Contact angle roughness factor

Contact angle, 0, and spreading coefficient for a liquid on a solid surface comparison of spreading coefficient S for a smooth surface with S for a surface of roughness factor r... 

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... 

At present, many authors I20-I26 follow another concept From the plot of pj p [M /t) versus the surface tension of the liquids, the geometric factor K is calculated for those liquids that should wet the solid completely. By inserting this K value and [t]/p- ] M2/t for these liquids into Eq. (13). their contact angles 0 are calculated and used for the interpretation of the solid-vapor surface tension of the porous material. This procedure is dubious, because it can be expected that the contact angles, calculated from the Washburn equation, are affected by roughness and porosity. If we apply this procedure to the PTFE powder for hexadecane, a contact tingle 0 = 88 would be obtained. However, it is well known that the contact angle of hexadecane on a flat and smooth... 

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... 

Table 1 Contact Angle, 9, and Spreading Coefficient for a Liquid on a Solid Surface. Comparison of Spreading Coefficient S for a Smooth Surface with for a Surface of Roughness Factor r...

In the Wenzel model, the apparent contact angle 0w is obtained by correcting the Young s contact angle 0 with a roughness correction factor r... 

The theoretical discussion of contact angle and wetting to this point has assumed implicitly that the solid surface in question is a smooth, ideal plane. In fact, of course, very few solid surfaces even begin to approach such a state. The finest polished glass surface, for example, will usually have asperities of 5 nm or more. Commonly encountered polished surfaces, will be much rougher by factors of 10-1000. The earliest, and still most useful, quantitative attempt to correlate the observed contact angle of a liquid on a solid with the surface roughness is the Wenzel relationship which proposes a thermodynamic relationship such that... 

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