Geometric Interpretation of Surface Tension Equilibrium in Superhydrophobic Systems

Abstract

Surface tension and surface energy are closely related, although not identical concepts. Surface tension is a generalized force; unlike a conventional mechanical force, it is not applied to any particular body or point. Using this notion, we suggest a simple geometric interpretation of the Young, Wenzel, Cassie, Antonoff and Girifalco-Good equations for the equilibrium during wetting. This approach extends the traditional concept of Neumann's triangle. Substances are presented as points, while tensions are vectors connecting the points, and the equations and inequalities of wetting equilibrium obtain simple geometric meaning with the surface roughness effect interpreted as stretching of corresponding vectors; surface heterogeneity is their linear combination, and contact angle hysteresis is rotation. We discuss energy dissipation mechanisms during wetting due to contact angle hysteresis, the superhydrophobicity and the possible entropic nature of the surface tension.

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“…As any other "entropic force", the value of increases with temperature [21,28]. The experimental observations evidence the opposite temperature trend: both surface and line tensions are decreased with temperature [4,21,10]. This means that the "interaction" part of the line tension in the studied systems prevails on the "entropic" one.…”

“…2 with the entropic contribution to the entire line tension seen as a sum of "interaction-" and "entropy"-inspired inputs. As any other "entropic force", the value of increases with temperature [21,28]. The experimental observations evidence the opposite temperature trend: both surface and line tensions are decreased with temperature [4,21,10].…”

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