An optimization algorithm for deriving the average flow velocity in a shallow microchannel through spatiotemporal concentration gradient

Precise measurement of the flow velocity in microfluidic channels plays an important role in the application of microfluidic chips for quantitative chemical analysis, sample preparation, drug synthesis, etc. In this study, based on the principle of mass transport in microchannels, an optimization algorithm is proposed to derive the average flow velocity within a shallow microchannel through the spatiotemporal concentration gradient. Firstly, based on the relationship between the flow field and the concentration field in the shallow microchannel governed by the Navier-Stokes equation and the Taylor-Aris dispersion equation, a direct inversion method and an optimization algorithm to derive the average flow velocity are demonstrated respectively. Secondly, the influence of the parameters of the spatiotemporal concentration signals (i.e. frequency, amplitude and diffusion coefficient) on the prediction accuracy of the average velocity has been analyzed using numerical simulation. Finally, experiments using fluorescent dye are carried out to verify the feasibility of the proposed method. Simulation results show that the correlation coefficient between the derived average velocity obtained by the optimization algorithm and the real velocity is one in the absence of noise interference, which indicates high calculation accuracy. In the case of noise interference, the accuracy of the optimization algorithm can be improved by increasing the frequency and amplitude of the dynamic concentration. And a low diffusion coefficient can also improve the accuracy. In the microfluidic experiments, a correlation coefficient between the inversion result of the optimization algorithm and the measurement of the flow sensor can be as high as 0.9814.