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Also, are there any exceptions that you know of?

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  • $\begingroup$ Welcome to Chemistry.SE. Would you share a little bit more about what you ope to learn? For example, do you want a low-friction or high-friction superhydrophobic surface? $\endgroup$ – Ben Norris Dec 17 '13 at 13:48
  • $\begingroup$ I want to find a high-friction superhydrophobic or preferably icephobic surface. $\endgroup$ – Thomas Dec 18 '13 at 14:34
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Since you are talking about hydrophobicity I am assuming you are interested in liquid-solid friction. If you are interested in solid-solid friction I can say only one thing: hydrophobicity and solid-solid friction are in general unrelated.

So for the liquid-solid case. I am going to give you an answer that gives some insight, but no concrete rules, because, as far as I know, there aren't any.

Superhydrophobic surfaces typically have some surface structure that allows the liquid to 'float' partly on air and partly on top of the surface structure . Friction is related to the amount of contact area where there is a no-slip boundary so that will decrease therefore friction will be lower. A cool application of this effect can be found in this 2013 PNAS article by Karatay et al.

However, if you have a droplet moving, instead of a full liquid stream, then there is a counter-acting effect which is called contact angle hysteresis, which allows a droplet to sustain a difference in contact angle at the front and back of the droplet. This causes a force counter-acting motion of the order of the surface tension of the liquid $\gamma$ and the difference between the contact angles $\Delta \theta$: $F=\gamma l \Delta \theta$, where $l$ is a lengthscale of the order of the droplet radius. This force basically acts as a static friction on the droplet.

The value of $\Delta \theta$ is a complex function of the amount of surface roughness, being 0 for a atomically smooth surface but also approaching 0 for roughness with a small typical lengthscale. Therefore it is hard to make a general statement whether superhydrophobic surfaces will have a lot or a little friction. It all depends on the details of the surface roughness.

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  • $\begingroup$ I agree with Michiel - solid/solid friction has to do with the roughness of the surface at both the macro and micro level more than it has to do with the chemical nature of the surface. $\endgroup$ – Ben Norris Dec 18 '13 at 14:38

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