Refilling characteristics of high frequency piezo driven ink jet print heads

Abstract

A piezo driven ink jet print head is in principle an open microfluidic system, there are no valves that control the direction of the flow. In order to avoid flooding of the nozzle plate at nozzle level a small under-pressure is maintained. In equilibrium the meniscus of the ink is retracted and pinned to the rim of the nozzle. This equilibrium is controlled by the surface tension of the ink and the setting of under-pressure controller. Operated at low frequencies, after droplet formation, there is ample time for the ink to return to the equilibrium state and to be ready for the next firing of a droplet. Driven at higher frequencies, in between droplets, there is no time to return to the equilibrium state and other mechanisms for refilling come into view. When the meniscus has retracted in the nozzle, the next pressure pulse needs to accelerate a relatively small amount of ink. Moreover the viscous drag in a partly filled nozzle is less compared to a completely filled nozzle. With a constant surface tension pressure, the Washburn equation learns that the refilling speed of a partly filled nozzle increases with decreasing filling of the nozzle. Both effects are supposed to cause that a print head driven at high frequency delivers enough fluid to nozzle to maintain droplet emission. In this paper this theoretical framework is extended by taken into account: <list list-type="bullet"> <list-item>• Droplet formation on the dynamics of the fluid motion,</list-item> <list-item>• Change of droplet volume at high frequencies,</list-item> <list-item>• Inertia effects due to the variable mass in the nozzle. A complete non-linear analysis will be outlined including:</list-item> <list-item>• Limitation of the capillary pressure; only close to the nozzle the capillary pressure becomes a linear function of the meniscus displacement, otherwise it is a constant,</list-item> <list-item>• The dependence of the viscous drag on the filling of the nozzle,</list-item> <list-item>• The effects of droplet formation,</list-item> <list-item>• Inertia effects due to the variable mass in the nozzle.</list-item> <list-item>• Calculations will be performed for a sample pump of which the dimensions are representative for a standard print head. Two inks will be investigated one with a viscosity of 0.01 Pa.s and another with a low viscosity equal to 0.002 Pa.s.</list-item> </list>The non-linear analysis will reveal many details of the fluid dynamics of the ink in a print head, including effects of surface tension, viscosity, droplet formation, pulse shape and repeat rate.