Exploring the Physics of Raindrops on a Train Window

[ChrisVer]

Today I was taking the train to a nearby city, where we passed through some rainy region.
As the raindrops fell on the window, one could see their trajectories almost followed a parabola depending on their initial conditions. That is something expected, due to gravity and the forces acted on them by the running wind.
However as you see them moving, they leave behind a water tail - something like a stream-, and that tail is the preferred way the rest drops will follow (they move up to it, and then they follow it). Why is this happening?
Also if there are no more drops to follow that tail, it will suddenly break apart to stationary drops. Why is this happening? I don't think it's due to statistics, because if it was that, you wouldn't see the whole line to be divided simultaneously. It's more like, due to tension forces on the water, it's an unstable "structure"- under some perturbations it falls apart all together.
I hope I made the questions clear. Looking forward to your answers.

 

[Vodkacannon]

I can say that the reason why rain drops will tend to follow the trails of other drops is because of the property known as cohesion. As water molecules come close to one another the hydrogen bonds attract the molecules together.

 

[borisgred]

I think there are two processes going.

The first is attraction between glass and water molecules. Glass is slightly hydroscopic, so water molecules can bond very weakly to the glass surface. This will tend to flatten the water drop that is in contact with the surface. This is basic surface wetting.

The second is surface tension of water. The system of water molecules will try to arrange itself to minimize its potential energy, which means minimizing total surface tension, which basically translates to maximizing volume-to-surface ratio. So a droplet, in absence of other forces, will be perfectly spherical.

So hydroscopic attraction will try to spread the water out, and surface tension will try to gather it up. The result is the trail that you see. A water trail is probably only metastable mechanically, so some mechanical disturbance (like the car shaking, or air turbulence) will shift it into the other stable state - a round droplet. When this happens, the trail breaks up.

The attraction also acts as friction. Attraction obviously drops off with distance from the surface. So a trail can sort of "shield" new droplets from the surface. They experience less friction and can travel faster along a trail.

 

[Andy Resnick]

<snip> Why is this happening?
<snip>

You have observed a simple phenomenon that contradicts a central assertion in fluid mechanics: the 'no-slip boundary condition'.

http://en.wikipedia.org/wiki/No-slip_condition

The complete answer to your question is still unknown- if you read the last few sentences in the 'exceptions' section above. Another good description of the no-slip condition is here:

http://arxiv.org/pdf/cond-mat/0501557.pdf

To your specific questions, you are observing contact line motion, which is still an active area of fundamental research:

http://www.annualreviews.org/doi/abs/10.1146/annurev-fluid-011212-140734

 

[PJC01]

Thank you for sharing your observations and questions about the physics of raindrops on a train window. I can provide some insights into the phenomena you described.

Firstly, the parabolic trajectory of the raindrops is indeed expected due to the force of gravity acting on them. This is a basic principle of classical mechanics and is also seen in other projectile motion, such as a ball being thrown through the air.

The formation of a water tail or stream behind the raindrops is due to the drag force of the air on the drops. As the raindrops move through the air, they experience resistance from the air molecules, causing them to slow down. This drag force is strongest at the back of the drop, causing the water to accumulate at the back and form a tail.

The fact that other raindrops tend to follow this water tail is due to the principle of least resistance. The water tail creates a low-pressure region behind the drop, making it easier for other drops to follow the same path. This is similar to how a boat creates a wake behind it, making it easier for other boats to follow.

As for the sudden breaking apart of the water tail, this is indeed due to surface tension forces. Surface tension is the property of liquids that causes them to minimize their surface area. In the case of the water tail, the surface tension causes the water to form a cohesive structure, but it is also easily disrupted by any perturbations. When the water tail becomes too long or thin, it becomes unstable and breaks apart into smaller droplets.

I hope this answers your questions and provides a better understanding of the physics behind the raindrops on the train window. Keep observing and asking questions - that's what science is all about.