# Contact angle

Edited by Pichet Adstamongkonkul, AP225, Fall 2011

## Introduction

The contact angle is a quantitative measure of the wettability of the surface, represented by the angle at which a liquid or vapor interface makes with a solid surface. The angle is specific and determined by the interactions across the three interfaces. Typically, the contact angle is illustrated by a drop of liquid on the surface. The shape of the drop is governed by the Young-Laplace equation (contact angle is incorporated as a boundary condition of the equation.) Normally, the contact angle can be measured using the so-calledgoniometer.

## Connection to Capillarity/Wettability

The figure (from the lecture) illustrated different contact angles corresponding to different wettability of the surface, which depends on the relative hydrophobicity/ hydrophilicity of the surface compared to the liquid. Conventionally, the contact angle is measured as the angle between the solid surface and the liquid drop surface. In other words, the contact angle is the angle between the solid-liquid interfacial (surface) force (denoted as gamma_SL) and the surface tension or the liquid-vapor interfacial force (denoted as gamma_LG). The larger the angle, the more the drop is repelled from the surface, indicating a relatively higher hydrophobicity of the surface, in the case of water drop.

If the liquid strongly attracts to the surface, the drop of the liquid would spread out on the solid surface. On highly hydrophobic surfaces, the contact angle can be as big as $-120^o$. However, materials with high degree of roughness on the surface can increase the angle up to $-150^o$; the materials in this group are called superhydrophobic surfaces.

From the surface tensions at all three interfaces, we can explicitly write the Young equation that the system must satisfy at equilibrium:

$0=\gamma_{SG}-\gamma_{SL}-\gamma_{LG}cos(\theta_c)$ where $\theta_c$ is the contact angle.

In the capillary effect, the driving force that causes water to go up the capillary is the net surface tension, balancing between the solid-vapor interfacial tension that pulls in the upward direction , and the solid-liquid interfacial tension that pulls downward.

Examples of surfaces where the contact angles play an important role:

• Lotus leaf: superhydrophobic surface that causes the water droplet to roll over the surface without “wetting” the surface.

• Human cornea: an extremely hydrophobic surface and, together with hydrophilic tears, maintain the lachrymal layer.
• Modified surfaces with enhanced hydrophilicity, via plasma treatment

## References

[1] Lecture on Capillarity and Wetting, AP225 Fall 2011

[2] Wikipedia contributors. “Contact angle.” Wikipedia, The Free Encyclopedia. 27 Nov 2011.

[3] Robert J. Good. “Contact angle, wetting, and adhesion: a critical review.” Journal of Adhesion Science and Technology. 6.12 (1992): 1269-302.

[4] Wikipedia contributors. “Lotus Leaf.” Wikipedia, The Free Encyclopedia. 27 Nov 2011.