Design of Channels with Enhanced Nonlinear Flow for Early Onset of Braess’s Paradox in Microfluidic Networks

Abstract

Microfluidics is a versatile platform that is increasingly being used to understand single-cell and organ responses to biochemical and biomechanical stimuli. Microfluidics is also being used for manufacturing in flow chemistry as well as in diagnostics and drug screening. Understanding and controlling fluid flow in individual microchannels and their networks is critical for the innovative use of microfluidic devices. In this study, we design microfluidic channels of rectangular cross-section with various arrangements of obstacles having varying shapes and sizes. We optimize the designs to maximize the inertia-driven nonlinear relationship between pressure drop and flow rate. This nonlinear pressure–flow relationship is essential for the observance of Braess’s paradox, where under certain conditions, incorporation of additional link channels to a microfluidic network results in a counterintuitive reduction of total flow through the network. The nonlinear relationship between pressure drop and flow rate was obtained using numerical simulation of flow in microfluidic channels and measured as the ratio of the change in hydraulic resistance due to the incorporation of obstacles at a given Reynolds number to the change in hydraulic resistance in the noninertial (linear) regime. A quadratic fit to the pressure–flow data was carried out and incorporated in one of the branches of a Wheatstone bridge-like microfluidic network model. All other branches of the network were modeled as elements with linear pressure–flow relationships. The model network was shown to exhibit Braess’s paradox with flow switching in the link channel. The onset of these phenomena was shown to be controllable through channel design. These findings present a promising strategy for advancing microfluidic channel and network design with potential applications across a broad spectrum of microfluidic technologies.