We engineered specific microfluidic devices based on the pervaporation of water through a PDMS membrane, to formulate continuous and steady concentration gradients of a binary aqueous molecular mixture at the nanoliter scale. In the case of a model complex fluid (a triblock copolymer solution), we demonstrate that such a steady gradient crosses the phase diagram from pure water up to a succession of highly viscous mesophases. We then performed in-situ spatially resolved measurements (confocal spectroscopy and small-angle X-ray scattering) to measure quantitatively the concentration profile and to determine the microstructure of the different textures. Within a single microfluidic channel, we thus screen quantitatively and continuously the phase diagram of a complex fluid. Beside, as such a gradient corresponds to an out-of-equilibrium regime, we also extract from the concentration measurement a precise estimate of the collective diffusion coefficient of the mixture as a function of the concentration. In the present case of the triblock copolymer, this transport coefficient features discontinuities as some phase boundaries that were never observed before.