Investigation of the vortex instability in a two-dimensional inkjet print-zone using numerical analysis
Physical Review Fluids, (January 2022)DOI: 10.1103/PhysRevFluids.7.013904
Abstract
A numerical model was employed to investigate the vortex instability in a two-dimensional inkjet print-zone. The simulation models the entrainment effect of the droplets on the airflow via a novel dispersed-phase continuum method that, due to the separation of length scales, treats the force exerted by the main droplets as a continuum smooth field. The trajectory and speed of the main droplets are also assumed to be unaffected by the airflow. The results indicate the existence of a dimensionless droplet density threshold (Nc) at which the vortex shifts from steady to oscillatory. This demonstrates that the two-dimensional instability has a super-critical Hopf type of bifurcation, i.e., the shift from stable to unstable is continuous but not smooth and the amplitude of oscillation follows the asymptotic square-root behavior characteristic of this type of bifurcation. Further, as shown by tests with stationary paper and no induced cross-flow, the mechanism of instability cannot be attributed to the interaction between the incoming cross-flow and the entrained airflow. Characterizing the two-dimensional airflow instabilities and their mechanism provides a better understanding of the airflow dynamics in the print gap of inkjet printers.