Nonlinear Flow Generation in Microfluidic Impedance Pumps

Abstract Purpose Impedance pumping offers a valveless flow generation mechanism with potential applications spanning microfluidic biomedical systems such as lab-on-chip and organ-on-chip devices, where membrane actuation is commonly used to manipulate fluid flow. Previous studies have proposed various mechanisms underlying impedance pumping, such as resonance, even in linear systems. However, the relative contributions of nonlinearity, wave dynamics, and resonance to net flow generation remain poorly understood, limiting optimal design of these systems. Methods A comprehensive set of fluid-structure interaction numerical simulations was performed on a mini-sized rectangular, membrane-actuated pump model. Each simulation employed three-dimensional, time-dependent, laminar, incompressible Navier-Stokes equations coupled with nonlinear, large-deformation membrane equations. The small-scale model resulted in low-Reynolds number and high-Womersley-number conditions, a previously under-explored regime relevant to such microfluidic biomedical applications. Results While previous studies have examined these mechanisms separately, none have established an explicit link between them. Three key findings emerge: (1) nonlinearity via steady streaming directly causes net flow rate (NFR) generation, (2) resonance and wave dynamics amplify velocity oscillations and enhance nonlinear effects but do not directly generate NFR, and (3) optimal pincher placement must align with standing-wave antinodes, an outcome that has not been previously recognized. These findings reconcile apparently contradictory wave-based and nonlinearity-based explanations in the literature. Conclusion This study provides novel mechanistic insight into the interaction between nonlinearity, resonance, and wave dynamics in valveless pumping. The antinode placement criterion and clarification of how nonlinearity, resonance, and wave dynamics interaction provide qualitative design guidelines for impedance pump design in microfluidic biomedical devices.