Drop Formation: From Dripping to Drop-on-demand Drop Production and Analysis Through Computation and Ultra High-speed Visualization
Friday, January 12, 2001 - 10:15am - 11:15am
Osman Basaran (Purdue University)
Drop formation plays a central role in applications as diverse as ink-jet printing, biochip arrayers for genomic analysis, spray coating, and separations. One objective of our research is to provide a fundamental understanding of drop production by so-called drop-on-demand (DOD) drop generators commonly found in ink-jet printers. In analyzing the complex problem of drop formation by a DOD device, we found it useful to first study the classical problem of continuous dripping from a capillary. We have tackled dripping through a dual-pronged approach relying on computation and high-speed visualization. In the computations, either the two-dimensional (2-d) Navier-Stokes system or else a one-dimensional (1-d) counterpart of it based on the slender-jet approximation is solved using the finite element method (FEM). Two versions of the 2-d FEM algorithm have been developed: one relies on algebraic and the other on elliptic mesh generation. Both are shown to predict the entire formation dynamics, including breakup, with 1% accuracy compared to experiments. When appropriate, the 1-d algorithm is used to study the formation of hundreds of drops in a sequence. This analysis makes it possible to develop an operability or a bifurcation diagram which at last provides the theory for the long-standing problem of a dripping faucet much fancied in the physics community. Since control of satellite droplets is a major issue in operation of printers as well as DNA arrayers, the 2-d algorithm is also used to study the fate of contracting slender filaments, which are precursors of satellites. Certain unexpected yet fascinating dynamical responses exhibited by satellites are confirmed by means of an ultra high-speed digital imaging system that is capable of recording multiple frames at an astounding frame rate down to 10 nanoseconds. The accuracy of our new 2-d algorithms will be highlighted by demonstrating that they can predict scaling laws, and transitions from one scaling law to another, determined from local analyses of the governing equations as breakup is approached. The talk will conclude by highlighting recent computational and experimental work underway in our group on DOD drop formation.