Ph.D. Thesis Defense by Steve Benintendi
(Dr. Marc K. Smith, advisor)
"Thermocapillary Migration Of A Three-Dimensional Liquid Droplet On A Solid Surface"
The behavior of a three-dimensional liquid droplet on a non-uniformly heated or cooled horizontal solid surface has been examined by developing a simplified model problem. For a thin viscous droplet, a two-dimensional evolution equation was derived using lubrication theory and includes the effects of viscosity, gravity, surface tension, slip at the contact line, and thermocapillarity. The evolution equation was then coupled to a dynamic contact-line boundary condition, relating the contact-line speed to the apparent contact angles, to describe the bulk motion of the droplet. The behavior of the droplet was examined in terms of the imposed thermal field of the solid surface when the mobility capillary number is assumed small and there is no contact-angle hysteresis.
The results showed that for any amount of imposed thermal gradient, the three-dimensional droplet evolved toward a steady state characterized by bulk droplet migration in the direction of cooler temperatures at constant velocity and without a change in contact line or interfacial shape. The quantities used to characterize the steady-state configuration were the migration speed, the droplet half-length and the droplet half-width. These were determined in terms of the thermal forcing parameters.
The three-dimensional system examined here exhibits an instability that has not been previously seen. The instability is characterized by an increase in the droplet half-length and half-width and is highlighted by the formation of a dimple at the center of the droplet. Although the nature of this instability is not completely clear at this time, the results indicate that it is caused by three-dimensional disturbances and arise when there is very little contact-line motion. Based on this, it is postulated that the observed behavior is initiated by a contact-line perturbation and not an interfacial disturbance. This project will be extended by examining the three-dimensional instability associated with the axisymmetric base state. This will shed some light on the nature of the instability and allow a physical explanation for the formation of the dimple.