Wenzel equation
Susanna Laurén Nov 26, ’24 < 5 min

Evaluate the influence of surface roughness on wettability through Wenzel equation

Understanding the interaction between surface roughness and contact angle is crucial in various scientific and industrial applications. This relationship plays a pivotal role in determining the wetting and adhesion properties of materials, which are essential in fields ranging from material science to biotechnology.

The Role of Surface Roughness

Surface roughness is a key factor that influences the contact angle of a liquid on a solid surface. The contact angle is the angle formed at the junction where the liquid, solid, and vapor phases meet. It provides insights into the wetting properties of a surface, which is important for applications such as coating, printing, and adhesion.
Traditional methods of measuring contact angles often overlook the influence of surface roughness, focusing solely on the chemical composition of the surface. However, surface roughness can significantly alter the apparent contact angle, thereby affecting the material's wettability.

Wenzel equation and 3D Topography 

The relationship between roughness and wettability was defined in 1936 by Wenzel who stated that adding surface roughness will enhance the wettability caused by the chemistry of the surface. For example, if the surface is chemically hydrophobic, it will become even more hydrophobic when surface roughness is applied. Wenzel’s statement can be described by: 

cosΘm = r * cosΘY 

where Θm is the measured contact angle, ΘY is Young’s contact angle and r is the roughness ratio. The roughness ratio is defined as the ratio between the actual and projected solid surface area (r=1 for a smooth surface and > 1 for a rough surface).

To utilize the Wenzel equation, the roughness ratio, r, needs to be known. The Attension Theta Topography offers a sophisticated approach to measuring surface roughness ratio alongside contact angles. Theta Topography combines the optical tensiometer Theta Flow and 3D topography module into one instrument. The topography module employs sinusoidal fringe projection phase-shifting, enabling high-resolution 3D characterization of surface features. By using structured lighting, it projects light patterns onto a sample and captures images to reconstruct the 3D shape of the surface. 

The module will give three-dimensional surface roughness parameters out of which Sdr is utilized to calculate the roughness ratio

r = 1+ Sdr/100 

Applications and Implications

The ability to measure both surface roughness and contact angle simultaneously allows for a more comprehensive analysis of material surfaces. This capability is particularly useful in optimizing surface treatments and coatings, where both chemical and physical surface properties must be considered.

For example, in the field of biocompatibility, the surface roughness of implants can influence cell adhesion and tissue integration. Similarly, in the development of catalytic materials, a high surface area is often desirable, and understanding the role of surface roughness can aid in optimizing these materials for better performance.

Conclusion

Evaluating the influence of surface roughness on contact angle is essential for optimizing material properties for specific applications. The 3D Topography Module provides a powerful tool for achieving this, offering detailed insights that can lead to improved material performance and innovation in various fields. By integrating surface roughness measurements with contact angle analysis, researchers and engineers can better understand and manipulate the wetting and adhesion characteristics of materials.

To learn more about the topography module and roughness-corrected contact angles, please download the white paper through the link below.

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White paper

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