Ph.D. Thesis Defense by Ashley James

(Dr. Marc K. Smith, advisor)

"Vibration Induced Droplet Ejection"

Abstract

Vibration induced droplet ejection is a novel way to create a spray. In this method, a liquid drop is placed on a vertically vibrating solid surface or membrane. The vibration leads to the formation of waves on the free surface. Secondary droplets break off from the wave crests when the forcing amplitude is above a critical value. When the forcing frequency is small, only low-order, axisymmetric wave modes are excited, and a single secondary droplet is ejected from the center of the primary drop. When the forcing frequency is high, many high-order, nonaxisymmetric modes are excited, the motion is chaotic, and numerous small secondary droplets are ejected simultaneously from across the surface of the primary drop. In both frequency regimes a crater may form which collapses to create a liquid spike from which droplet ejection occurs.

 Experiments were performed in which a drop was placed on a membrane vibrating at high frequency. The driving amplitude required for waves to form, and the driving amplitude required for secondary droplets to be ejected, were determined. The effects of the system parameters were investigated. In some cases droplet ejection began slowly, but after a delay became so rapid that the droplet seemed to instantaneously burst into a spray.

Droplet ejection changes the loading of the membrane, and thus changes the response of the membrane to the forcing. Because of this, there is an interaction between the ejection process and the vibration of the coupled drop-membrane system. A simple model was developed to describe this interaction. The model describes the resonance characteristics of the coupled system and provides an explanation for the sudden bursting behavior seen in the experiments.

An axisymmetric, incompressible, Navier-Stokes solver was developed to simulate the low-frequency ejection process. A volume-of-fluid method was used to track the free surface. Surface tension was incorporated using the continuum surface force method. Time sequences of the simulated interface shape were compared to experimentally obtained images. The conditions under which ejection occurs and the effect of the system parameters on the process were determined. The dynamics of the droplet ejection process was investigated.