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Rubber balloons - taken seriously. (English) Zbl 0625.73008

Trends in applications of pure mathematics to mechanics IV, Pap. 4th Symp., Bratislava/Czech. 1981, Monogr. Stud. Math. 20, 37-58 (1983).
[For the entire collection see Zbl 0612.00020.]
Three different systems involving rubber balloons are studied for their stability properties. Special attention is given to the case of two balloons that are connected by a pipe. The problem of stability treated here is akin to the stability problem of two soap bubbles which is often talked about in elementary physics courses: a small bubble connected by a pipe to a bigger one disappears as its air inflates the big bubble. A similar observation can be made with two moderately inflated rubber balloons.
This is surprising, since one might have thought that the two bubbles or balloons would exchange air until they were equal in size. However, that situation is not stable, because if two moderately inflated balloons of equal size are connected, one grows at the expense of the other.
The analysis will reduce this subject to a fairly complex thermodynamic stability problem. It will turn out that indeed at moderate inflation in stable equilibrium the two balloons are unequal in size, while at very small and very large inflations the balloons are equal in size. At some inflations both situations are possible in stable equilibrium.

MSC:

74A15 Thermodynamics in solid mechanics
74B20 Nonlinear elasticity
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76A02 Foundations of fluid mechanics
74A20 Theory of constitutive functions in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)