Continuous Ink Jet technology, printer, droplets on demand, electrostatic field, Coulomb force, Lorentz force, ballistic trajectories, LiveLink™  for MATLAB®


Context / Goal

During continuous ink jet process, an ink jet is electrically charged by electrodes, scattered into several droplets and eventually printed onto the product. The charged droplets’ trajectories directly depend on the electric field generated by a second pair of electrodes under constant voltage. These are called deflexion electrodes. To ensure the best printing quality, mastering and controlling the droplets’ trajectories during their flight is of the utmost importance.

In order to aid future print heads design, a numerical model is created with COMSOL Multiphysics® to simulate the flight trajectories of the droplets as they undergo different forces : gravity, droplet-to-droplet interaction (Coulomb force), electrostatic force due to the deflexion electrodes (Lorentz force).


SIMTEC's Achievements / Results

Markem-Imaje and SIMTEC have designed a 2D print head model matching the droplets’ trajectories plane.

(Left) Print head photography and (right) 2D simplified geometry


The model was built according to the following steps :

  • 2D simplified geometry
  • Used experimental data in MATLAB® to set the charges of the droplets, thanks to COMSOL LiveLink™ for MATLAB®
  • Computed deflexion electrodes’ electric field through Maxwell-Gauss equation stationary solving

(Left) Electric field norm and (right) electric potentialoriginated by the deflexion electrodes

  • Computed the particle trajectories by applying the fundamental principle of dynamics to ink droplets, with the support of COMSOL Multiphysics® Particle Tracing module. Electric-field-provoked Lorentz force, gravity and electric droplets’ interactions (Coulomb force), which are repulsive because all droplet charges have the same sign, were taken into account

Influence of the charge of the droplet on the trajectory : (left) charge=0.48 pC vs(right) charge= 1.93 pC

The numerical model has been verified according to simplified analytical results, while the final droplets’ positions on the printing zone is in good agreement with the experimental results. This numerical work highlights the fruitful collaboration between Markem-Imaje and SIMTEC, in the perspective of a mastered and ambitious technology innovation.