Two-balloon experiment

This result is surprising, since most people assume that the two balloons will have equal sizes after exchanging air.

The behavior of the balloons in the two-balloon experiment was first explained theoretically by David Merritt and Fred Weinhaus in 1978.

[1] The Karan–Guth stress–strain relation[2] for a parallelepiped of ideal rubber can be written Here, fi is the externally applied force in the ith direction, Li is a linear dimension, k is the Boltzmann constant, K is a constant related to the number of possible network configurations of the sample, T is the absolute temperature, Li0 is an unstretched dimension, p is the internal (hydrostatic) pressure, and V is the volume of the sample.

In the case of a thin-walled spherical shell, all the force which acts to stretch the rubber is directed tangentially to the surface.

On the other hand, if the total number of molecules exceeds Np, the only possible equilibrium state is the one described above, with one balloon on the left of the peak and one on the right.

This is due to a number of physical effects that were ignored in the James/Guth theory: crystallization, imperfect flexibility of the molecular chains, steric hindrances and the like.

[4] In addition, natural rubber exhibits hysteresis: the pressure depends not just on the balloon diameter, but also on the manner in which inflation took place and on the initial direction of change.

One consequence is that equilibrium will generally be obtained with a lesser change in diameter than would have occurred in the ideal case.

[1] The system has been modeled by a number of authors,[6][7] for example to produce phase diagrams[8] specifying under what conditions the small balloon can inflate the larger, or the other way round.

[10] However Tronstad et al.[11] found that when the two sets of lungs had very different elasticities or airway resistance, there could be large discrepancies in the amount of air delivered.