Droplet Impact on a Solid Surface: Analytical Modeling and Experimentation for Spreading Phase

A normal droplet impacting a flat, stationary, solid surface exhibits symmetric spreading. A key aspect of this symmetric spreading, particularly during deposition at low Weber numbers, is the formation of a rim along the lamella edge. The rim is crucial for predicting maximum spreading, and its dynamics can be captured using a set of ordinary differential equations in numerical calculations. However, establishing a reasonable initial condition remains challenging.

In addition to symmetric spreading, various studies have explored how to disrupt symmetry for industry demands, for example, reducing contact time for anti-icing purposes. However, no attempts to date have been conducted to restore symmetry from asymmetric spreading, such as spreading over an inclined or moving surface, where tangential velocity naturally breaks the symmetry.

To address these issues, this thesis investigates: 1) the rim genesis for a normal impact at low Weber numbers; 2) a model that elaborates how wettability can be manipulated to guide an asymmetric lamella towards a symmetric shape; and 3) experimental validation of this model.

This work demonstrates that rim formation is driven by a developing motion at the lamella edge — the rim region — induced by deceleration due to capillary forces. The dynamic pressure from this motion creates a difference in curvature, and hence the dynamic pressure must be balanced by the Laplace pressure within the rim region. The rim forms when the rim region becomes thicker than the lamella. An analytical model was developed to predict the time when the rim starts to form and the configuration of the droplet at this moment, validated by OpenFOAM simulations and experimental recordings.

Experimental results also support the proposed model for symmetry restoration based on the Taylor-Culick theory, demonstrating that manipulating wettability can accelerate the receding of the stretched contact line to counteract the stretch. A method for fabricating a patch with tunable wettability contrast has been developed for surface design to achieve symmetry restoration. Experimental results confirm the effectiveness of this patch design in correcting asymmetric spreading for water droplets impacting a surface under the following Weber number conditions: Wen ≤ 300, Wet ≤ 300, and 0.51 ≤Wen ⁄ Wet≤2.04.