15 Feb 2019

Bursting Some Bubbles

Photo via goodfreephotos.com

Kids love soap bubbles. So do adults. What’s not to love? They’re pretty colours, they float and you can pop them. Couldn’t be simpler. Until you get into the science of soap bubbles. There’s a lot of math, physics and chemistry in them.

What are they made of?  Good enough to eat?

If you look up recipes to make your own bubble liquid, you’ll find instructions to mix water with dishwashing liquid and glycerine. Glycerine is an edible sweetener which dissolves in the water. Bubbles are a sandwich: a thin layer of water between two layers of soap molecules. The soap molecules have a hydrophilic (water-loving) side and hydrophobic (water-hating) side. The molecules align themselves with the hydrophilic side attached to the water. The soap decreases the surface tension of the water, allowing it to stretch into a very thin sheet. The bubbles usually pop after a few seconds. That’s because the water evaporates out of the sandwich. The dissolved glycerine slows down the evaporation process, making the bubbles last a little longer. 

Touching the bubbles with anything dry will cause them to pop immediately. But if you catch them with, or allow them to land on something wet, they’ll last longer. 

Colours

More fun physics here. The colours are created because of thin film interference (like the colours in an oil slick on the surface of water). Some light waves (B in the diagram below) are reflected off the outside surface of the bubble; some (A below) go through the water and then are reflected off the inside surface. 

The reflected waves A and B could be in the same phase and reinforce each other, as in diagram 1. In this case C (the reflected A and B waves) is stronger than either A or B. Or, as in diagram 2, the reflected waves could be out of phase with each other. They essentially cancel each other out and the combined C wave is very weak. 

Whether the waves reinforce or destroy each other depends on the exact thickness of the film and the wave length (colour) of the waves. 


Diagram 1: Waves reinforce each other

Diagram 2: Waves interfere and destroy each other
Jhbdel [CC BY-SA 3.0], via Wikimedia Commons



Shapes

A single bubble will form as a perfect sphere. A sphere is the shape that has the smallest surface area to enclose a given volume of air. Surface tension everywhere on the bubble will be the same force in all directions. But things get more interesting and complicated when you have multiple bubbles touching. With two bubbles of the same size you get


With three bubbles of the same size you get

In both cases the surfaces meet at an angle of 120°.

Math

This is unexpectedly complicated. In 1760 the legendary mathematician Jean-Louis Lagrange posed the problem of finding the minimal surface area to enclose a given boundary.  The Belgian physicist Joseph Plateau experimented with soap bubbles in the mid-1800’s, formulated some laws and the general problem has been known as Plateau’s Problem. 

Work has continued on more and more general solutions to the problem. It’s hard enough that Jesse Douglas earned a Field’s Medal (the Math “Nobel Prize”) in 1936 for his work on the problem. More recently, “in 2015 Jenny Harrison and Harrison Pugh used cohomology to define spanning sets and Hausdorff measure weighted by a bounded Lipschitz function to define area, and solved the problem in this setting. Their paper is currently under review”. (Full disclosure: I have no idea what this math is. But it’s impressive so I just copied and pasted). 

Neat Trivia

Joseph Plateau is also known for being the first to demonstrate that when you see multiple successive pictures with small differences, it creates the illusion of movement. In other words, he invented the idea of movies!

Jenny Harrison completed her PhD in England on a prestigious Marshall scholarship. She did post-doctoral work at Princeton’s Institute for Advanced Study (that’s where Einstein, von Neuman and Godel worked) and then taught at Oxford University for three years. Then, after five years as an associate prof at University of California – Berkeley, she was repeatedly denied tenure. She eventually filed a lawsuit based on gender discrimination. After four year years, a settlement was reached whereby an new independent committee reviewed her tenure application, and unanimously recommended approving tenure.