Theoretical study on wettability of microstructured surface

Abstract

Wettability is a material property which characterizes how well a liquid is spread on a solid substrate, and is measured by a contact angle, that is, the angle between a solid substrate and the interface between liquid and the vapor. The contact angle is determined by the relation between surface tensions between a liquid, substrate and the vapor. Materials with a small contact angle are called hydrophilic materials, while those with a large one are called hydrophobic materials. Leaves of plants such as lotuses, roses, etc. have many small bumps on their surface, and the geometry makes the leaf have special wetting properties. Based upon this observation, research for developing technologies of self-cleaning, anti-fogging or droplet transportation by roughening the substrate has been carried out intensively. Conventionally, wettability of rough surfaces has been explained with the Wenzel and Cassie-Baxter modelling. In the conventional modellings, the size of the droplet has been assumed to be infinitely larger than the geometry of the surface textures, and the contact angle is predicted or the most stable wetting mode is chosen based on the assumption. However, when the surface is roughened with microstructures, the size of the droplet often comparable with the size of the surface textures, and the assumption of the infinitely large droplet size does not hold anymore. Therefore, the wetting phenomena of the surface with microstructures could not fully explained with the classical wetting modellings or theories. In this dissertation, I present new theories and modelling that can explain various wetting phenomena on microstructured surfaces, based on a free energy analysis which takes into consideration of local energy minima and energy barriers between them. First, we analyze the free energy of a finite sized droplet on a textured surface, and show that the droplet has many local energy minima points on the surface. Additionally, we show that the droplet at global minimum state can only have its contact angle of the value from the conventional wetting theory when the droplet is sufficiently larger than the characteristic size of the textured surface. Second, we show that there exists a new thermodynamically stable wetting state between Cassie-Baxter and Wenzel state, possessing curved bottom surface, if the droplet size is comparable with the size of the surface textures. In addition, we explain that the wetting transition of evaporating droplet occurs through the new wetting states. Third, we discuss how gravity affects the advancing and receding of the tip of the droplet. Conventionally, the gravitational effect on the droplet smaller than the capillary length has been known to be negligible. However, with the geometrical and free energy based stability analysis, we show the gravity can affect the advancing and receding of the droplet smaller than the capillary length, even for the droplet smaller than the capillary length. Also, we could explain the advancing and receding of the droplet of the gradually changing volume with the gravitational effect on the phenomenon. Fourth, we predict the sliding condition of the droplet on the tilted textured surface based on the droplet contour prediction and the free energy stability analysis, and find the droplet shape when it starts to slide down on the surface. Finally, we develop a new numerical methodology which enables us to model wetting phenomenon on rough surfaces, capturing the attachment and detachment between liquid interface and substrate. With the numerical methodology, we validate the effects of gravity on the advancing and receding a droplet, and clarify the condition that the droplet starts to slide on a tilted surface. Although the experimental research for developing surfaces with special wetting properties has been widely conducted, the design rules for surfaces with required wetting properties have not been made so far. The present study provides more sophisticated theories and modelling for various wetting phenomena on microstructured surfaces, offering a deeper physical understanding of wetting on the surfaces, and ultimately, can be used to make design rules for developing surfaces with specific wettability.