We present a theoretical model for the non-linear pressure-flow relationship of a microvalve which exploits the non-linear behavior of two horizontal parallel membranes for autonomous flow regulation. The analysis, buttressed by numerical studies correctly illustrates the nonlinear behavior of the valve based on the experimental study presented in our earlier report. We study the elastic deformation of the PDMS membranes under varied pressure loads to the point of contact, and their resultant effects on flow restriction which counteractively changes - without any external energy input - to balance pressure variations, thereby ensuring a stable output flow. We demonstrate analytically how structural parameters and material properties influence the performance of the device in terms of saturation of flow and the minimum pressure required to kick-start the autonomous regulation. The outputs of our approach are in very good conformity with our experimental investigations, giving us all confidence to follow it for the delivery of designs with specific performance targets. We expect this model to provide insights and guidelines for optimized designs of microfluidic actuators for various lab-on-a-chip applications.

我们提出了一种微型阀的非线性压力-流量关系的理论模型，该模型利用两个水平平行膜的非线性行为进行自主流量调节。该分析在数值研究的支持下，根据我们先前报告中提供的实验研究正确地说明了阀门的非线性行为。我们研究了压力变化到接触点时PDMS膜的弹性变形，以及它们对流量限制的最终影响，该流量反作用地变化-在没有任何外部能量输入的情况下-平衡压力变化，从而确保稳定的输出流量。我们通过分析证明了结构参数和材料特性如何根据流动的饱和度和启动自主调节所需的最小压力影响设备的性能。我们的方法的输出与我们的实验研究非常吻合，使我们所有人都有信心遵循它来交付具有特定性能目标的设计。我们希望该模型能够为各种芯片实验室应用的微流体执行器的优化设计提供见识和指导。