  We study avalanche dynamics and local activity of forced-flow imbibition
fronts in disordered media. We focus on the front dynamics as the mean velocity
$\bar{v}$ of the interface is decreased and the pinning state is approached.
Scaling arguments allow us to obtain the statistics of avalanche sizes and
durations, which become power-law distributed due to the existence of a
critical point at $\bar{v}= 0$. Results are compared with phase-field numerical
simulations.
