A nondimensional model of droplet ejection for drop-on-demand inkjet printing

Abstract

A nondimensional model is established within the framework of the OpenFOAM® volumeof-fluid (VOF) method for computational fluid dynamics (CFD). In terms of the Reynolds number Re and capillary number Ca, which explicitly appear in the nondimensional VOF version of the Navier-Stokes equations, another dimensionless parameter Z = sqrt(Re/Ca) can be derived to characterize the ink properties (for a given nozzle size), and Re/Z = sqrt(ReCa) to serve as the nondimensional actuation strength. Most of the fundamental behavior of droplet ejection in drop-on-demand (DOD) inkjet printing appears to be controlled by Z and Re/Z, as noted by many previous authors. But the boundaries of the operational window in a Re/Z versus Z diagram are shown to change when the nondimensional actuation pulse width Δ˜τ (which determines the relative droplet size with respect to the nozzle size) is changed—a fact less discussed in the literature. By reducing Δ˜τ , the possibility of generating droplets of sizes smaller than a given nozzle size is systematically studied herewith. Moreover, the effect of the ink wetting property on the wall of the nozzle orifice is also briefly examined. Such a nondimensional model analysis could provide fresh insights into the complex droplet ejection behavior in DOD inkjet printing.