Short- and long-term avalanche dynamics in 1D-printed microfluidic crystals

TL;DR

This study investigates the avalanche-like collapse of 1D microfluidic crystal chains of monodisperse water-in-oil droplets, revealing dynamics influenced by substrate roughness and packing fraction, with implications for microfluidic printing.

Contribution

It provides the first detailed analysis of avalanche dynamics in 1D microfluidic crystals, including effects of substrate roughness and packing density.

Findings

Collapse waves propagate with variable acceleration or deceleration.

Coarse-grained dynamics are initially linear in time, then plateau.

Roughened substrates can prevent collapse.

Abstract

We report arrays of monodisperse water-in-oil microdroplets printed onto a substrate in a form of a compact linear chain -- a 1D-crystal -- pinned at one end. The chain spontaneously collapses under capillary forces via a sequence of avalanche-like rearrangement waves, resembling the rearrangements in a flowing microfluidic crystal, yet limited by the hydrodynamic friction at the substrate. While the propagation of the subsequent waves, separated by highly ordered metastable states, is either accelerating or decelerating depending on the direction of collapse, the coarse-grained dynamics of multiple waves -- at moderate packing fractions $\phi$ -- is initially linear in time, before leveling off. We further demonstrate how the collapse can be prevented via the use of a roughened substrate. Our study provides insight into the short- and long-term avalanche dynamics in granular systems with free interfaces and opens way to precision-printing of microfluidic assays.