Activity-induced instability of phonons in 1D microfluidic crystals

The Stability of a Hydrodynamic Bravais Lattice

We present the results of a theoretical investigation of the stability and collective vibrations of a two-dimensional hydrodynamic lattice comprised of millimetric droplets bouncing on the surface of a vibrating liquid bath. We derive the linearized equations of motion describing the dynamics of a generic Bravais lattice, as encompasses all possible tilings of parallelograms in an infinite plane-filling array. Focusing on square and triangular lattice geometries, we demonstrate that for relatively low driving accelerations of the bath, only a subset of inter-drop spacings exist for which stable lattices may be achieved. The range of stable spacings is prescribed by the structure of the underlying wavefield. As the driving acceleration is increased progressively, the initially stationary lattices destabilize into coherent oscillatory motion. Our analysis yields both the instability threshold and the wavevector and polarization of the most unstable vibrational mode. The non-Markovian nature of the droplet dynamics renders the stability analysis of the hydrodynamic lattice more rich and subtle than that of its solid state counterpart.

Collective excitations in active fluids: Microflows and breakdown in spectral equipartition of kinetic energy

The effect of particle activity on collective excitations in active fluids of microflyers is studied. With an in silico study, we observed an oscillating breakdown of equipartition (uniform spectral distribution) of kinetic energy in reciprocal space. The phenomenon is related to short-range velocity-velocity correlations that were realized without forming of long-lived mesoscale vortices in the system. This stands in contrast to well-known mesoscale turbulence operating in active nematic systems (bacterial or artificial) and reveals the features of collective dynamics in active fluids, which should be important for structural transitions and glassy dynamics in active matter.

Microfluidic formation of crystal-like structures

Crystal-like structures find application in several fields ranging from biomedical engineering to material science. For instance, droplet crystals are critical for high throughput assays and material synthesis, while particle crystals are important for particles and cell encapsulation, Drop-seq technologies, and single-cell analysis. Formation of crystal-like structures relies entirely on the possibility of manipulating with great accuracy the micrometer-size objects forming the crystal. In this context, microfluidic devices offer versatile tools for the precise manipulation of droplets and particles, thus enabling fabrication of crystal-like structures that form due to hydrodynamic interactions among droplets or particles. In this review, we aim at providing an holistic representation of crystal-like structure formation mediated by hydrodynamic interactions in microfluidic devices. We also discuss the physical origin of these hydrodynamic interactions and their relation to parameters such as device geometry, fluid properties, and flow conditions.

Collective vibrations of a hydrodynamic active lattice

Recent experiments show that quasi-one-dimensional lattices of self-propelled droplets exhibit collective instabilities in the form of out-of-phase oscillations and solitary-like waves. This hydrodynamic lattice is driven by the external forcing of a vertically vibrating fluid bath, which invokes a field of subcritical Faraday waves on the bath surface, mediating the spatio-temporal droplet coupling. By modelling the droplet lattice as a memory-endowed system with spatially non-local coupling, we herein rationalize the form and onset of instability in this new class of dynamical oscillator. We identify the memory-driven instability of the lattice as a function of the number of droplets, and determine equispaced lattice configurations precluded by geometrical constraints. Each memory-driven instability is then classified as either a super- or subcritical Hopf bifurcation via a systematic weakly nonlinear analysis, rationalizing experimental observations. We further discover a previously unreported symmetry-breaking instability, manifest as an oscillatory-rotary motion of the lattice. Numerical simulations support our findings and prompt further investigations of this nonlinear dynamical system.

Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers

It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.