Designing Colloidal Molecules with Microfluidics

Impact of non-reciprocal interactions on colloidal self-assembly with tunable anisotropy

Non-reciprocal (NR) effective interactions violating Newton's third law occur in many biological systems, but can also be engineered in synthetic, colloidal systems. Recent research has shown that such NR interactions can have tremendous effects on the overall collective behavior and pattern formation, but can also influence aggregation processes on the particle scale. Here, we focus on the impact of non-reciprocity on the self-assembly of a colloidal system (originally passive) with anisotropic interactions whose character is tunable by external fields. In the absence of non-reciprocity, that is, under equilibrium conditions, the colloids form square-like and hexagonal aggregates with extremely long lifetimes yet no large-scale phase separation [Kogler et al., Soft Matter 11, 7356 (2015)], indicating kinetic trapping. Here, we study, based on Brownian dynamics simulations in 2D, an NR version of this model consisting of two species with reciprocal isotropic, but NR anisotropic interactions. We find that NR induces an effective propulsion of particle pairs and small aggregates ("active colloidal molecules") forming at the initial stages of self-assembly, an indication of the NR-induced non-equilibrium. The shape and stability of these initial clusters strongly depend on the degree of anisotropy. At longer times, we find, for weak NR interactions, large (even system-spanning) clusters where single particles can escape and enter at the boundaries, in stark contrast to the small rigid aggregates appearing at the same time in the passive case. In this sense, weak NR shortcuts the aggregation. Increasing the degree of NR (and thus, propulsion), we even observe large-scale phase separation if the interactions are weakly anisotropic. In contrast, systems with strong NR and anisotropy remain essentially disordered. Overall, the NR interactions are shown to destabilize the rigid aggregates interrupting self-assembly and phase separation in the passive case, thereby helping the system to overcome kinetic barriers.

Gas-assisted microfluidic step-emulsification for generating micron- and submicron-sized droplets

Micron- and submicron-sized droplets have extensive applications in biomedical diagnosis and drug delivery. Moreover, accurate high-throughput analysis requires a uniform droplet size distribution and high production rates. Although the previously reported microfluidic coflow step-emulsification method can be used to generate highly monodispersed droplets, the droplet diameter (d) is constrained by the microchannel height (b), d ≳ 3 b , while the production rate is limited by the maximum capillary number of the step-emulsification regime, impeding emulsification of highly viscous liquids. In this paper, we report a novel, gas-assisted coflow step-emulsification method, where air serves as the innermost phase of a precursor hollow-core air/oil/water emulsion. Air gradually diffuses out, producing oil droplets. The size of the hollow-core droplets and the ultrathin oil layer thickness both follow the scaling laws of triphasic step-emulsification. The minimal droplet size attains d ≈ 1.7 b , inaccessible in standard all-liquid biphasic step-emulsification. The production rate per single channel is an order-of-magnitude higher than that in the standard all-liquid biphasic step-emulsification and is also superior to alternative emulsification methods. Due to low gas viscosity, the method can also be used to generate micron- and submicron-sized droplets of high-viscosity fluids, while the inert nature of the auxiliary gas offers high versatility.

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.

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.

Mesoscale modelling of droplets' self-assembly in microfluidic channels

A recently proposed mesoscale approach for the simulation of multicomponent flows with near-contact interactions is employed to investigate the early stage formation and clustering statistics of soft flowing crystals in microfluidic channels. Specifically, we first demonstrate the ability of the aforementioned mesoscale model to accurately reproduce main mechanisms leading to the formation of two basic droplet patterns (triangular and hexagonal), in close agreement with experimental evidence. Next, we quantitatively evaluate the device-scale clustering efficiency of the crystal formation process by introducing a new orientational order parameter, based on the Delaunay triangulation and Voronoi diagrams analysis of the droplet patterns. The mesoscale computational approach employed in this work proves to be an efficient tool to shed new light on the complex dynamics of dense emulsions, from short-scale thin-film hydrodynamics, all the way up to global structure formation and statistics of the resulting droplets ensembles.

Controlled packing and single-droplet resolution of 3D-printed functional synthetic tissues

3D-printing networks of droplets connected by interface bilayers are a powerful platform to build synthetic tissues in which functionality relies on precisely ordered structures. However, the structural precision and consistency in assembling these structures is currently limited, which restricts intricate designs and the complexity of functions performed by synthetic tissues. Here, we report that the equilibrium contact angle (θDIB) between a pair of droplets is a key parameter that dictates the tessellation and precise positioning of hundreds of picolitre-sized droplets within 3D-printed, multi-layer networks. When θDIB approximates the geometrically-derived critical angle (θc) of 35.3°, the resulting networks of droplets arrange in regular hexagonal close-packed (hcp) lattices with the least fraction of defects. With this improved control over droplet packing, we can 3D-print functional synthetic tissues with single-droplet-wide conductive pathways. Our new insights into 3D droplet packing permit the fabrication of complex synthetic tissues, where precisely positioned compartments perform coordinated tasks.

Three-Dimensional Printed Devices in Droplet Microfluidics

Droplet microfluidics has become the most promising subcategory of microfluidics since it contributes numerous applications to diverse fields. However, fabrication of microfluidic devices for droplet formation, manipulation and applications is usually complicated and expensive. Three-dimensional printing (3DP) provides an exciting alternative to conventional techniques by simplifying the process and reducing the cost of fabrication. Complex and novel structures can be achieved via 3DP in a simple and rapid manner, enabling droplet microfluidics accessible to more extensive users. In this article, we review and discuss current development, opportunities and challenges of applications of 3DP to droplet microfluidics.

On the role of hydrodynamic interactions in the engineered-assembly of droplet ensembles

Droplets, as they flow inside a microchannel, interact hydrodynamically to result in spatio-temporal patterns. The nature of the interaction decides the type of collective behaviour observed. In this context, we study the application of droplet microfluidics in the area of complex-shape particle synthesis. We show how the dynamics of droplet motion, the steady-state characteristics, the short and long-range hydrodynamics, the dependence on inlet conditions etc. are all related to the features that characterize a device like the functionality (producing many shapes) and robustness (insensitivity to fluctuations). Two primary operating regimes are identified, one where long-range interactions are dominant and the other where they are short-range. In the former, the shapes formed by droplets are steady-state solutions to the governing equations, while in the latter they are a function of how the droplets enter the channel (frequency of entry). We show that identifying the inlet conditions for producing a particle of the desired shape requires the use of a systematic approach to design which involves solving an optimization problem (using genetic algorithms) to identify the optimal operating strategy. With the knowledge of the hydrodynamics between the droplets, we demonstrate how one can reduce the complexity of the design process. We also discuss the control strategies required if one were to realize the identified operating strategy experimentally.

Monodisperse droplet formation by spontaneous and interaction based mechanisms in partitioned EDGE microfluidic device

The partitioned EDGE droplet generation device is known for its’ high monodisperse droplet formation frequencies in two distinct pressure ranges, and an interesting candidate for scale up of microfluidic emulsification devices. In the current study, we test various continuous and dispersed phase properties and device geometries to unravel how the device spontaneously forms small monodisperse droplets (6–18 μm) at low pressures, and larger monodisperse droplets (>28 μm) at elevated pressures. For the small droplets, we show that the continuous phase inflow in the droplet formation unit largely determines droplet formation behaviour and the resulting droplet size and blow-up pressure. This effect was not considered as a factor of significance for spontaneous droplet formation devices that are mostly characterised by capillary numbers in literature. We then show for the first time that the formation of larger droplets is caused by physical interaction between neighbouring droplets, and highly dependent on device geometry. The insights obtained here are an essential step toward industrial emulsification based on microfluidic devices.

Flow-assisted droplet assembly in a 3D microfluidic channel

Self-assembly of soft matter, such as droplets or colloids, has become a promising scheme to engineer novel materials, model living matter, and explore non-equilibrium statistical mechanics. In this article, we present detailed numerical simulations of few non-Brownian droplets in various flow conditions, specifically, focusing on their self-assembly within a short distance in a three-dimensional (3D) microfluidic channel, cf. [Shen et al., Adv. Sci., 2016, 3(6), 1600012]. Contrary to quasi two-dimensional (q2D) systems, where dipolar interaction is the key mechanism for droplet rearrangement, droplets in 3D confinement produce much less disturbance to the underlying flow, thus experiencing weaker dipolar interactions. Using confined simple shear and Poiseuille flows as reference flows, we show that the droplet dynamics is mostly affected by the shear-induced cross-stream migration, which favors chain structures if the droplets are under an attractive depletion force. For more compact clusters, such as three droplets in a triangular shape, our results suggest that an inhomogeneous cross-sectional inflow profile is further required. Overall, the accelerated self-assembly of a small-size droplet cluster results from the combined effects of strong depletion forces, confinement-mediated shear alignments, and fine-tuned inflow conditions. The deterministic nature of the flow-assisted self-assembly implies the possibility of large throughputs, though calibration of all different effects to directly produce large droplet crystals is generally difficult.

Photonics of Template-Mediated Lattices of Colloidal Clusters

The recent progress in microfluidic microfabrication enables mass production of "colloidal molecules" with a preprogrammed geometry (e.g., dumbbells, tetrahedrons, etc.). Such colloids can be used as elementary building blocks in the fabrication of colloidal crystals with unique optical properties. Anisotropic clusters, however, cannot be readily assembled into regular lattices. In this paper, we study photonic properties of compact cubic templates of microdrops encapsulating complex "colloidal molecules". Because monodisperse droplets can be easily packed into dense cubic lattices and encapsulation techniques (e.g., using microfluidics) are well developed, such a material is experimentally feasible. The rationale behind such a methodology is that for a particular alignment of the encapsulated "colloidal molecules" (e.g., by applying an external magnetic or electric field), the resulting structures resemble a diamond lattice, which is known to exhibit a wide complete photonic band gap. The photonic properties of two cubic templates encapsulating dumbbells (symmetric and asymmetric) and tetrahedrons are investigated numerically. In particular, we show the emergence of the complete 3D band gap (∼8% wide for the dielectric contrast ε = 14) for symmetric dumbbells embedded within a face-centered cubic template and oriented along the space diagonal of the elementary cubic cell.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

Highly Multiplexed Single-Cell Protein Profiling with Large-Scale Convertible DNA-Antibody Barcoded Arrays

Highly multiplexed detection of proteins secreted by single cells is always challenging. Herein, a multiplexed in situ tagging technique based on single-stranded DNA encoded microbead arrays and multicolor successive imaging for assaying single-cell secreted proteins with high throughput and high sensitivity is presented. This technology is demonstrated to be capable of increasing the multiplexity exponentially. Upon integration with polydimethylsiloxane microwells, this platform is applied to detect ten immune effector proteins from differentiated single macrophages stimulated with lipopolysaccharide. Significant heterogeneity is observed when the derived human primary macrophages are analyzed. This versatile technology is expected to open new opportunities in systems biology, immune regulation studies, signaling analysis, and molecular diagnostics.

Integral representation of channel flow with interacting particles

We construct a boundary integral representation for the low-Reynolds-number flow in a channel in the presence of freely suspended particles (or droplets) of arbitrary size and shape. We demonstrate that lubrication theory holds away from the particles at horizontal distances exceeding the channel height and derive a multipole expansion of the flow which is dipolar to the leading approximation. We show that the dipole moment of an arbitrary particle is a weighted integral of the stress and the flow at the particle surface, which can be determined numerically. We introduce the equation of motion that describes hydrodynamic interactions between arbitrary, possibly different, distant particles, with interactions determined by the product of the mobility matrix and the dipole moment. Further, the problem of three identical interacting spheres initially aligned in the streamwise direction is considered and the experimentally observed "pair exchange" phenomenon is derived analytically and confirmed numerically. For nonaligned particles, we demonstrate the formation of a configuration with one particle separating from a stable pair. Our results suggest that in a dilute initially homogenous particulate suspension flowing in a channel the particles will eventually separate into singlets and pairs.

Dynamic self-assembly of charged colloidal strings and walls in simple fluid flows

Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing the general principles of self-assembly under non-equilibrium conditions. Here, we report a simple microfluidic experiment, where charged colloidal particles self-assemble into flow-aligned 1D strings with regular particle spacing near a solid boundary. Using high-speed confocal microscopy, we systematically investigate the influence of flow rates, electrostatics and particle polydispersity on the observed string structures. By studying the detailed dynamics of stable flow-driven particle pairs, we quantitatively characterize interparticle interactions. Based on the results, we construct a simple model that explains the intriguing non-equilibrium self-assembly process. Our study shows that the colloidal strings arise from a delicate balance between attractive hydrodynamic coupling and repulsive electrostatic interaction between particles. Finally, we demonstrate that, with the assistance of transverse electric fields, a similar mechanism also leads to the formation of 2D colloidal walls.

Two-dimensional flow of driven particles: a microfluidic pathway to the non-equilibrium frontier

We discuss the basic physics of the flow of micron-scale droplets in 2D geometry.

Passive and active droplet generation with microfluidics: a review

Precise and effective control of droplet generation is critical for applications of droplet microfluidics ranging from materials synthesis to lab-on-a-chip systems. Methods for droplet generation can be either passive or active, where the former generates droplets without external actuation, and the latter makes use of additional energy input in promoting interfacial instabilities for droplet generation. A unified physical understanding of both passive and active droplet generation is beneficial for effectively developing new techniques meeting various demands arising from applications. Our review of passive approaches focuses on the characteristics and mechanisms of breakup modes of droplet generation occurring in microfluidic cross-flow, co-flow, flow-focusing, and step emulsification configurations. The review of active approaches covers the state-of-the-art techniques employing either external forces from electrical, magnetic and centrifugal fields or methods of modifying intrinsic properties of flows or fluids such as velocity, viscosity, interfacial tension, channel wettability, and fluid density, with a focus on their implementations and actuation mechanisms. Also included in this review is the contrast among different approaches of either passive or active nature.