Wenzel roughness factor

Where the surface roughness is not very great it might be adequately expressed by a simple Wenzel roughness factor [27,28],... 

Since the Wenzel roughness factor is an important parameter in many theoretical considerations of wetting phenomena [11-21], it was also calculated as the ratio between the actual surface area to the projected one (Eq. 4). A surface of hexagonally packed hemispheres is considered. In this case, the roughness factor is independent of the particle radii and approximately equal to 1.91 [31,40,41] ... 

In this work, ordered arrays of core-shell particles were used as model surfaces to study the water wetting behaviour of these surfaces. Two factors were varied in the wetting experiments (i) the shell chemistry and hence the solid surface tension of the organic shell, and (ii) the height roughness from sub- xm up to xm roughness values whereas the Wenzel roughness factor was kept constant. 

The effect of roughness on the apparent contact angle of a solid surface has been given quantitative form by R. N. Wenzel.8 If r, the roughness factor , is the ratio between the real and the apparent area of the surface, then... 

Some clarification of this problem resulted after Wenzel [103] developed a relation between the macroscopic roughness of a solid surface and the contact angle. Wenzel discussed the roughness factor, r (defined as the ratio of the true area of the solid to the apparent area or envelope), and its relation to the apparent or measured contact angle, 0 , between the liquid and the envelope to the surface of the solid and to the true contact angle, 0, between the liquid and the surface at the air-liquid-solid contact boundary. He derived the well known relation... 

The Cassie-Baxter-Wenzel theory [44, 47,48] defines the critical contact angle value on the smooth surface above this value, the Cassie-Baxter model is more stable wetting state and below this value the Wenzel model is the most stable wetting state. If the measured contact angle on a smooth surface is lower than this critical value and if the superhydrophobic behaviour is observed, the transition between the two models should be possible like, for example, with the LDPE surface treated in both plasmas. In this case, the roughness factor is 1.043, the contact angle on the dried surface reaches a value of 171° and the contact angle on the same surface partially wetted with water vapour or dipped in water is only 140°. 

In the Wenzel (W) state the topographic properties of the surface are descrihed hy a roughness factor r [4], which gives the ratio of the effective area of actual, rough surface to the ideal flat surface, i.e. r 1. The apparent contact angle is given by... 

The effect of roughness of the solid surface is to increase the actual area of contact between solid and liquid and also that of the unwetted solid per unit geometric area. The roughness factor, r, is defined as the real area of the solid divided by this geometrical area described by a boundary. Wenzel therefore proposed that Young s Eqn. 1 be modified as... 

Presenting the data in a cosine-cosine plot facilitates comparison with the Wenzel predictions (area E), a Unear function of surface energy (cosine of Young contact angle) with the roughness factor as slope and axis intercept of zero. 

Wenzel [15] considered the true area of a rough surface A (which takes into account all the surface topography, peaks and valleys) and the projected area A (the macroscopic or apparent area). A roughness factor r can be defined as... 

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