Microfluidic ballistic regime for the generation of linear gradients inside a capillary column: Proof-of-concept and application to the miniaturized acid-base volumetric titration.

This work details a simple and original approach for the generation of linear gradients inside straight cylindrical microchannels such as a capillary column. The concept takes advantage of an oft-overlooked regime of dispersion of flowing liquids inside narrow channels: the ballistic regime. The ballistic regime is a pure convective regime and is produced by imposing a high velocity flow in a pre-filled capillary thus limited diffusion takes place. This is obtained by forcing the injection of a plug of solution on a short time scale t, much shorter than t<110×D/r, D is the diffusion coefficient and r the capillary radius. The result is a stretched solution of a given length or depth of penetration, inside the capillary column. This leads to a linear mean concentration field through the mixing zone forming a linear gradient. In miniaturized systems, this transient regime is followed by mainly radial diffusion of the solution inside the capillary due to the short characteristic diffusion time of narrow channels. A convection-diffusion simulation was used to model the gradient formed under this ballistic regime. A specific experimental prototype set-up was designed to investigate this ballistic regime and the formation of a linear gradient of titrant NaOH solution inside a capillary tubing of 500 µm inner diameter and 35-cm total length pre-filled with nitric acid solution. With this prototype, the linear gradient was then pushed in a non-ballistic regime over a confocal fluorescence point detection system in order to measure the fluorescence emission of a fluorescent dye added to the solutions. Considering strong acid-base reaction, fluorescein was used due to its strong fluorescence dependency with pH near its pKa, i.e 6.4. A first set of experiments was realized to demonstrate the validity of such an approach and to determine the optimal condition for the formation of a linear gradient over 300 mm of the 350-mm capillary length. An injection pressure of 1000-mbars over 0.75 s was chosen. The first result was the stability of the system in its ability to produce reproducible linear gradients. As further proofs of feasibility, samples of different nitric acid concentrations were titrated with a 0.25 M NaOH solution. The result was rapid and reproducible titration curves obtained with a fully automated system that consumes less than approximately 70 µL of sample solution.