Wednesday, March 12, 2008

Surface Tension and the "Floating Needle"

At some point in the early years of my science education I was shown how to float a needle in a cup of water by placing it ever so gingerly on the surface, and it was explained to me that this was the result of "surface tension", a mysterious phenomenon which occurs at the surface of a liquid, where it meets the air. Exactly how this tension developed and why it could support a needle (or pond-skating bugs, the other canonical example) was never made very clear to me.

Years later it is still not very clear to me. After considerable thought, it seems to me that surface tension actually has nothing to do with the flotation of needles and bugs. The following is my best understanding this phenomenon; should any liquid physics experts happen by, I hope they will comment.

First, let us recognize that the molecules in a liquid are held together by mutual attraction. Where the attraction comes from is another subject, but without it one would have a gas and not a liquid.

Within the liquid, the molecules are packed as densely as possible, since otherwise the attraction would draw them yet closer. At the surface, however, the situation is more complicated. One might think that the surface molecules would have the same density as in the interior - but in fact this simple situation is not stable.

The surface molecules feel the attraction from their next-nearest neighbors on the surface, and also from molecules even farther away, and they would like to pop out of the surface so they can get around their near neighbor and draw closer to their further neighbors. In other words, the surface would like to crumple into a ball (i.e., a droplet) just as it would if it were an isolated sheet of water floating in the air.

Of course the surface layer can't crumple because it is attached to the rest of the water, but what happens is that it partially crumples, and some molecules do pop out, with the result that the layers near the surface have a decreasing density compared to the liquid bulk. In particular, the molecules on the surface are farther apart than those in the bulk. Since they are farther apart, yet still experiencing mutual attraction, they are in a state of "tension" compared to their colleagues in the bulk of the liquid.

We can picture the liquid as a collection of balls connected together by springs. Inside the liquid, the balls are packed so close together that the springs are mostly slack - they have lost their tension. At the surface, however, the balls are farther apart and the springs are stretched and tense. This tension tends to pull the liquid into the shape having the smallest surface area possible - a spherical droplet, for example.

So surface tension arises because the surface wants to crumple but it can't. Now we ask, does surface tension have any relevance for the "floating" of needles and bugs? This would mean that the tension makes it more difficult to penetrate the surface of the liquid, i.e., makes it more difficult to break the bonds between the liquid molecules at the surface. But as far as I can see, surface tension doesn't make these bonds any harder to break. If anything, since the surface molecules are already farther apart, they are easier to separate than those in the bulk.

Therefore it seems to me that the "floating" of needles and bugs is a separate phenomenon from surface tension. Needles and bugs are held up more by virtue of their shape, and by being placed very flat against the water, than by any special condition of surface tension.

When an object is placed with its broad side flat on a surface, then it can only penetrate the surface by breaking a bunch of molecular bonds at once; if the object is light enough, it can then rest on the surface. Conversely, if the narrow end is against the surface, only a few bonds need to be broken for the object to slide in.

Once the object is already submerged, regardless of how it is oriented, it will sink steadily because molecular bonds broken beneath it are replaced by bonds re-forming above it, so there is no overall retarding effect from the bonds. (More precisely, there is a smaller effect, because molecules still have to rearrange and their bonds give rise to viscosity).


Anonymous said...

I think you are ignoring a crucial observation. When you see an object held on the surface of a fluid by surface tension you will see that the surface is curved. The curvature is actually quite pronounced where the object touches the fluid. Clearly the fluid surface is exhibiting quite a lot of cohesive force. It is behaving very much as if it were a thin sheet of elastic fabric. It is the elastic forces associated with this curvature that provide the reaction forces holding the small object in place.

I once saw a photo of a man standing in a pool of mercury. It was not buoyancy alone that kept him aloft; he was not floating - no part was submerged. It was surface tension. And the surface of the mercury pool was very curved. It might be interesting to calculate if the volume of the displaced fluid is equal to the weight of the object held aloft. I suppose it must be.

As a physicist, you must surely be prepared to tell us why the atoms in a fluid have this strong cohesive property and how it is that surfactants decrease it. As an engineer, I can only say that it must be so.

santosh kumar said...

i dont know why , but the argument here seems very loosely attached !...

Will Nelson said...

Yeah, I definitely need to revisit this. If anyone knows of really cogent explanations out there on the web, please post. Obviously the resistance of a surface to penetration relates to breaking molecular bonds, but those bonds are also present throughout the liquid. What's not clear to me is, after once breaking surface, why it becomes easier to push something further in, because it seems that in doing so one is still breaking as many bonds as were broken when first penetrating the surface.

Igor Karlić said...

Simmilar efect you would find if you spin pipe and water is running quickly through pipe.