The Mathematical Physics             When one blows a bubble, the soap and water mix to combine a sphere of soapy water suspended in the air that is under constant barrage from multiple variables. The surface tension and size of the bubble are what decide the pressures on both the inside and outside walls of the bubble. The bubble will pop unless the inside pressure is slightly higher than the outside pressure. Normally, two unequal pressures would cause a bubble to pop. However, it is the surface tension on the bubble that prevents this from happening. The equation that relates surface tension, internal pressure, and external pressure is below:                                                                                                                                                       http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html Where                         Pi is the internal pressure             Po is the external pressure             T is the surface tension             r is the radius of the bubble         The above relationship is found by treating the bubble as two separate hemispheres where the forces of the upper and lower hemispheres are in balance with each other. Unless the relationships of the forces of the two hemispheres are equal, the bubble will cease to exist.             The forces on the upper hemisphere equal the difference in internal and external pressure multiplied by the area of the equatorial circle where the two hemispheres meet.                                                                                                                                                                                                                                                             http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html         The forces on the lower hemisphere equal twice the surface tension multiplied by the circumference of the equatorial surface where the hemispheres meet. This equation similarly demonstrates the downward forces of both the upper and lower hemispheres.                                                                                                                                                                                                                                                               http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html         While the formation of a single bubble is rather straightforward, when two or bubble meet, the multiple pressures add a smidgen more of complication due to smaller bubbles having higher internal pressure than large bubbles. The pressure difference can be modeled by the Young Laplace equation which is below:                                                                                                                                                                                                                                                                      http://en.wikipedia.org/wiki/Young%E2%80%93Laplace_equation             Where                         is the difference in pressure is the tension in the wall                         γ     is the tension in the wall                          is the unit vector normal to the shared surface of the two bubbles                         H is the average curvature                         R1 and R2 are the radii of curvature of the two bubbles