Computational and experimental analysis of drop formation for MEMS applications

Formation of incompressible Newtonian liquid drops of density ρ, viscosity μ, and surface tension σ from a nozzle into air is studied using high-speed, high-resolution visualization and large-scale, high-accuracy computation. Two drastically different physical problems are considered: (1) formation of millimeter-sized drops from capillary tubes by dripping and (2) ejection of drops from drop-on-demand (DOD) ink-jet nozzles of 10–50 μm radius. Since both DOD drop formation and drop-air interface pinch-off occur over very short time periods, novel experimental techniques are developed to image drop dynamics occurring within 100 μs. The computational modeling techniques developed here are indispensable as many quantities of interest such as pressure and velocity fields within growing drops are typically unavailable from experiments. The powerful experimental and theoretical tools are used to advance DOD drop production methods. Computational predictions are validated using experimental measurements and scaling theories describing local dynamics of liquid threads as they thin and pinch off. The interfaces of low-viscosity drops, where viscous forces remain negligible compared to surface tension and inertial forces, are shown to overturn before pinch-off for the first time by both experiment and computation. By contrast, moderate-viscosity drops undergo transitions from this potential flow (PF) scaling regime where viscous force is negligible to the inertial-viscous (IV) scaling regime where all three forces are important. The computed value of the minimum thread radius under IV scaling follows Eggers\u27s universal solution, demonstrating heretofore unparalleled accuracy from simulations. Numerical results uncover when Eggers\u27s solution ceases to be valid and probe the unexpected role played by viscosity in setting transitions from PF to IV regimes. The combined experimental and computational approach is used to overcome an obstacle present since the advent of DOD ink-jet printing. The new approach allows, for the first time, formation of drops with radii much smaller than the radius of the nozzle from which they are produced. Electric fields, due to deliberate voltage imposition or unwanted static charge accumulation, are well known to affect drop formation dynamics. Computations show that radial electric fields shorten the breakup length of low-viscosity liquid threads but have the opposite effect on high-viscosity threads