# What is the maximum net force of surface tension per gram of water?

I've always wondered how much force water exerted through surface tension. By maximum I mean the theoretical pulling/attracting power.

Also, what would happen if you raised or lowered the power? Would it affect life? And how much would you have to raise it in order to get a drop of water 1 ft. in height?

Thanks guys!

• What do you understand surface tension to be? Commented Apr 21, 2015 at 0:12
• It is a force that attracts water molecules to one another via water's high polarity. There has to be a force squeezing water into spheres when the lowest energy "option" for them would be a flat out puddle :P Commented Apr 21, 2015 at 14:11

Okay, I have a few guesses on what you are trying to say.

I've always wondered how much force water exerted through surface tension. By maximum I mean the theoretical pulling/attracting power.

If you mean to ask about a water-water interaction similar to that of a magnet-magnet interaction, then surface tension of water has very little to do with whatever you are talking about, rather the inter-molecular interactions matter more. But if you are talking about capillary action, which I suppose you mean here:

And how much would you have to raise it in order to get a drop of water 1 ft. in height?

Then yeah. It's surface tension. I'll just talk about both possibilities and more.

Clarification: What is Surface Tension? Listen, surface tension is not only about the water. Water does not move on its own. Its unit is Newtons per Meter. Why? Because it measures the net force being applied at the edges of contact between a liquid and its surroundings. Think of a glass of water (with gravity). There are a number of forces acting on it:

1. its weight
2. the inter-molecular forces of attraction (from hydrogen-bonds and Van der Waals' forces), which are called cohesive forces $F_{co}$,
3. inter-molecular forces between (a) water and the glass material and (b) water and the air above, these two kinds are the adhesive forces $F_{ad}$.

The contact edge on this glass is the line where water-glass contact meets water-air contact (I hope I didn't lose you there). And that's effectively the internal perimeter, $L$, of the glass at that level (red line on the image).

So the force from the surface tension, $F_{st}$, would be $F_{st}=F_{co}-F_{ad}$. Giving us the Surface Tension, $\gamma$, as $$\gamma=\frac{F_{st}}{L}=\frac{F_{co}-F_{ad}}{L}$$

Now, hopefully you've noticed where this is going. This Surface Tension $\gamma$ will vary for every single system. The $F_{co}$ won't change but the $F_{ad}$ would.

Examples? In the glass water system the $F_{ad}$ comes from two separate adhesive forces, water-glass and water-air. at the edge of contact, the $F_{ad}$ from water-glass contact is greater than the cohesive forces in the water, so some of the water climb up along the surface of the glass.

But in case of mercury-glass the cohesion is stronger, so the higher energy part at the edge bends downwards towards the rest of the liquid. Yet a mercury-copper case behaves like the water-glass case.

The Surface Tension $\gamma$ keeps changing as you change the material of the container. And it's that high adhesion between water and the surfaces that help it to stick on glass, steel and that tiny ant of yours.

Coming to your actual query: The maximum you say? There's no maximum, it purely depends on the material of the container or the material it's in contact with and also the shape of the material plays a huge role.

Well, instead of newton/gram we will talk about simply newtons, it makes more sense. The idea is, on Earth the adhesive forces need to be strong enough to cause this $F_{st}>W_{water}$ to make water climb through a pipe. And that is the case in capillary tubes, the water climbs up until the $F_{st}$ has been cancelled by its weight. If the tubes are thin enough, like in trees and plants, the water will already reached its destination before the force gets cancelled out.

Now, if we suddenly boost up this adhesion a billion times stronger (limit: imagination) from what is the real and cohesion stays same, then it's gonna suck. Literally. Everything the water or any liquid comes to contact with, it will immediately start to evenly spread out, clothing every nooks and cranny on that surface of that object. It'd be much like when we spill water on the floor. But now it'd be happening EVERYWHERE, on the sides and on the roofs. The rivers, lakes and oceans start allowing a layer of water to swallow everything up, and a carpet of water will cover the world. Trees and plants burst as there is an immense rush of water inside them. The large droplets of water we adored will never form, a droplet release in the air will torn into tiny minuscule droplets, that we can't see. Maybe into water vapor. And Life? I wonder... ;)

Hope that helped. Went a little overboard. :D

• That's what I was looking for +50. However I have a follow up question: If I gave you a contact material(s) could you calculate the force of the attraction? Commented May 2, 2015 at 12:16

As you can see here http://www.funsci.com/fun3_en/exper2/exper2_05.gif the surface tension depends on the width of the film you are pulling. At the extreme case you would make two surfaces with each water molecule of one half of the water attached to a polar group of the surface. Then contact the surfaces so that each water molecule is opposite to another water molecule of the other surface, of course always matching a negative (oxygen) side with a positive (hydrogen side). The force depends on the distance. If you push the molecules into each other you will have repulsion. If you pull them apart, the repulsion will decrease and attraction will dominate. If you pull them too far apart, the attraction will decrease. At the maximum net attraction the force with 1 g water will be immense. I can't say how much, though.

Surface tension certainly plays an important role in cellular life, so adding detergent (which lowers surface tension) to water or ingesting it would be unhealthy, but you can buy detergents without a special license, so it's not that bad, within limits. I would advise you not to drink detergent on a regular basis, though.

• Sorry, I should have clarified, by raising and lowering I meant like instantaneously and without any extra ingredients, i.e. magically. So I meant what would happen if the surface tension force was raised and lowered intrinsically. Especially if it was raised. One interesting phenomenon that I have observed is that after falling into water, ants cannot "shake" off the 'sticking' water and eventually die of drowning. Would the same happen to us if the surface tension was raised? Commented Apr 22, 2015 at 11:42