Compact model for the characterization of a piezoelectric bend-mode droplet generator

In the present paper a compact model for a piezoelectric drop-on-demand (DoD) printhead is derived from basic electrical, mechanical and fluid mechanical relationships. The model covers the whole droplet generation process, spanning over the electrical as well as the mechanical and fluidmechanical domains. It allows predictions about essential droplet characteristics, such as droplet volume and flight velocity, for a given set of droplet generator (DG) dimensions, material and fluid properties and a predetermined electrical excitation. This enables the targeted adaption of the droplet generator´s design to varying application requirements, such as different fluid properties, with a minimum number of design iterations. The model is implemented by transferring the resulting differential equations to the Matlab/SIMULINK™ simulation environment. It is verified by comparing its output with an extensive empirical dataset which is obtained by fabricating a selection of droplet generators with different geometrical dimensions and testing them with several different fluids. Despite the fact that the model is based on strongly simplified physical relationships, it is able to accurately predict the minimum excitation voltage needed for droplet generation as well as the droplet velocity. However, the volume of the ejected droplets could not be predicted with satisfactory results, which is attributed to the limited accuracy of the nozzle submodel.