  Catastrophic phase inversion, the sudden breakdown of a dense emulsion,
occurs when the dispersed majority phase irreversibly exchanges role with the
continuous minority phase. This common process has been extensively studied
over the past decades and yet its fundamental physical mechanism has remained
largely unexplored. Here we experimentally and numerically study the dynamics
of catastrophic phase inversion as it occurs when the volume fraction of the
dispersed phase exceeds a critical volume fraction (typically around 92% in
experiments). Our data accurately quantify the abrupt change of both the global
torque and average droplet size at approaching and across the phase inversion
point, exhibiting strong hysteresis. Most importantly, we reveal that the
fluctuations in the global torque diverge as a power-law while approaching the
critical volume-fraction and we connect their growth to the formation of highly
heterogeneous spatial droplet structures. The present finding, unveiling the
tight connection between fluctuations in dynamic heterogeneity and the critical
divergence of torque fluctuation, paves the way to a quantitative description
of catastrophic phase inversion as an out-of-equilibrium critical-like
phenomena.
