Computational analysis of drop-on-demand drop formation

Abstract

Motivated by the desire to improve the theoretical understanding of drop-on-demand (DOD) ink-jet printing, a computational analysis is carried out to simulate the formation of liquid drops of incompressible Newtonian fluids from a simple capillary tube by imposing a transient flow rate upstream of the nozzle exit. Since the flow in a typical ink-jet nozzle is toward the nozzle outlet during part of the time and away from the nozzle outlet at other times, an inflow rate is adopted here that captures the essential physics and is given in dimensionless form by Q=(πWe∕2)sinΩt, where We is the Weber number (inertial/surface tension force), Ω is the frequency, and t is time. The dynamics are studied as functions of We, Ω, and the Ohnesorge number Oh (viscous/surface tension force). For a common ink forming from a nozzle of 10μm radius, Oh=0.1. For this typical case, a phase or operability diagram in (We,Ω)-space is developed that shows that three regimes of operation are possible. In the first regime, where We is low, breakup does not occur, and drops remain pendant from the nozzle and undergo time periodic oscillations. Thus, the simulations show that fluid inertia, and hence We, must be large enough if a DOD drop is to form, in accord with intuition. A sufficiently large We causes both drop elongation and onset of drop necking, but flow reversal is also necessary for the complete evacuation of the neck and capillary pinching. In the other two regimes, at a given Ω, We is large enough to cause drop breakup. In the first of these two regimes, where Wec1<We<Wec2, DOD drops do form but have negative velocities, i.e., they would move toward the nozzle upon breakup, which is undesirable. In the second breakup regime, where We>Wec2, not only are DOD drops formed, but they do so with positive velocities.