# Superhydrophobic surfaces

Started by Lauren Hartle, Fall 2011.

Entry has been combined with Superhydrophobicity, Superhydrophicity (misspelled) and Superhydrophobic. (LH 2011)

## Introduction

A water droplet on a superhydrophobic surface has a contact angle of greater than 150 degrees and a very low roll-off angle. In nature and in man-made materials, this has been achieved with Structured Surfaces. Advantages of such surfaces include the ability to repel water and self-clean.[3] Industrial applications include "self-cleaning window glasses, paints, and textiles to low-friction surfaces for fluid flow and energy conservation."[2] To predict when a droplet will wet the surface and when it will be repelled, one can compare the contact angle for complete wetting to the contact angle for a droplet resting atop the surface structure with no penetration. When a droplet is in intimate contact with the surface, the Wenzel state, the following equation applies:

<math>\cos{\theta}_c = r \cos{\theta}</math>

where r is the ratio of the actual area to the projected contact area and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material.. When the droplet rests atop the surface structure, it is in the Cassie-Baxter state, modeled by:

<math>\cos{\theta}_{c} = \phi \left( cos \theta + 1 \right) - 1</math>

where <math>\phi</math> is the area fraction of the solid in contact with the liquid, and <math>\theta</math> is the contact angle of the droplet on a flat surface of the same material. Setting the two contact angles equal gives the following critical condition for the transition between the Cassie-Baxter and Wenzel states.

<math>cos \theta = \frac {\phi - 1}{r -\phi}</math>

What, if any, is the relation between "r" and \phi ? Why would we expect a "transition" from the Cassie-Baxter to the Wenzel states?

By this prediction, a droplet resting atop surface structures might be a lower energy state than intimate contact when the cosine of the contact angle on a flat surface is less than the right hand side of the equation.

What is the difference in "behavior" between the two states?

It is argued that surface structure can produce superhydrophobic effects, even on a hydrophilic surface. For example, lotus leaves have been shown to be superhydrophobic, despite the waxy, weakly hydrophilic coating on the surface.[1] It has been demonstrated that the surface of a lotus leaf is superhydrophobic in part due to the presence of hierarchical surface structures structures consisting of micro- and nano-scale features. [2] Figure 1 contrasts the state of a droplet on a flat surface and surfaces of increasingly complex structure.

Butterfly wings and parts of pitcher plants have observed superhydrophobic properties. Figure 2 shows an image of real lotus leaf structures at different scales from reference 2.

## References

[1]"Design parameters for superhydrophobicity and superoleophobicity". Anish Tuteja, Wonjae Choi, Gareth H. McKinley, Robert E. Cohen, and Michael F. Rubner. *MRS Bulletin* 33 (8), 752-758 (August 2008)

[2]"Fabrication of artificial Lotus leaves and significance of hierarchical structure for superhydrophobicity and low adhesion". Kerstin Koch, Bharat Bhushan, Yong Chae Jung and Wilhelm Barthlott. *Soft Matter*, 2009, 5, 1386–1393.

[3]"Self-cleaning materials: Lotus leaf inspired nanotechnology" Peter Forbes, *Scientific American* 30 July 2008.

## See also

Superhydrophobic surfaces in Effects of contact angles in Capillarity and wetting from Lectures for AP225.

## Keyword in References

Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity

Growth of polygonal rings and wires of CuS on structured surfaces