Bubble Magic

Photo courtesy Neetu Aggarwal

Now there would hardly be a being on this planet who hasn't played with Bubbles. Ah those refreshing childhood memory of dipping the wands in a soap solution and blowing air through them and Whoosh!!  Hundreds of transparent balls flying everywhere. There is surely something magical about Bubbles that even adults rejoice in this activity. I would personally look forward to this activity with my toddler. During one of those times, i was drawn into the science and math of Bubbles. Yes, even these innocent frolicky transparent balls are Mathemagical. You would say "Whats in a Bubble?"
Apparently a lot ! Lets just start with how various people look at Bubbles:

Child                    :  Lovely transparent balls bouncing around 
Parent                  :  Some silly bouncing balls that keep the kids entertained
Artist                    :  Lovely transparent balls trapping the colors of the rainbow
Scientist               :  A stretched thin film of soapy water filled with air.

Mathematician      : Spheres, almost always Spheres!



Simple, isnt it !? Now if you thought that Bubbles were as simple as that, then think again! 

First, some facts. Bubbles consist of a thin film of soapy water filled with air. When you blow a bubble the film expands outward to its maximum capacity and then blows away. 

Did you know that whatever the shape of the wand the bubbles are always spherical in shape. You take a triangular or a rectangular wand but the bubbles that escape out are always Spheres. The Sphere is the shape that minimizes the surface area of the structure, which makes it the shape that requires the least energy to achieve i.e. it encloses the most volume with the least surface area.

Picture courtesy Wikipedia

But wait till you see these Bubbles come together. The moment they form a a cluster (as in foam) they act differently. Lets see the 2-D drawing of layer of bubbles. In a cluster they always stick to each other tightly and hence form hexagonal shape. Regular hexagons fit together perfectly, leaving no gaps thus minimizing surface area. Three neighboring bubbles will together form a Triple Junction i.e. three 120 degree angles. 


  "Soap films always meet in threes along an edge called a Plateau Border, and they do so at an angle of 120 degrees" -Plateau's Law on soap films formulated by the Belgian scientist Joseph Plateau in the Nineteenth century.

         

         

       
Triple Junction 

2-D illustration of layer of bubbles

The detailed mathematics of bubbles is more complex and beyond the scope of this blog.

But why this immense interest in the mathematical behavior of bubbles? Foams are of immense importance in firefighting, mineral processing, radioactive dust recovery, oil recovery, crop spraying, food technology and also the brewing industry( where the formation of foam is not beneficial). 

 

Did you know

   

Many of the processed food we eat are actually foams: bread, chocolate, ice cream, cake, coke, soda and beer !   

          

Trivia

One of the Olympic venues, at the Beijing 2008 Olympics, was the National Aquatic Centre, named the Water Cube. It seems to be sliced from a giant foam of bubbles, an effect that is enhanced when it glows blue against the night sky.

The Water Cube at night. Image © Chris Bosse.       

                                 
So are you ever going to look at bubbles the same way? No way !