# Difference between revisions of "Uni-directional liquid spreading on asymmetric nanostructured surfaces"

Title: Uni-directional liquid spreading on asymmetric nanostructured surfaces

Reference: E.N. Wang, K.-H. Chu, R. Xiao G.C. Rutledge, G.H. McKinley, “Science” 318, 1618 (2007).

## Soft matter keywords

asymmetry, contact angle, wetting, surface force, surface tension, nanopillars

## Abstract from the original paper

Controlling surface wettability and liquid spreading on patterned surfaces is of significant interest for a broad range of applications, including DNA microarrays, digital lab-on-a-chip, anti-fogging and fog-harvesting, inkjet printing and thin-film lubrication. Advancements in surface engineering, with the fabrication of various micro/nanoscale topographic features, and selective chemical patterning on surfaces have enhanced surface wettability and enabled control of the liquid film thickness and final wetted shape. In addition, groove geometries and patterned surface chemistries have produced anisotropic wetting, where contact-angle variations in different directions resulted in elongated droplet shapes. In all of these studies, however, the wetting behavior preserves left–right symmetry. Here, we demonstrate that we can harness the design of asymmetric nanostructured surfaces to achieve uni-directional liquid spreading, where the liquid propagates in a single preferred direction and pins in all others. Through experiments and modelling, we determined that the spreading characteristic is dependent on the degree of nanostructure asymmetry, the height-to-spacing ratio of the nanostructures and the intrinsic contact angle. The theory, based on an energy argument, provides excellent agreement with experimental data. The insights gained from this work offer new opportunities to tailor advanced nanostructures to achieve active control of complex flow patterns and wetting on demand.

## Background

This paper presents a new method for manipulating the wetting behavior of liquid droplets on solid surfaces. Wang et al. demonstrate unidirectional wetting of droplets on surface by imparting tilted micro- and nanometer scale patterned texture on the surface.

Fig 1: Time-lapse images showing uni-directional spreading of a droplet of water atop nanopillars bent at a 12◦ deflection angle, the left image showing the side view, and the right image showing the above view. The parameters of the nanopillars are 500 nm diameters, 3.5 µm spacings, heights of 10 µm deﬂected at 12◦ as shown in Fig. 2.

## Soft Matter Example

The examples of soft-matter research within this paper relate to the surface forces that govern surfaces’ liquid-solid interfaces and wetting behaviors. While this research and paper do not pursue variation in the chemical dependence of surface forces, the research does employ the surface forces at the liquid solid interface in order to manipulate the wetting behavior. Regarding surface tensions of a liquid, solid, and surrounding medium, wetting of a droplets on flat surfaces act according to the Young-Dupre equation, which balances solid-gas, solid-liquid, and liquid-gas surface tensions acting on the droplets:

$\gamma_{SG}= \gamma_{SL} + \gamma_{LG}\cos\theta$

When anisotropic roughness is introduced, the wetting behavior of otherwise flat surfaces act according to the Wenzel model, which follows the equation:

$\cos\theta$* = $r\cos\theta$,

where r is the roughness ratio of the textured surface. As described by the Young-Dupre equation, the change in contact angle due to roughness corresponds to a change in the overall liquid-solid surface tension. Because of the asymmetric tilting of the posts that are detailed in the paper, the roughness ratio of the surfaces is different along different axes. Accordingly, the surface tension forces in respective directions along the tilting will be varied, and this is the cause of the unidirectional wetting that is described in the paper.

Fig. 2: Side view comparison of wetting behavior on symmetric and asymmetric nanostructured surfaces. The above image shows the symmetric liquid spreading of a 1 µl droplet of water on typical vertical nanopillars. The below image shows the uni-directional liquid spreading droplet a droplet of the same size on the similar nanostructures as the top image, but with a 12◦ deflection angle. Insets are the SEM images of the upright and bent posts, respectively, with scale bars at 10 µm.

## Results

As evident in Fig 2, the wetting of a droplet on the asymmetrically patterned surfaces flows toward the direction of the tilting. This indicates that, along the axis of tilting and in accordance with the Young-Dupre equation, the force applied by the surface tension of the liquid-solid interface is greater in the direction away from the tilting, where the contact angle is greater, than in the direction toward the tilting. The conclusion that the attractive surface force would be greater away from the tilting is somewhat intuitive, because more of the surface of each post is exposed away from the tilting than in the direction toward the tilting. Since surface tension induced forced attracts the droplet, the larger liquid-solid surface tension force limits the spreading of the droplet, and the droplet is inclined to flow in the direction of the tilting, where less surface force is applied to the liquid by the solid.

## References

[1] E.N. Wang, K.-H. Chu, R. Xiao, G.C. Rutledge, G.H. McKinley, “Science” 318, 1618 (2007).