# Why does water remain as a "hemispherical bubble" when it falls on a page?

Today while drinking water, a drop of it accidentally felt on a page of my book, and I was thinking that, "Oh my god! The water will spread instantly, making the part of page wet". But, I observed, the drop remained as a drop, or to be precise, it didn't spread, it remained like a hemisphere over the page, and it's bottom was getting wet slowly. Also as wind was blowing tangentially over it, it was shaking just like a solid, thin ball. Actually I have observed it for long time, but never thought about it. My question is, what makes water, a liquid with weak intermolecular forces, which has no form of itself, can take up such a form? And also, why does it shake when there is wind blowing tangentially? Thanks. Looking for answers to clear my doubt.;)

• No offence, but why did you choose the surface tension tag for this question?
– user81619
Commented Sep 16, 2015 at 16:14
• Because I thought that it might be related to surface tension. Can you suggest proper tag? Commented Sep 16, 2015 at 16:14
• It is related to surface tension. Commented Sep 16, 2015 at 16:17
• That's what I tagged. Commented Sep 16, 2015 at 16:17
• My point, and again I don't want to offend you in any way, is that if you thought (or knew) that surface tension was the reason, then any search on Google would give you the complete answer in 5 seconds. As far as why water shakes in a wind goes, it's simply just being subjected to a force...
– user81619
Commented Sep 16, 2015 at 16:29

## 1 Answer

There are three questions here:

1. Why didn't the water spread in the paper ?

2. What defines its shape ?

3. Why does it shake ?

Answer 1: when the drop approaches the surface, air trapped between them needs to escape. In some conditions (speed and size of drop, roughness of the paper, absorption properties of paper,... ), this is slow and consumes enough energy to use up all the momentum of the drop before a significant liquid-solid contact is established. The drop then sits there (possibly on a thin film of air above the substrate which will escape gradually under the pressure exerted by the drop due to its weight -- which is small,) hence the slow process.

Answer 2: the balance of surface tension, gravity, and pressure on the drop define the shape of the drop. If the drop is small enough, gravity can be neglected. Thus you have a spherical dome at the top (due to surface tension) and a flattened bottom (because air pressure is higher in the center, balancing the pressure in the drop).

Answer 3: Consider very short times compared to the time taken for absorption of the water . Everything is at equilibrium. The shearing wind will exert a transient force on the drop, which will elongate in some direction. When the wind force changes, the surface tension force tends to bring back the drop to the previous equilibrium, when this is reached the liquid has acquired some momentum and will thus go beyond that shape and shake until its viscosity dissipates away its kinetic energy.

• Your answer 1 is flawed. The thin film effect only matters when the area is large compared to the height gap. In this case since one of the surfaces is liquid and therefore very curved, the height gap can never be small over a large enough area to be relevant.
– Rick
Commented Oct 1, 2015 at 16:25
• Liquids are deformable... Upon splashing this is what happens. Cf. e.g. MacKay and Mason 1963, DOI: 10.1002/cjce.5450410504.
– Joce
Commented Oct 2, 2015 at 14:54
• That's for a liquid-liquid interface where the impacting surface (which is smooth given it's a liquid) will conform to the incoming surface. Unless the paper is so smooth that you can get consistent spacing, the peaks will penetrate into the droplet before the pressure could build enough to support the droplet. This might trap air pockets between the water and the paper, but I would hypothesize that the air would evacuate through the porous paper faster than the pressure could build up. That's a very different scenario than a liquid interface where the air has no where to go.
– Rick
Commented Oct 2, 2015 at 15:12
• My bet would be that the slow spread has to do with the surface energy of the liquid paper interface being lower than normal so there is much lower capillary effect than expected. This would make sense as to why with this particular paper the droplet wetted very slowly while often time when you drop a drop onto paper it gets absorbed very quickly.
– Rick
Commented Oct 2, 2015 at 15:15
• An additional reason why a layer of air trapped could not be the cause for the water not spreading quickly. The shape of the droplet was claimed as hemispherical, but if there was an air layer supporting it it would remain spherical. If the water droplet had skittered across the paper and not wetted it at all, then an air layer would be a valid hypothesis, but the op stated that there was wetting; it just happened slowly.
– Rick
Commented Oct 2, 2015 at 15:22