Moving liquid droplets with inertia

Abstract

This thesis is a work on a contact line instability at a finite Reynolds number, 0 < Re < O(100). This problem corresponds to an immersion droplet applied in a liquid- immersion lithography machine. We perform extensive works to understand this instability problem by means of experimental, numerical, and theoretical ways. First, in order to measure the 3D internal flow pattern, we perform 3D-3C velocimetry techniques, i.e. tomographic particle image velocimetry and 3D particle tracking velocimetry. Furthermore, we observe droplet shape changes by shadowgraphy. Second, based on these experimental results, we develop a modified three-dimensional lubrication model including inertial effects. In this model, the pressure is described as a combination of dynamic pressure effects and capillary pressure effects. By this extended model, we obtain an analytical solution describing the relationship between opening angles and receding angles. Additionally, we show a self-similar flow pattern near the dewetting contact lines. Last, a simplified numerical model is introduced for a liquid immersion droplet. For the numerical computation, we adopt a flat cylinder and apply a zero flux boundary condition at the gas-liquid interface. The numerical results are compared with measurement results and give a good agreement.