Mathematical modelling of superhydrophobic surfaces for determining the correlation between water contact angle and geometrical parameters

Abstract

Water-repellent surfaces have recently become an active area of research due to the desire to achieve self-cleaning, anti-sticking, and non-wetting properties on surfaces. These surfaces are required for different engineering applications. A superhydrophobic (SHP) surface achieves a water contact angle (CA) of 150° or greater. The physical understanding of the process by which surfaces attain superhydrophobicity is still limited, making it difficult to fabricate such surfaces by machining due to the hierarchical scale of the features involved. This work, therefore, aims to shed light on the physical understanding of the behaviour of a water droplet as it rests on a micro textured surface. In the first part of the work, a mathematical model is developed that follows a basic and novel approach of force balance considering a water drop sitting on a surface under static conditions. The various forces responsible for equilibrium are individually evaluated. The model used to describe a surface's interaction with water establishes the relationships between various parameters in the force balance system. From these relationships, the water contact angle (CA) required for superhydrophobicity was found through a simulation. In the second part of this work, arrays of projected micro-features were fabricated on different materials using deep X-Ray lithography (DXRL), micro wire EDM, and the wire wound method. The measured values of the CA on the fabricated surfaces were similar to the values obtained from the model. The proposed model, therefore, helps in designing SHP surfaces (SHSs) on large-scale arrayed micro-features based on several geometrical parameters.