Stability and non-linear response of 1D microfluidic-particle streams

Abstract

In this paper, we study the dynamic response of 1D microfluidic-droplet streams to finite-amplitude longitudinal perturbations and demonstrate experimentally that the excitation of localized jams results in the propagation of shock waves. The shock velocity is shown to vanish as the average particle density approaches a critical value thereby leaving long-lived disturbance in the spatial organization of the streams. Using a gradient expansion of the hydrodynamic coupling between the advected particles, we then theoretically derive the non-linear constitutive equation relating particle current to particle density, and show that it leads to the Burgers equation for the droplet stream density.