One Dimensional Simulation of Droplet Ejection of Drop-on-Demand Inkjet

In this study, we present a 1D method to predict the droplet ejection of a drop-on-demand (DoD) inkjet which includes the drop breakup, coalescence, and the meniscus movement at nozzle orifice. A simplified 1D slender-jet analysis based on the lubrication approximation is used to study the drop breakup. In this model, the free-surface (liquid-air interface) is represented by a shape function so that the full Navier-Stokes (NS) equations can be linearized into a set of simple partial differential equations (PDEs) which are solved by method of lines (MOL). The shape-preserving piecewise cubic interpolation and third-order polynomial curve are employed to merge approaching droplets smoothly. The printhead is simplified into a circular tube, and a 2D axisymmetric unsteady Poiseuille flow model is adopted to acquire the relationship between the time-dependent driving pressure and velocity profile of the meniscus. Drop breakup and meniscus movement are coupled together by a threshold of meniscus extension to complete a full simulation of droplet ejection. These algorithms and simulations are carried out using MATLAB code. The result is compared with a high fidelity 2D simulation which was previously developed [10], and good agreement is found. This demonstrates that the proposed method enables rapid parametric analysis of DoD inkjet droplet ejection as a function of nozzle dimensions, driving pressure and fluid properties.