformation tensor. The entire jetting and breakup process is simulated, including the flow through the nozzle, which results in an inhomogeneous initial radial stress distribution that affects the subsequent breakup dynamics. The evolution of the velocity field and the elastic stresses in the nozzle are validated against analytical solutions and the early-stage dynamics of the jet is compared favourably to linear instability predictions. We elucidate how the thinning rate of the viscoelastic filament is determined by both the jet speed and the polymeric extensibility, highlighting their effect on the total stress balance of the non-Newtonian ligament. We also probe how the secondary droplet formation can be controlled by the finite extensibility of the polymeric chains, as well as the wavenumber of the forced oscillation of the injected liquid at the nozzle inlet.