We investigate the behavior of a binary surfactant solution (AOT/water) as it is progressively concentrated in microfluidic evaporators. We observe in time a succession of phase transitions from a dilute solution up to a dense state, which eventually grows and invades the microchannels. Analyzing these observations, we show that, with a few experiments and a limited amount of material, our microdevices permit a semiquantitative screening of the equilibrium phase diagram as well as a few kinetic observations.