One-dimensional simulation of drop breakup in inkjet

H. Jiang, H. Tan
Washington State University Vancouver,
United States

Keywords: inkjet printing, drop breakup, method of lines


Drop-on-demand (DoD) inkjet printing technology has a wide variety of applications in research and manufacturing, such as 3D printing, functional material printing, MEMS fabrication and tissue engineering, due to its advantage of high precision, simple process, low cost and high use ratio of material. When the liquid is ejected from the DoD inkjet device, it undergoes a series of physical events: 1. liquid jet emerging from the nozzle due to actuation; 2. the jet pinching off from the nozzle; 3. the jet breaking up into head droplet followed by multiple satellite droplets due to surface tension. The satellite droplets often cause detrimental effect on printing quality, because they tend to scatter on the substrate. Therefore, fundamental understanding of the breakup of inkjet-printed droplets is vital to the various applications of the inkjet technology. In the past, we have successfully developed a full 3D computational fluid dynamics (CFD) to model the droplet ejection process from inkjet print-heads. Although the full-scale CFD simulations can reveal the physical detail in droplet breakup, it is not suitable for optimizing the device design because of high computational costs. Therefore, in this study, we use a simplified 1D slender-jet analysis based on the lubrication approximation to study the breakup of droplet. In the slender-jet approximation, the free-surface (liquid-air interface) is represented by a shape function so that the full Naiver-Stokes can be linearized into a set of simple partial different equations (PDEs). The discrete PDEs are solved by method of lines (MOL) in which PDEs are transformed into a system of ordinary differential equations (ODEs). Because of the motion of slender-jet and droplets, the surface evolution is tracked by a moving staggered mesh in Lagrangian coordinates. The MATLAB is used to implement the algorithm and simulation. We validate the model and code using the experimental data as well as CFD simulations. Owing to the high repeatability of physical events in inkjet process, a stroboscopic high speed imaging system is established and successfully records the process in videos. A MATLAB code is developed to measure the edge, volume and velocity of droplets in these videos and good agreement is found between experiment and simulation. The research demonstrates that the proposed model enables rapid parametric analysis of jet breakup and droplets formation as a function of nozzle dimensions, driving pulse configurations, and fluid properties.