# Contact angle

*Edited by Pichet Adstamongkonkul, AP225, Fall 2011*

## Contents

## 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.[1] 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-called*goniometer*.[2]

The contact angle is independent of geometry and hence a material property. Recent publications on contact angles on deformable surfaces can be included.

## 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 <math>-120^o</math>. However, materials with high degree of roughness on the surface can increase the angle up to <math>-150^o</math>; the materials in this group are called superhydrophobic surfaces.[2]

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

<math>0=\gamma_{SG}-\gamma_{SL}-\gamma_{LG}cos(\theta_c)</math> where <math>\theta_c</math> is the contact angle.[3]

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.

This is commonly stated but is incorrect. The Young-Dupre equation resolves all the inbalances in energy - no unresolved force is left to cause a lift. Capillary rise is due to Laplace pressures.

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.[4]

- Human cornea: an extremely hydrophobic surface and, together with hydrophilic tears, maintain the lachrymal layer.

- Modified surfaces with enhanced hydrophilicity, via plasma treatment

This entry needs references to advancing and receding contact angles.

## 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.

## Keyword in references:

Contact angle associated with thin liquid films in emulsions

Dewetting-Induced Membrane Formation by Adhesion of Amphiphile-Laden Interface

Surface-Tension-Induced Synthesis of Complex Particles Using Confined Polymeric Fluids

Substrate Curvature Resulting from the Capillary Forces of a Liquid Drop

Steering nanofibers: An integrative approach to bio-inspired fiber fabrication and assembly

Liquid-infused structured surfaces with exceptional anti-biofouling performance

Liquid-Infused Nanostructured Surfaces with Extreme Anti-Ice and Anti-Frost Performance

Wetting in Color: Colorimetric Differentiation of Organic Liquids with High Selectivity

Elastic Instability in Growing Yeast Colonies

Electric-field-induced capillary attraction between like-charged particles at liquid interfaces

Dynamic mechanisms for apparent slip on hydrophobic surfaces

Linear stability and transient growth in driven contact lines

Evaporation-Driven Assembly of Colloidal Particles

Thermal bending of liquid sheets and jets

Self-Assembly of Spherical Particles on an Evaporating Sessile Droplet

Kinks, rings, and rackets in filamentous structures

The wall-induced motion of a floating flexible train

Confined developable elastic surfaces: cylinders, cones and the Elastica