How many times since I was a child I`ve got distracted while I wash the dishes by making soap bubbles? so many, because they are enigmatic, like the most beautiful things in nature. Why his shape is so perfectly espherical?Why they shine in iridescent colors? What is the cause of the way they arrange when they stick each other together? How could I make they take longer to explode?
I give you some formal mathematical expressions that need to be commented but give an idea about how something so simple hides complexity.
For a bubble of radius r, the pressure from the film surface tension is given by the Laplace-Young law
(1) |
where and are the inner and outer radii of the bubble, respectively, and is the surface tension of the fluid. Letting r be the average of and (actually, ) gives
(2) |
About the sound the bubble make when it explode there is another equation for the natural frequency
given in the following expression:
where:
gamma is the ratio of specific heat of the fluid
P sub zero is the steady state pressure
R sub zero is the steady state radius
rho is the density of the fluid
And here the instant when the subject of study disappear
Some thing else to think about….
Leave a Reply