# Why are water droplets shaped like that?

With nothing to do, I stared at the droplets that get condensed on the glass panel of my window.

Upon examination, these droplets appear to be in some sorta pattern. There are big droplets as well as small ones that fill the space between the big ones.

The ones in the middle, between rows of small droplets are usually big one.

All these intrigue me to think about what are that factors that contribute to this pattern.

My guess: I think vapor gets condensed on dust particles thus forms those droplets in the picture. But what accounts for the different sizes of the droplets?

• The reason water takes up a spherical form is due the water's cohesive forces. Basically the water 'droplets' will take the shape of a sphere as an effort to reduce surface area. – AlanZ2223 Feb 28 '15 at 2:49

From the Wikipedia article on surface tension:

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be approximately spherical. The spherical shape minimizes the necessary "wall tension" of the surface layer according to Laplace's law.

In short, the more surface tension is, the rounder shapes of water you get. And the opposite goes for gravitational potential energy: The lesser gravitational acceleration results in more spherical droplets of water.

The symbol for surface tension is $\gamma$.

$\gamma (\ce{H2O}) = 72.8~\mathrm{dyn~cm^{-1}}$ (at $20~\mathrm{^\circ C}$)
$\gamma (\text{mercury}) = 465~\mathrm{dyn~cm^{-1}}$ (at $20~\mathrm{^\circ C}$)[1]

That's the reason you hardly ever see mercury drops out of their spherical shape.

In short

The spherical shape minimizes then necessary "wall tension" of the surface layer according to Laplace's law.[2]

Oh and I almost forgot: This great article - Antonin Marchand, Joost H. Weijs, Jacco H. Snoeijer, and Bruno Andreott, Why is surface tension a force parallel to the interface?. Physique et Mecanique des Milieux Heterogenes, 2012 - is very nice in case you wanted to do additional study in the case.

References:

1. R Nave. Surface Tension. URL (accessed April 25th, 2018)
2. R Nave. Surface Tension and Droplets. URL (accessed April 25th, 2018)
• I think that Doeser knows well what surface tension is and his question is much more specific – Mithoron Feb 28 '15 at 22:46
• But I don't think that way @Mithoron. The OP says: "I think vapor gets condensed on dust particles thus forms those droplets in the picture." We have to correct that misconception and then go on. But, I can expand if they aren't satisfied. – It's Over Mar 1 '15 at 12:30
• Is surface tension the cause of the effect, or the name of the effect? From that wikipedia link: "surface tension results from the greater attraction of water molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion)." – John Snow Mar 4 '15 at 21:09
• @JohnSnow It's better to put it this way: There is a war between the surface tension tribe and gravity tribe (among other factors). :) You see, gravitational potential energy always tends to make water droplets get more, say, flat and surface tension is getting them rounder. And not only is surface tension one of the causes (and the main cause) of the shape water droplets take, it also affects the size of the water droplets. – It's Over Mar 5 '15 at 17:16
• I would like to add that the sizes in this picture are also a result of droplets getting big enough to touch each other, at which point they merge. Then the shape changes toward making a sphere again, but with the water from both droplets. The ones at the bottom are likely bigger because gravity has pulled more smaller droplets together. At the very bottom, it seems they get large enough for gravity to "win," and they just run down the window. – MysteriousWhisper Mar 13 '15 at 23:27

Falling drop of a liquid is always spherical in shape due to surface tension. The inward forces on the surface molecules of the liquid droplet tend to cause the surface to volume ratio as small as possible. Since surface to volume ratio is minimum for the spherical shape that’s why falling drop of a liquid is spherical.

for a given volume sphere is having minimum surface area as compare to circle it means sphere have less surface tension as compare to circle (surface tension have tendency to the liquid to keep it free surface area minimum) which in turn means minimum surface area