Droplet clusters: exploring the phase space of soft mesoscale atoms

Microfluidic Formulation of Topological Hydrogels for Microtissue Engineering

Microfluidics has recently emerged as a powerful tool in generation of submillimeter-sized cell aggregates capable of performing tissue-specific functions, so-called microtissues, for applications in drug testing, regenerative medicine, and cell therapies. In this work, we review the most recent advances in the field, with particular focus on the formulation of cell-encapsulating microgels of small "dimensionalities": "0D" (particles), "1D" (fibers), "2D" (sheets), etc., and with nontrivial internal topologies, typically consisting of multiple compartments loaded with different types of cells and/or biopolymers. Such structures, which we refer to as topological hydrogels or topological microgels (examples including core-shell or Janus microbeads and microfibers, hollow or porous microstructures, or granular hydrogels) can be precisely tailored with high reproducibility and throughput by using microfluidics and used to provide controlled "initial conditions" for cell proliferation and maturation into functional tissue-like microstructures. Microfluidic methods of formulation of topological biomaterials have enabled significant progress in engineering of miniature tissues and organs, such as pancreas, liver, muscle, bone, heart, neural tissue, or vasculature, as well as in fabrication of tailored microenvironments for stem-cell expansion and differentiation, or in cancer modeling, including generation of vascularized tumors for personalized drug testing. We review the available microfluidic fabrication methods by exploiting various cross-linking mechanisms and various routes toward compartmentalization and critically discuss the available tissue-specific applications. Finally, we list the remaining challenges such as simplification of the microfluidic workflow for its widespread use in biomedical research, bench-to-bedside transition including production upscaling, further in vivo validation, generation of more precise organ-like models, as well as incorporation of induced pluripotent stem cells as a step toward clinical applications.

A double-step emulsification device for direct generation of double emulsions

In microfluidic step emulsification, the size of droplets generated in the dripping regime is predominantly determined by the nozzle's height and only weakly depends on the applied flow rates or liquid properties. While the generation of monodisperse emulsions at high throughput using step emulsifiers has been well established, the generation of double emulsions, i.e., liquid core-shell structures, is still challenging. Here, we demonstrate a novel double-step emulsification method for the direct generation of multi-core double-emulsions and provide a predictive model for the number of cores. While the mechanism of the formation of the core droplets or empty shell droplets follows the well-established scenario of simple step emulsification, the formation of double-emulsion droplets is strongly affected by the presence of the cores. Passing of the cores through the narrowing neck of the shell postpones shell pinch-off. In particular, we demonstrate that our system can be used for the generation of arbitrary large, tightly packed droplet clusters consisting of a controllable number of droplets. Finally, we discuss the options of upscaling the system for high-throughput generation of tailored double emulsions.

Stochastic Jetting and Dripping in Confined Soft Granular Flows

We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behavior of individual grains-here, monodisperse emulsion droplets-to the level of the entire system as the emulsion is focused into a narrow orifice by an external viscous flow. We observe avalanching dynamics and the formation of remarkably stable jets-single-file granular chains-which occasionally break, resulting in a non-Gaussian distribution of cluster sizes. We find that the sequences of droplet rearrangements that lead to the formation of such chains resemble unfolding of cancer cell clusters in narrow capillaries, overall demonstrating that microfluidic emulsion systems could serve to model various aspects of soft granular flows, including also tissue dynamics at the mesoscale.

From dynamic self-organization to avalanching instabilities in soft-granular threads

We study the dynamics of threads of monodisperse droplets, including droplet chains and multi-chains, in which the droplets are interconnected by capillary bridges of another immiscible liquid phase. This system represents wet soft-granular matter - a class of granular materials in which the grains are soft and wetted by thin fluid films-with other examples including wet granular hydrogels or foams. In contrast to wet granular matter with rigid grains (e.g., wet sand), studied previously, the deformability of the grains raises the number of available metastable states and facilitates rearrangements which allow for reorganization and self-assembly of the system under external drive, e.g., applied via viscous forces. We use a co-flow configuration to generate a variety of unique low-dimensional regular granular patterns, intermediate between 1D and 2D, ranging from linear chains and chains with periodically occurring folds to multi-chains and segmented structures including chains of finite length. In particular, we observe that the partially folded chains self-organize via limit cycle of displacements and rearrangements occurring at a frequency self-adapted to the rate of build-up of compressive strain in the chain induced by the viscous forces. Upon weakening of the capillary arrest of the droplets, we observe spontaneous fluidization of the quasi-solid structures and avalanches of rearrangements. We identify two types of fluidization-induced instabilities and rationalize them in terms of a competition between advection and propagation. While we use aqueous droplets as the grains we demonstrate that the reported mechanisms of adaptive self-assembly apply to other types of soft granular systems including foams and microgels. We discuss possible application of the reported quasi-1D compartmentalized structures in tissue engineering, bioprinting and materials science.

Dynamics of polydisperse multiple emulsions in microfluidic channels

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.

Translocation Dynamics of High-Internal Phase Double Emulsions in Narrow Channels

We numerically study the translocation dynamics of double emulsion drops with multiple close-packed inner droplets within constrictions. Such liquid architectures, which we refer to as HIPdEs (high-internal phase double emulsions), consist of a ternary fluid, in which monodisperse droplets are encapsulated within a larger drop in turn immersed in a bulk fluid. Extensive two-dimensional lattice Boltzmann simulations show that if the area fraction of the internal drops is close to the packing fraction limit of hard spheres and the height of the channel is much smaller than the typical size of the emulsion, the crossing yields permanent shape deformations persistent over long periods of time. Morphological changes and rheological response are quantitatively assessed in terms of the structure of the velocity field, circularity of the emulsion, and rate of energy dissipated by viscous forces. Our results may be used to improve the design of soft mesoscale porous materials, which employ HIPdEs as templates for tissue engineering applications.

Stem Cells as a Source of Pancreatic Cells for Production of 3D Bioprinted Bionic Pancreas in the Treatment of Type 1 Diabetes

Type 1 diabetes (T1D) is the third most common autoimmune disease which develops due to genetic and environmental risk factors. Often, intensive insulin therapy is insufficient, and patients require a pancreas or pancreatic islets transplant. However, both solutions are associated with many possible complications, including graft rejection. The best approach seems to be a donor-independent T1D treatment strategy based on human stem cells cultured in vitro and differentiated into insulin and glucagon-producing cells (β and α cells, respectively). Both types of cells can then be incorporated into the bio-ink used for 3D printing of the bionic pancreas, which can be transplanted into T1D patients to restore glucose homeostasis. The aim of this review is to summarize current knowledge about stem cells sources and their transformation into key pancreatic cells. Last, but not least, we comment on possible solutions of post-transplant immune response triggered stem cell-derived pancreatic cells and their potential control mechanisms.

One-Step Generation of Multisomes from Lipid-Stabilized Double Emulsions

Multisomes are multicompartmental structures formed by a lipid-stabilized network of aqueous droplets, which are contained by an outer oil phase. These biomimetic structures are emerging as a versatile platform for soft matter and synthetic biology applications. While several methods for producing multisomes have been described, including microfluidic techniques, approaches for generating biocompatible, monodisperse multisomes in a reproducible manner remain challenging to implement due to low throughput and complex device fabrication. Here, we report on a robust method for the dynamically controlled generation of multisomes with controllable sizes and high monodispersity from lipid-based double emulsions. The described microfluidic approach entails the use of three different phases forming a water/oil/water (W/O/W) double emulsion stabilized by lipid layers. We employ a gradient of glycerol concentration between the inner core and outer phase to drive the directed osmosis, allowing the swelling of lamellar lipid layers resulting in the formation of small aqueous daughter droplets at the interface of the inner aqueous core. By adding increasing concentrations of glycerol to the outer aqueous phase and subsequently varying the osmotic gradient, we show that key structural parameters, including the size of the internal droplets, can be specifically controlled. Finally, we show that this approach can be used to generate multisomes encapsulating small-molecule cargo, with potential applications in synthetic biology, drug delivery, and as carriers for active materials in the food and cosmetics industries.

The vortex-driven dynamics of droplets within droplets

Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The observed dynamic regimes range from long-lived NES at low core-area fraction, characterised by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.

Particle Stabilization of Oil-Fluorocarbon Interfaces and Effects on Multiphase Oil-in-Water Complex Emulsion Morphology and Reconfigurability

Stabilization of oil-oil interfaces is important for nonaqueous emulsions as well as for multiphase oil-in-water emulsions, with relevance to a variety of fields ranging from emulsion polymerization to sensors and optics. Here, we focus on examining the ability of functionalized silica particles to stabilize interfaces between fluorinated oils and other immiscible oils (such as hydrocarbons and silicones) in nonaqueous emulsions and also on the particles' ability to affect the morphology and reconfigurability of complex, biphasic oil-in-water emulsions. We compare the effectiveness of fluorophilic, lipophilic, and bifunctional fluorophilic-lipophilic coated nanoparticles to stabilize these oil-oil interfaces. Sequential bulk emulsification steps by vortex mixing, or emulsification by microfluidics, can be used to create complex droplets in which particles stabilize the oil-oil interfaces and surfactants stabilize the oil-water interfaces. We examine the influence of particles adsorbed at the internal oil-oil interface in complex droplets to hinder the reconfiguration of these complex emulsions upon addition of aqueous surfactants, creating "metastable" droplets that resist changes in morphology. Such metastable droplets can be triggered to reconfigure when heated above their upper critical solution temperature. Thus, not only do these bifunctional silica particles enable the stabilization of a broad array of oil-fluorocarbon nonaqueous emulsions, but the ability to address the oil-oil interface within complex O/O/W droplets expands the diversity of oil chemical choices available and the accessibility of droplet morphologies and sensitivity.

Phase-field-based lattice Boltzmann model for immiscible incompressible N-phase flows

In this paper, we develop an efficient and alternative lattice Boltzmann (LB) model for simulating immiscible incompressible N-phase flows (N≥2) based on the Cahn-Hilliard phase field theory. In order to facilitate the design of LB model and reduce the calculation of the gradient term, the governing equations of the N-phase system are reformulated, and they satisfy the conservation of mass, momentum and the second law of thermodynamics. In the present model, (N-1) LB equations are employed to capture the interface, and another LB equation is used to solve the Navier-Stokes (N-S) equations, where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term. The developed model is first validated by two classical benchmark problems, including the tests of static droplets and the spreading of a liquid lens, the simulation results show that the current LB model is accurate and efficient for simulating incompressible N-phase fluid flows. To further demonstrate the capability of the LB model, two numerical simulations, including dynamics of droplet collision for four fluid phases and dynamics of droplets and interfaces for five fluid phases, are performed to test the developed model. The results show that the present model can successfully handle complex interactions among N (N≥2) immiscible incompressible flows.

Flow-induced nanostructuring of gelled emulsions

Although the phase behavior of emulsions has been thoroughly investigated, the effect of flow on emulsion morphology, which is relevant for many applications, is far from being fully elucidated. Here, we investigate an emulsion based on two common nonionic surfactants in a range of water concentration where complex and diverse microstructures are found at rest, such as multilamellar and bicontinuous phases. In spite of such complexity, once subjected to shear flow, all the emulsions investigated are characterized by thinning filaments which eventually break up into a concentrated suspension of micro-sized water-based droplets dispersed in a continuous oil phase. The so-formed droplets tend to align in string-like structures. The emulsions exhibit a yield stress, whose value can be estimated by the plug-core velocity profiles in pressure-driven capillary flow, thus providing evidence of weakly attractive interdroplet interactions. The latter are consistent with droplet clustering and percolation observed at rest. These results can also be relevant to the flow behavior of other liquid-liquid systems, such as polymer blends, where the flow-induced microstructure is under debate as well.

A new droplet-forming fluidic junction for the generation of highly compartmentalised capsules

A new oscillatory microfluidic junction is described, which enables the consistent formation of highly uniform and complex double emulsions, and is demonstrated for the encapsulation of four different reagents within the inner droplets (called cores) of the double emulsion droplets. Once the double emulsion droplets had attained a spherical form, the cores assumed specific 3D arrangements, the orchestration of which appeared to depend upon the specific emulsion morphology. Such double emulsion droplets were used as templates to produce highly compartmentalised microcapsules and multisomes. Based on these construct models, we numerically demonstrated a model chemical reaction sequence between and within the liquid cores. This work could provide a platform to perform space/time-dependent applications, such as programmed experiments, synthesis, and delivery systems.

Controlled droplet microfluidic systems for multistep chemical and biological assays

Droplet microfluidics is a relatively new and rapidly evolving field of science focused on studying the hydrodynamics and properties of biphasic flows at the microscale, and on the development of systems for practical applications in chemistry, biology and materials science.

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.

3D spherical-cap fitting procedure for (truncated) sessile nano- and micro-droplets & -bubbles

In the study of nanobubbles, nanodroplets or nanolenses immobilised on a substrate, a cross-section of a spherical cap is widely applied to extract geometrical information from atomic force microscopy (AFM) topographic images. In this paper, we have developed a comprehensive 3D spherical-cap fitting procedure (3D-SCFP) to extract morphologic characteristics of complete or truncated spherical caps from AFM images. Our procedure integrates several advanced digital image analysis techniques to construct a 3D spherical-cap model, from which the geometrical parameters of the nanostructures are extracted automatically by a simple algorithm. The procedure takes into account all valid data points in the construction of the 3D spherical-cap model to achieve high fidelity in morphology analysis. We compare our 3D fitting procedure with the commonly used 2D cross-sectional profile fitting method to determine the contact angle of a complete spherical cap and a truncated spherical cap. The results from 3D-SCFP are consistent and accurate, while 2D fitting is unavoidably arbitrary in the selection of the cross-section and has a much lower number of data points on which the fitting can be based, which in addition is biased to the top of the spherical cap. We expect that the developed 3D spherical-cap fitting procedure will find many applications in imaging analysis.

How a Surface Nanodroplet Sits on the Rim of a Microcap

The location and morphology of femtoliter nanodroplets that nucleate and grow on a microcap-decorated substrate in contact with a liquid phase were investigated. We experimentally examined four different wetting combinations of the flat area and the microcaps. The results show that depending on the relative wettability, the droplets sit either on the plain surface or on the top of the microcap or on the rim of the microcap. The contact angle and, for the last case, the radial positions of the nanodroplets relative to the microcap center were characterized, in reasonable agreement with our theoretical analysis, which is based on an interfacial energy minimization argument. However, the experimental data show considerable scatter around the theoretical equilibrium curves, reflecting pinning and thus nonequilibrium effects. We also provide the theoretical phase diagram in parameter space of the contact angles, revealing under which conditions the nanodroplet will nucleate on the rim of the microcap.

Ternary free-energy lattice Boltzmann model with tunable surface tensions and contact angles

We present a ternary free-energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model presented here can be extended to include an arbitrary number of fluid components.

Clusters of polyhedra in spherical confinement

Dense particle packing in a confining volume remains a rich, largely unexplored problem, despite applications in blood clotting, plasmonics, industrial packaging and transport, colloidal molecule design, and information storage. Here, we report densest found clusters of the Platonic solids in spherical confinement, for up to [Formula: see text] constituent polyhedral particles. We examine the interplay between anisotropic particle shape and isotropic 3D confinement. Densest clusters exhibit a wide variety of symmetry point groups and form in up to three layers at higher N. For many N values, icosahedra and dodecahedra form clusters that resemble sphere clusters. These common structures are layers of optimal spherical codes in most cases, a surprising fact given the significant faceting of the icosahedron and dodecahedron. We also investigate cluster density as a function of N for each particle shape. We find that, in contrast to what happens in bulk, polyhedra often pack less densely than spheres. We also find especially dense clusters at so-called magic numbers of constituent particles. Our results showcase the structural diversity and experimental utility of families of solutions to the packing in confinement problem.

Nonequilibrium structure in sequential assembly

The assembly of monomeric constituents into molecular superstructures through sequential-arrival processes has been simulated and theoretically characterized. When the energetic interactions allow for complete overlap of the particles, the model is equivalent to that of the sequential absorption of soft particles on a surface. In the present work, we consider more general cases by including arbitrary aggregating geometries and varying prescriptions of the connectivity network. The resulting theory accounts for the evolution and final-state configurations through a system of equations governing structural generation. We find that particle geometries differ significantly from those in equilibrium. In particular, variations of structural rigidity and morphology tune particle energetics and result in significant variation in the nonequilibrium distributions of the assembly in comparison to the corresponding equilibrium case.

Compound droplet manipulations on fiber arrays

Recent works demonstrated that fiber arrays may constitute new means of designing open digital microfluidic systems. Various processes, such as droplet motion, fragmentation, trapping, release, mixing and encapsulation, may be achieved on fiber arrays. However, handling a large number of tiny droplets resulting from the mixing of several liquid components is required for developing microreactors, smart sensors or microemulsifying drugs. Here, we show that the manipulation of tiny droplets onto fiber networks allows for creating compound droplets with a high complexity level. Moreover, this cost-effective and adjustable method may also be implemented with optical fibers in order to develop fluorescence-based biosensor.