Abstract

According to the principle that the contact angle of liquid droplet always increases on a limited liquid-solid interface, it is suggested that the integration of many small-size limited liquid-solid interfaces results in the increase of the hydrophobicity of lotus-leaf-like micro-convex-concave surfaces. Mathematical equations of the stability of liquid-droplets on the surface of lotus-leaf-like structure were established. The relationship between the theoretical critical-radius of the void of micro-convex-concave surface and the nature of the solid and the liquid was drawn. The three conditions of realizing hydrophobicity were described. The result of computation has shown that when the radius of the void of micro-concave-convex surface is less than the theoretical critical-radius rc, the droplets may always be in a stable state on the solid surface with the contact angle greater than 90°. The minimum area of the liquid-solid interface and low surface energy of solids are important factors in realizing hydrophobicity. The effective work of adhesion Wa′ was proposed as a criterion for measuring the hydrophobic ability of the solid surface.

Highlights

  • According to the principle that the contact angle of liquid droplet always increases on a limited liquid-solid interface, it is suggested that the integration of many small-size limited liquid-solid interfaces results in the increase of the hydrophobicity of lotus-leaf-like micro-convex-concave surfaces

  • The current research only clarifies the special constructs of the surface of hydrophobic materials, that is, the hydrophobic material should have a rough surface and low surface energy [5,6]

  • Cassie [8] believed that there existed two interfaces when water droplets were on the rough surface, namely, the contact interface between the water droplets and the solid and the interface between the water droplets and the air formed because the water droplets were not able to enter microscopic holes due to the capillary phenomenon

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Summary

The theoretical critical-radius of the void

When a water droplet covers a limited liquid-solid surface with microscopic holes, it is assumed that the thickness of the secondary structure in Figure 6 is δ = 0.001 m, and Figure 7 is a relationship curve between the critical radius rc of the hole and the contact angle θ when the water droplet is in the stable state, which is obtained by calculating eq (5). The surface of the pore canal was designed to be ideally smooth and the included angle of the surface of each cylinder was 90°, while the surface of the actual hydrophobic materials is moderately curved rather than the sharp pore canal boundary, and the environment is very complex and harsh

The effective work of adhesion
Conclusions

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