Droplet charging regimes for ultrasonic atomization of a liquid electrolyte in an external electric field

Distinct regimes of droplet charging, determined by the dominant charge transport process, are identified for an ultrasonic droplet ejector using electrohydrodynamic computational simulations, a fundamental scale analysis, and experimental measurements. The regimes of droplet charging are determined by the relative magnitudes of the dimensionless Strouhal and electric Reynolds numbers, which are a function of the process (pressure forcing), advection, and charge relaxation time scales for charge transport. Optimal (net maximum) droplet charging has been identified to exist for conditions in which the electric Reynolds number is of the order of the inverse Strouhal number, i.e., the charge relaxation time is on the order of the pressure forcing (droplet formation) time scale. The conditions necessary for optimal droplet charging have been identified as a function of the dimensionless Debye number (i.e., liquid conductivity), external electric field (magnitude and duration), and atomization drive signal (frequency and amplitude). The specific regime of droplet charging also determines the functional relationship between droplet charge and charging electric field strength. The commonly expected linear relationship between droplet charge and external electric field strength is only found when either the inverse of the Strouhal number is less than the electric Reynolds number, i.e., the charge relaxation is slower than both the advection and external pressure forcing, or in the electrostatic limit, i.e., when charge relaxation is much faster than all other processes. The analysis provides a basic understanding of the dominant physics of droplet charging with implications to many important applications, such as electrospray mass spectrometry, ink jet printing, and drop-on-demand manufacturing.