# Difference between revisions of "Wetting and Roughness: Part 1"

Wetting and Roughness: Part 1

Authors: David Quere

Annu. Rev. Mater. Res. 2008. 38:71–99

## Contents

#### 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 1, we look at the introductory chapter and consider the sections Microtextured Solids and Hemiwicking


## Soft matters

### Brief Intro

One of the authors of our course text, David Quere, authored this lovely review paper, which focuses on how the roughness of a solid affects its wettability. Controlling wettabilty of a solid surface is of great interest in many engineering contexts. The extremes, complete wetting and complete drying, are particularly desirable. Windshields should have a uniform film to maintain the glass transparency, and to remove dust particles under gravity or air flow. Surfaces that must have no liquid contamination should force drops to be spherical and virtually without contact, so that they roll off.

In the classical case of flat and chemically homogeneous solids explored by Young and Laplace, the relationship between the three interfacial surface tensions (equivalent to surface energies) determines the wetting condition. As Marangoni explained, a film extends from a liquid reservoir on a wetting solid, replacing $\gamma_{SA}$ by $(\gamma_{SL} + \gamma_{LA})$ if the spreading coefficient

$S = \gamma_{SA} - \gamma_{SL} - \gamma_{LA}$ > 0.


For S> 0 a drop spreads, while oppositely it coalesces into a spherical cap. Now, the chemical (or Young-Dupre) contact angle on a homogeneous flat surface is defined by our favorite equation:

$\gamma_{SA} = \gamma_{SL} + \gamma_{LA}cos\theta$

Fig. 1

The contact angle is fixed by the chemical nature of the three phases if the solid surface is flat. If the solid is rough, the rules of the game change. This Quere considers shortly.

To digress briefly, we can also define a drying parameter

$D = \gamma_{SL} - \gamma_{SA} -\gamma_{LA}$


If D > 0 the contact line will be withdrawn by surface forces until a film of air comes between the solid and the liquid. In other words, complete drying of the surface occurs. Interestingly this happens if water on freshly cleaned glass (high $\gamma_{SA}$) has an air bubble at the water-glass interface. And in the Leidenfront effect, D goes to zero. This is when a liquid is placed on a solid surface whose temperature greatly exceeds the liquid's boiling point, and the liquid rests on a film of its own vapor, therefore not contacting the solid. However D is never greater than 0 for any liquid on any flat solid, i.e., complete drying of a liquid resting on a flat solid is not possible. The emphasis is on "flat" because superhydrophobic rough surfaces enable complete drying (dewetting).

Before we consider roughness of surfaces, let's briefly consider wicking, or capillary draw into a porous material. The simple wicking parameter tells us whether a liquid will be drawn into a capillary tube:

$W = \gamma_{SA} - \gamma_{SL}$


Wicking or penetration occurs if W > 0, which corresponds to the contact angle being less than 90°, or the Laplace pressure behind the advancing meniscus being lower than the atmospheric pressure. When S > 0, W > 0 as well, and what happens is that a molecular thickness liquid film precursor advances along the tube walls, reducing interfacial energy; then the meniscus advances on the prewet tube surface, driven by the reduction of liquid-air interface. In this complete wetting scenario (not a bad approximation for a clean glass tube), $W = \gamma_{LA}$

1.