Nonlinear dynamics of oscillations and breakup of supported drops

Abstract

The controlled production of liquid drops is of technological and scientific interest because of applications in fields as diverse as inkjet printing, genomic analysis, drug discovery, solvent extraction, atomization coating, and crop spraying. This thesis develops numerical algorithms of high accuracy based on the Galerkin/finite element method that are then used to analyze certain classical and novel free boundary problems that arise in drop formation. First, the much studied problem of drop formation from a capillary at constant flow rate, which had heretofore been inadequately understood, is analyzed. The new algorithm is demonstrated to have superior accuracy and convergence properties compared to existing algorithms in that its predictions are shown to be within 1–2% of new and old experimental measurements and that it is capable of simulating the dynamics of dripping at all values of the relevant dimensionless groups. Once the robustness of the new algorithm is demonstrated, attention is turned to novel ways of forming small drops in the drop-on-demand mode where the force of gravity is negligible compared to that of surface tension. New situations investigated include drop ejection from an oscillating rod, drop formation from a capillary when the flow rate in it is oscillatory in time, and detachment of a portion of a pendant drop by the application of a heat flux to a section of the wall near the exit of the capillary. As a preliminary to studying the complex problem of satellite drop formation, the thesis also solves the long standing problem of recoiling and end-pinching of an initially static slender filament. It is demonstrated in all of the problems considered that the interfaces of drops overturn prior to breakup, thereby resolving once and for all the long-standing controversy over whether the surface of a viscous drop can overturn prior to rupture