Self-organizing microfluidic crystals

Low-cost fluorescence microscope with microfluidic device fabrication for optofluidic applications

Optofluidic devices have revolutionized the manipulation and transportation of fluid at smaller length scales ranging from micrometers to millimeters. We describe a dedicated optical setup for studying laser-induced cavitation inside a microchannel. In a typical experiment, we use a tightly focused laser beam to locally evaporate the solution laced with a dye resulting in the formation of a microbubble. The evolving bubble interface is tracked using high-speed microscopy and digital image analysis. Furthermore, we extend this system to analyze fluid flow through fluorescence-Particle Image Velocimetry (PIV) technique with minimal adaptations. In addition, we demonstrate the protocols for the in-house fabrication of a microchannel tailored to function as a sample holder in this optical setup. In essence, we present a complete guide for constructing a fluorescence microscope from scratch using standard optical components with flexibility in the design and at a lower cost compared to its commercial analogues.

Exceptional topology in ordinary soft matter

Hydrodynamics is shown to induce non-Hermitian topological phenomena in ordinary, passive soft matter. This is demonstrated by subjecting a two-dimensional elastic lattice to a low-Reynolds viscous flow. The interplay of hydrodynamics and elasticity splits Dirac cones into bulk Fermi arcs, pairing exceptional points with opposite half-integer topological charges. The bulk Fermi arc is a generic hallmark of the system exhibited in all lattice and flow symmetries. An analytic model and simulations explain how the emergent singularities shape the spectral bands and give rise to a web of van Hove singularity lines in the density of states. The present findings suggest that non-Hermitian physics can be explored in a broad class of ordinary soft matter, living and artificial alike, opening avenues for topology-based technology in this regime.

Oscillatory shear-induced bcc-fcc martensitic transformation in a colloidal suspension with long-range repulsive interactions

We perform non-equilibrium Brownian dynamics simulations to investigate the out-of-equilibrium phase behavior of a suspension of charged colloids under external oscillatory shear. We independently vary the frequency f and the maximum strain amplitude γ_max of the oscillations and map out an out-of-equilibrium phase diagram in the f-γ_max plane. Similar to what has been observed in earlier studies on colloidal hard spheres, we find the formation of a twinned face-centered-cubic phase in a specific range of γ_max, which displays a martensitic transition to a body-centered-cubic crystal within half of the oscillation cycle. We provide a comprehensive analysis of these structures and show how the system transforms from one to the other. We also report evidence of a sliding layer phase and a string phase.

Scanning two-photon continuous flow lithography for the fabrication of multi-functional microparticles

In this work, we demonstrate the high-throughput fabrication of 3D microparticles using a scanning two-photon continuous flow lithography (STP-CFL) technique in which microparticles are shaped by scanning the laser beam at the interface of laminar co-flows. The results demonstrate the ability of STP-CFL to manufacture high-resolution complex geometries of cell carriers that possess distinct regions with different functionalities. A new approach is presented for printing out-of-plane features on the microparticles. The approach eliminates the use of axial scanning stages, which are not favorable since they induce fluctuations in the flowing polymer media and their scanning speed is slower than the speed of galvanometer mirror scanners.

Universal motion of mirror-symmetric microparticles in confined Stokes flow

Comprehensive understanding of particle motion in microfluidic devices is essential to unlock additional technologies for shape-based separation and sorting of microparticles like microplastics, cells, and crystal polymorphs. Such particles interact hydrodynamically with confining surfaces, thus altering their trajectories. These hydrodynamic interactions are shape dependent and can be tuned to guide a particle along a specific path. We produce strongly confined particles with various shapes in a shallow microfluidic channel via stop flow lithography. Regardless of their exact shape, particles with a single mirror plane have identical modes of motion: in-plane rotation and cross-stream translation along a bell-shaped path. Each mode has a characteristic time, determined by particle geometry. Furthermore, each particle trajectory can be scaled by its respective characteristic times onto two master curves. We propose minimalistic relations linking these timescales to particle shape. Together these master curves yield a trajectory universal to particles with a single mirror plane.

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.

Change in collective motion of colloidal particles driven by an optical vortex with driving force and spatial confinement

We studied the change in collective behavior of optically driven colloidal particles on a circular path. The particles are simultaneously driven by the orbital angular momentum of an optical vortex beam generated by holographic optical tweezers. The driving force is controlled by the topological charge l of the vortex. By varying the driving force and spatial confinement, four characteristic collective motions were observed. The collective behavior results from the interplay between the optical interaction, hydrodynamic interaction and spatial confinement. Varying the topological charge of an optical vortex not only induces changes in driving force but also alters the stability of three-dimensional optical trapping. The switch between dynamic clustering and stable clustering was observed in this manner. Decreasing the cell thickness diminishes the velocity of the respective particles and increases the spatial confinement. A jamming-like characteristic collective motion appears when the thickness is small and the topological charge is large. In this regime, a ring of equally-spaced doublets was spontaneously formed in systems composed of an even number of particles.

Different bending models predict different dynamics of sedimenting elastic trumbbells

The main goal of this paper is to examine theoretically and numerically the impact of a chosen bending model on the dynamics of elastic filaments settling in a viscous fluid under gravity at low-Reynolds-number. We use the bead-spring approximation of a filament and the Rotne-Prager mobility matrix to describe hydrodynamic interactions between the beads. We analyze the dynamics of trumbbells, for which bending angles are typically larger than for thin and long filaments. Each trumbbell is made of three beads connected by springs and it exhibits a bending resistance, described by the harmonic or - alternatively - by the 'cosine' (also called the Kratky-Porod) bending models, both often used in the literature. Using the harmonic bending potential, and coupling it to the spring potential by the Young's modulus, we find simple benchmark solutions: stable stationary configurations of a single elastic trumbbell and attraction of two elastic trumbbells towards a periodic long-lasting orbit. As the most significant result of this paper, we show that for very elastic trumbbells at the same initial conditions, the Kratky-Porod bending potential can lead to qualitatively and quantitatively different spurious dynamics, with artificially large bending angles and unrealistic shapes. We point out that for the bead models of an elastic filament, the range of applicability of the Kratky-Porod model might not go beyond bending angles smaller than π/2 for touching beads and beyond an even much lower value for beads well-separated from each other. The existence of stable stationary configurations of elastic trumbbells and a family of periodic oscillations of two elastic trumbbells are very important findings on their own.

Calculating the motion of highly confined, arbitrary-shaped particles in Hele-Shaw channels

We combine theory and numerical calculations to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an effective quasi-two-dimensional description of the Stokes flow around the particle via the Brinkman equation, which can be solved in a time that is two orders of magnitude faster than the three-dimensional problem. The computational speedup enables us to calculate the full trajectories of particles in the channel. To validate our scheme, we study the motion of dumbbell-shaped particles that are produced in a microfluidic channel using 'continuous-flow lithography'. Contrary to what was reported in earlier work (Uspal et al. in Nat Commun 4:2666, 2013), we find that the reorientation time of a dumbbell particle in an external flow exhibits a minimum as a function of its disk size ratio. This finding is in excellent agreement with new experiments, thus confirming the predictive power of our scheme.

Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow

Driven or active suspensions can display fascinating collective behavior, where coherent motions or structures arise on a scale much larger than that of the constituent particles. Here, we report numerical simulations and an analytical model revealing that deformable particles and, in particular, red blood cells (RBCs) assemble into regular patterns in a confined shear flow. The pattern wavelength concurs well with our experimental observations. The order is of a pure hydrodynamic and inertialess origin, and it emerges from a subtle interplay between (i) hydrodynamic repulsion by the bounding walls that drives deformable cells towards the channel midplane and (ii) intercellular hydrodynamic interactions that can be attractive or repulsive depending on cell-cell separation. Various crystal-like structures arise depending on the RBC concentration and confinement. Hardened RBCs in experiments and rigid particles in simulations remain disordered under the same conditions where deformable RBCs form regular patterns, highlighting the intimate link between particle deformability and the emergence of order.

Steering particles by breaking symmetries

We derive general equations of motions for highly-confined particles that perform quasi-two-dimensional motion in Hele-Shaw channels, which we solve analytically, aiming to derive design principles for self-steering particles. Based on symmetry properties of a particle, its equations of motion can be simplified, where we retrieve an earlier-known equation of motion for the orientation of dimer particles consisting of disks (Uspal et al 2013 Nat. Commun. 4), but now in full generality. Subsequently, these solutions are compared with particle trajectories that are obtained numerically. For mirror-symmetric particles, excellent agreement between the analytical and numerical solutions is found. For particles lacking mirror symmetry, the analytic solutions provide means to classify the motion based on particle geometry, while we find that taking the side-wall interactions into account is important to accurately describe the trajectories.

Advances in colloidal manipulation and transport via hydrodynamic interactions

In this review article, we highlight many recent advances in the field of micromanipulation of colloidal particles using hydrodynamic interactions (HIs), namely solvent mediated long-range interactions. At the micrsocale, the hydrodynamic laws are time reversible and the flow becomes laminar, features that allow precise manipulation and control of colloidal matter. We focus on different strategies where externally operated microstructures generate local flow fields that induce the advection and motion of the surrounding components. In addition, we review cases where the induced flow gives rise to hydrodynamic bound states that may synchronize during the process, a phenomenon essential in different systems such as those that exhibit self-assembly and swarming.

Activity-induced instability of phonons in 1D microfluidic crystals

One-dimensional crystals of passively-driven particles in microfluidic channels exhibit collective vibrational modes reminiscent of acoustic 'phonons'. These phonons are induced by the long-range hydrodynamic interactions among the particles and are neutrally stable at the linear level. Here, we analyze the effect of particle activity - self-propulsion - on the emergence and stability of these phonons. We show that the direction of wave propagation in active crystals is sensitive to the intensity of the background flow. We also show that activity couples, at the linear level, transverse waves to the particles' rotational motion, inducing a new mode of instability that persists in the limit of large background flow, or, equivalently, vanishingly small activity. We then report a new phenomenon of phonons switching back and forth between two adjacent crystals in both passively-driven and active systems, similar in nature to the wave switching observed in quantum mechanics, optical communication, and density stratified fluids. These findings could have implications for the design of commercial microfluidic systems and the self-assembly of passive and active micro-particles into one-dimensional structures.

Seeing the unseen: Imaging rotation in cells with designer anisotropic particles

Cellular functions are enabled by cascades of transient biological events. Imaging and tracking the dynamics of these events have proven to be a powerful means of understanding the principles of cellular processes. These studies have typically focused on translational dynamics. By contrast, investigations of rotational dynamics have been scarce, despite emerging evidence that rotational dynamics are an inherent feature of many cellular processes and may also provide valuable clues to understanding those cell functions. Such studies have been impeded by the limited availability of suitable rotational imaging probes. This has recently changed thanks to the advances in the development of anisotropic particles for rotational imaging. In this review, we will summarize current techniques for imaging rotation using particle probes that are anisotropic in shape or optical properties. We will highlight two studies that demonstrate how these techniques can be applied to explore important facets of cellular functions.

Dynamic clustering of driven colloidal particles on a circular path

We studied the collective motion of particles forced to move along a circular path in water by utilizing an optical vortex. Their collective motion, including the spontaneous formation of clusters and their dissociation, was observed. The observed temporal patterns depend on the number of particles on the path and the variation of their sizes. The addition of particles with different sizes suppresses the dynamic formation and dissociation of clusters and promotes the formation of specific stationary clusters. These experimental findings are reproduced by numerical simulations that take into account the hydrodynamic interaction between the particles and the radial trapping force confining the particles to the circular path. A transition between stationary and nonstationary clustering of the particles was observed by varying their size ratio in the binary-size systems. Our simulation reveals that the transition can be either continuous or discontinuous depending on the number of different-size particles. This result suggests that the size distribution of particles has a significant effect on the collective behavior of self-propelled particles in viscous fluids.

Collective waves in dense and confined microfluidic droplet arrays

Excitation mechanisms for collective waves in confined dense one-dimensional microfluidic droplet arrays are investigated by experiments and computer simulations. We demonstrate that distinct modes can be excited by creating specific 'defect' patterns in flowing droplet trains. Excited longitudinal modes exhibit a short-lived cascade of pairs of laterally displacing droplets. Transversely excited modes obey the dispersion relation of microfluidic phonons and induce a coupling between longitudinal and transverse modes, whose origin is the hydrodynamic interaction of the droplets with the confining walls. Moreover, we investigate the long-time behaviour of the oscillations and discuss possible mechanisms for the onset of instabilities. Our findings demonstrate that the collective dynamics of microfluidic droplet ensembles can be studied particularly well in dense and confined systems. Experimentally, the ability to control microfluidic droplets may allow the modulation of the refractive index of optofluidic crystals, which is a promising approach for the production of dynamically programmable metamaterials.

Two spheres translating in tandem through a colloidal suspension

Using laser tweezers, two colloidal particles are held parallel to a uniformly flowing suspension of similarly sized bath particles at an effective volume fraction ϕ(eff)=0.41. The local deformation in the bath suspension is imaged by confocal microscopy, and, concurrently, the drag forces exerted on both the leading and the trailing probe particles are measured as a function of probe separation and velocity. The bath structure changes in response to the velocity and separation of the probes. A depleted region between probes is observed at sufficiently high velocities. Both probes experience the same drag force and the drag force increases with probe separation. The results indicate that bath-probe and probe-probe hydrodynamic interactions contribute microstructure and drag force and that drag exerted by direct bath-probe collisions is reduced compared to an isolated probe.