# Flattening of large liquid drops

I have read that liquid drops are spherical in shape due to the surface tension of the liquid which tend to minimise the $$\frac{surface}{volume}$$ ratio of a given volume of a liquid. But in real life, it is found that only small liquid drops are perfectly spherical in shape. As the drops become larger, they get flattened. I had read somewhere that gravity may have some role to play but I don't know how. So my question is:-

What is/are the possible reason(s) behind the flattening of large drops and how do the reason(s) work together in flattening a large drop? I'm considering both situations (i) when drops are airborne (eg. when falling down as rain) as well as (ii) when large drops are on some surface. I want to get a complete picture behind the mechanism of flattening of a large drop (just an intuitive one and not a very mathematical one).

A water droplet is a shape of a given volume, where surface tension tries to minimize the surface energy. Without any other forces the solution would be a sphere. But when other forces are present the solution will have another shape.

Niels Nielsen gave an excellent answer on how falling droplets get flattened by air resistance.

A droplet resting on a hydrophobic surface (i.e. a surface it does not wet) will experience gravity, and take a shape with a flat bottom surface in contact with it and a curved top that minimizes surface energy. Something similar, but with an angle between the droplet and the surface, emerges when there is some wetting. The exact shape requires a fair bit of math to derive.

The general shape of a droplet needs to be described using variational calculus, where you minimize the total volume energy (typically due to gravity) and the surface energy (due to surface tension) constrained by a fixed volume and that the local surface forces balance (dealing with air etc). This can get tricky since some surface forces change with the shape: in many situations there are no static solutions, and the droplet will oscillate or break up.

• Thank you for the answer. The two answers together along with the link to Wikipedia article completely answers the question. May 21, 2021 at 11:09

Droplets of water falling through the air experience drag forces that get significant as their speed increases. Since the water droplet is flexible, those drag forces tend to deform the droplets into flattened shapes, and the airflow over the flattish droplet becomes uneven as the droplet wobbles. At a certain speed, the airflow forces are strong enough to split the nonspherical water droplet into smaller pieces which fall at a slower speed and are more resistant to deformation. By the time the droplets make it down to the ground, they are mostly the same (small) size and fall at almost the same terminal velocity, which for typical droplets is about 30 MPH.

You can see this process at work when someone dumps a bucket of water off the top of a tall building. The water begins falling as an elongated lump until the aerodynamic forces take over and the lump is broken up into smaller and smaller and smaller pieces. The very smallest pieces of spray- mist- fall so slowly that they are left behind in a cloud that persists after the rest of the water has hit the ground.

• @neils_nielson Nice answer. But could you please add the reason behind flattening of large liquid drops when they are on some surface as well to complete the answer? May 9, 2021 at 9:54
• Edited the question to highlight both situations for which I'm seeking answers. May 9, 2021 at 12:24