The decompression rate of magma is correlated with explosivity of volcanic eruptions. We present a series of decompression experiments in a shock tube apparatus to investigate the effect of decompression rate on the expansion and eruption style of bubbly fluids. We also consider the effects of the pressure change ΔP and initial vesicularity $phi$i. As an analogue for magma we use viscoelastic polymer solutions. For fast decompression, we observe fragmentation and rupture of bubble walls only for large ΔP and large $phi$i. For slow decompression, however, bubbles maintain spherical shapes, and the bubbly fluid does not fragment, irrespective of ΔP and $phi$i. We consider two theoretical estimates for the expansion of bubbles, which we refer to as "equilibrium expansion," in which the pressures inside and outside the bubbles are assumed to be equal, and "disequilibrium expansion," in which the enthalpy change caused by the pressure change is converted into kinetic energy. The observed expansion velocity is governed by the slower estimate. For slow decompression, where bubbles expand while maintaining their spherical shape, the measured expansion is well explained by equilibrium expansion. In contrast, for fast decompression, in which we observe the rupture of bubble walls and fragmentation, the expansion follows disequilibrium expansion. We conclude that the disequilibrium estimate is an upper limit velocity for the bubble expansion and fragmentation and the rupture of bubble walls require disequilibrium expansion. The calculated threshold decompression rate for disequilibrium expansion is consistent with the estimated decompression rate for the explosive/effusive transition in natural basaltic eruptions.