Spatiotemporal periodicity of dislocation dynamics in a two-dimensional microfluidic crystal flowing in a tapered channel

Abstract

When a many-body system is driven away from equilibrium, order can spontaneously emerge in places where disorder might be expected. Here we report an unexpected order in the flow of a concentrated emulsion in a tapered microfluidic channel. The velocity profiles of individual drops in the emulsion show periodic patterns in both space and time. Such periodic patterns appear surprising from both a fluid and a solid mechanics point of view. In particular, when the emulsion is considered as a soft crystal under extrusion, a disordered scenario might be expected based on the stochastic nature of dislocation dynamics in microscopic crystals. However, an orchestrated sequence of dislocation nucleation and migration is observed to give rise to a highly ordered deformation mode. This discovery suggests that nanocrystals can be made to deform more controllably than previously thought. It can also lead to novel flow control and mixing strategies in droplet microfluidics.many-body system | order | microfluidic crystal | dislocation dynamics | plasticity T he emergence of order and spontaneous self-organization have been of long-standing interest (1). They are key not only to the understanding of complex phenomena from chemical oscillators to swarming behavior in animals (2, 3), but also to novel engineering solutions if harnessed (4, 5). Two-phase flow in microfluidics offers a simple platform for the study of dissipative nonequilibrium systems, where hydrodynamic interactions have led to the emergence of collective dynamics and order (6-10). Most works thus far have focused on dilute emulsions or foams in simple channel geometries. Whereas rich physics has been revealed, these phenomena have yet to find implications in the broader technological context. Nevertheless, concentrated emulsions, bubble rafts, and colloids have long been used as models of crystals for studying grain boundaries, dislocations, plasticity, and other processes central to materials science and solid mechanics (11-16). Such systems have not been applied to model the deformation modes of nanocrystals, however. Recent work on crystal plasticity in microscopic samples found that in contrast to their macroscopic counterparts, both the external geometry and internal structure of the material determine material strength (17). Furthermore, the size and timing of dislocation-induced strain bursts are found to be intermittent, stochastic, and unpredictable (17-20). The stochastic nature of dislocation dynamics complicates the control of the shape of the materials during deformation, and renders their subsequent manipulation and manufacturing challenging (18). What is unknown, however, is whether plasticity remains stochastic as the sample shrinks to the nanoscale, and whether the dimensionality and loading conditions influence the stochasticity. Given the increasing importance of low-dimensional nanodevices in applications from optoelectronics to energy conversion, it is critical to understand how nanomaterials can be shaped, manipulated, and manufactured.In t...

Universal Features of Metastable State Energies in Cellular Matter

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Collective nucleation dynamics in two-dimensional emulsions with hexagonal packing

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“…We process the images to obtain both the position, solid fraction nS, and statistical distributions of solid-drop cluster sizes based on Voronoi analysis [31][32][33]. Temperature variation across the capillary was considered negligible since the number density of solidified droplets in the left section of the capillary was not significantly different from the right section.…”

Microfluidic Formation of Honeycomb-Patterned Droplets Bounded by Interface Bilayers via Bimodal Molecular Adsorption

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