We design near-autonomous microfluidic devices for draining and concentrating aqueous solutions steadily over days in a very controlled manner. We combine linear suction pumps, that drive the solution and concentrate it steadily, with a nL-sized storage pool where the solute accumulates. The fine balance between advection and diffusion in the pump and diffusion only in the accumulation pool yields several filling regimes. One of them is universal as being steady and independent of the solute itself. It results a specific equivalence between time and concentration which we use to build the phase quantitative diagram of a water soluble polymer in brine on the nL scale.