We demonstrate a compact and low consumption (60 nL) method for generating concentration gradients along microchannels with shallow parabolic cross-sections. The regimes of dispersion at work in such systems and the resulting concentration fields are described theoretically and experimentally. Experiments are performed in PDMS (polydimethylsiloxane) microchannels actuated by integrated valves. Detailed comparison between theory and experiment for the "short time" and "long time" regimes leads to excellent agreement. The system is used to successfully set up a series of isolated microchambers with mixtures of increasing solute concentrations, which may be a first step towards devices for screening.