# Why does a metal paper clip float on water despite having an acute contact angle?

We know that a metal paper clip floats on water when it is carefully placed over the surface. This is attributed to the phenomenon of surface tension. I understand that, due to its weight it creates a depression in the fluid as seen in the image below:

Image source: Wikipedia

Due to this depression, there exists a vertical component of the otherwise horizontal force which supports the weight of the paper clip and ensures it stays on the surface. This is similar to placing a metal ball on a flexible rubber sheet. The following diagram shows a cross section of the paper clip and the forces acting on it:

Image source: My own work :)

I've learnt that the angle between the tangent planes at the solid surface and the liquid surface at the point of contact, is defined as the contact angle. Here it's $$\theta$$ and is obtuse. However, I've seen from different sources that metal-water contact angle is acute even in the presence of some surface contaminants, totally opposite to what is expected if it needs to be on top of water. The following statement is one such example:

Hydrophilic metal surfaces (copper, nickel) are completely wetted by water only if the surfaces are extremely clean. Surface contamination reduces the wettability drastically. Under most industrial conditions advancing contact angles between 40° and 80°, and receding contact angles smaller than 20° can be expected, and the contact angle hysteresis is large.

Source: The wettability of industrial surfaces: Contact angle measurements and thermodynamic analysis

Even though the above quote is for metals like copper and nickel, I think, even aluminium and iron (of which paper clips are made of) show a similar behaviour. If so, why does a metal paper clip float on top of water? Shouldn't it simply sink if there were no surface tension? Or is the obtuse contact angle (observed) related to the difference in contact angle near the top of a capillary tube of insufficient length?

Since we observe obtuse contact angle for an interface which ought to have an acute contact angle, will the result be same if we consider the other case? Or in other words, will a paper clip made of an ultrahydrophobic material (contact angle $$>150^\circ$$) float when placed on water?

If the normal paper clip had an obtuse contact angle, I wouldn't have had this doubt. The following statement from this answer to the question - How does surface tension enable insects to walk on water?, resonates with my idea of floating hydrophilic paper clips and sinking metal paper clips (the latter is not true as per our observations):

It is not simply the water-air surface tension that allows the insect to walk on water. It is the combination of the legs not being wetted and the surface tension. The legs of water striders are hydrophobic.

So, it would be very helpful if you could explain why does a metal paper clip float even though it has an acute contact angle with water.

Please note that the question Surface tension: the paper clip experiment is not same as this one. It doesn't discuss about the obtuse contact angles observed between metal paper clip and water which is the central theme of this question.

• Are you asking if a paper clip would float were surface tension removed? Without surface tension, isn't the only force present buoyancy? That only depends upon the relative density between the two materials really and last I checked, iron and aluminum both have higher densities than water. So if you could generate water without surface tension, I am guessing most metals would just sink. May 27, 2020 at 13:50
• @honeste_vivere: That wasn't my main point. I understand that if there were no surface tension any 'denser than water' objects would sink. The problem was with the acute contact angle normally observed with metal surfaces. If we were to consider acute angles here instead of obtuse angles, clearly there will not be any sufficient vertically upward force to support the weight of the pin and eventually it would sink. May 27, 2020 at 13:54

## 1 Answer

When there is no wetting, the contact angle is obtuse. When wetting takes place, the contact angle becomes acute. A certain amount of pressure is needed to break the surface of the liquid so that wetting takes place. If wetting were to take place, the paperclip would sink (likewise it would sink if there were no surface tension).

When wetting does not take place, the contact angle is obtuse. The paper clip can float because wetting does not take place (or only a small amount of wetting takes place) - the clip is light enough that does not push hard enough on the surface of the water to break surface tension. This is undoubtedly helped by contaminants, such as oils picked up from fingers (it is opposite to capillary action, in which wetting does take place).

• Thank you for your answer. Regarding wetting and contact angles, I learnt the other way round, i.e., 'when the contact angle is acute, wetting takes place' and vice versa instead of 'when wetting takes place, contact angle is acute' and vice versa. The latter part has been used in your answer. Could you tell what is the reason behind this choice? It seems the same substance can have both acute and obtuse contact angles depending upon whether wetting takes place or not. I thought contact angles always have the same value for a given set of substances. Jun 26, 2020 at 4:11
• The contact angle depends on whether wetting takes place. In general, a sufficient pressure between the material and the liquid is needed to initiate wetting --how much depends on material and the liquid. A paperclip has a large ratio of surface area to mass, so the pressure can be low enough that wetting does not take place. Jun 26, 2020 at 4:27