Continuous droplets' charge method for the Lagrangian simulation of electrostatic sprays

• Classical Lagrangian simulations of electrosprays are slow.
• Calculating the droplet–droplet interactions dominates such numerical simulations.
• Treating the droplets' space charge as a continuum is proposed.
• Spray regions where droplets' charge cannot be treated as a continuum are identified.
• Spray system comprising 26000 droplets computes 112 times faster by the new method.

A main drawback of classical simulation of electrostatic sprays based on the Lagrangian description of droplet trajectories is the large number of droplet-to-droplet electrical interactions that must be computed. We present and assess a new methodology in which some of these interactions are computed using a mean electrical field due to the droplets space charge considered as a continuum. This method has been applied to two systems, comprising 26000 droplets and 3500 droplets, resulting in 112 and 9 times faster computation, without loosing accuracy, as demonstrated in the predictions of impinging flux, droplet number density, and local droplet diameter.