# Wetting and Roughness: Part 3

Authors: David Quere

Annu. Rev. Mater. Res. 2008. 38:71–99

#### Soft matter keywords

microtextures, superhydrophobicity, wicking, slip

By Alex Epstein

### Abstract from the original paper

We discuss in this review how the roughness of a solid impacts its wettability. We see in particular that both the apparent contact angle and the contact angle hysteresis can be dramatically affected by the presence of roughness. Owing to the development of refined methods for setting very well-controlled micro- or nanotextures on a solid, these effects are being exploited to induce novel wetting properties, such as spontaneous filmification, superhydrophobicity, superoleophobicity, and interfacial slip, that could not be achieved without roughness.

In Part 3, we examine the sectionsSuperhydrophobicityandSpecial Properties

## Soft matters

If a hydrophobic solid is rough enough, the liquid will not conform to the solid surface as assumed by the Wenzel model, and instead air pockets will form under the liquid and support it. This is the Cassie state. It is observed if the energy of the liquid-vapor interfaces is lower than the energy of wetting the solid. In the case of our beloved micro/nanoposts, we can assume that the liquid-air interfaces are flat (since the Laplace pressure can be assumed zero at the bottom of the drop) and that the wet surface area <math> \sim\ (r - \phi_s)</math> and liquid-air area <math> \sim\ (1 - \phi_s)</math>. The Cassie state is favored when

<math>(r - \phi_s)(\gamma_{SL} - \gamma_{SA}) > (1 - \phi_s)\ \gamma_{LA}</math>

and the corresponding critical Young angle is

<math>cos\ \theta_c = -\frac{1 - \phi_s}{r - \phi_s)</math>

For very rough solids (<math>r \gg 1</math>)

### References

1. Quere, David. Wetting and Roughness. Annu. Rev. Mater. Res. 2008. 38:71-99

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