基于时空浓度梯度反演扁平微通道中平均流速的优化算法

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

微流控通道内流速的准确测量在利用微流控芯片开展定量化学分析、样品制备、药物合成等领域具有重要应用价值。基于物质输运原理,提出了一种通过测量物质时空浓度梯度反演扁平微通道中平均流速的优化算法。首先,基于Navier-Stokes方程与Taylor-Aris弥散方程建立扁平微通道中速度场与浓度场的定量关系,分别提出了用直接反演法和优化算法求解平均流速的方法;其次,通过数值仿真系统地分析了时空浓度变化频率、振幅和扩散系数对反演流速准确度的影响;最后,通过荧光素实验验证了该方法的可行性。结果表明:无噪声情况下,优化算法反演结果与真实速度相关系数为1,具有很高的精度;有噪声情况下,增大物质浓度信号的频率与振幅、采用扩散系数较小的物质有助于提高算法的准确度;在微流控装置中,优化算法反演结果与流量传感器测量计算结果的相关系数为0.9814。

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.