# Surface tension, Bernoulli, and soap bubbles II – bubble size

The first demonstration on surface tension and soap bubbles was highly qualitative and the soap bubbles were merely a prop for talking about surface tension. There was a calculation of the gauge pressure in the bubble (Pi) which is given by

Pi= 4 σ/R

where R is the bubble radius and σ is the surface tension of the soap film, though this result was not taken any further. It is, however, possible to go a little further once you have gone over Bernoulli’s equation with your class.

Equipment

One container of soap bubble fluid and wand

Demonstration

The demonstration is similar to the previous one. You blow bubbles. Except this time you vary how hard you blow. If you blow very slowly you can get bigger bubbles whereas if you blow a little harder the bubbles get smaller. For a given wand shape there is a limit to the range of bubble sizes you can get. I have found it hard to get really small bubbles. I have also found it hard to get the really big bubbles to pinch off. They often just burst.

Analysis

The analysis requires the result above on the pressure in the bubble and Bernoulli’s equation.

When you blow into the loop in the bubble wand the air stream from your mouth stagnates on the soap film creating high pressure point there. This produces a curvature in the soap film. Therefore, there is a balance between the pressure in the cured film and the stagnation pressure. Eventually, the film pinches off and a bubble forms with the pressure in the bubble related to the stagnation pressure from your breath.

Recalling that the stagnation pressure is given by

P= ½ρV2

one can write an expression for the bubble radius as a function of the air speed (related to how hard you blow)

R=8σ/ρV2.

That is, the harder you blow (larger V) the smaller the resulting bubbles.

It would also be possible to leave this result unstated, run the demonstration and ask the students to discuss the relationship between pressure, surface tension, and radius. If the demonstration is done well you should be able to lead the class to discover that there is an inverse relationship between the pressure and radius. One could then introduce the exact relationship which they may have a greater ability to comprehend having observed it first.

An index of all the demonstrations posted on this blog can be found here. Don’t forget to follow @nbkaye on twitter for updates to this blog. If you have a demonstration that you use in class that you would like to share on this blog please email me (nbkaye@clemson.edu). I also welcome comments (through the comments section or via email) on improving the demonstrations.