What happens to a soap bubble as the outside pressure is increased? Imagine you blow a soap bubble at atmospheric pressure. The bubble equilibrates to some radius, $R_{0}$, with some internal pressure, $P_{0}$, due to the surface tension, $T_{0}$, of the soap-water film. If you then place the bubble in a sealed chamber and gradually increase the pressure in the chamber from 1 atm to $P_0$, what happens to the bubble? Logic would dictate that the bubble would shrink as the outside pressure increases.

On the other hand, Laplace's law states that $dP \propto \frac{T}{R}$. As the outside pressure increases from 1 atm to $P_0$, the gauge pressure, $dP$, of the bubble decreases, which implies that the radius should increase (expand). So does the bubble shrink or expand? What is the source of the apparent contradiction?

Thanks!