Theoretical modeling of the behavior of a parallel membrane passive flow regulator

Abstract

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.