Encapsulated drop breakup in shear flow

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.

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.

Interfacial behavior of surfactant-covered double emulsion in extensional flow

We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. Upon surfactant application, the outer droplet deformation increases and the inner droplet deformation decreases. The concentrated surfactants on the outer interface increase deformation, and the inner droplet is affected by the inner flow. At a fixed Péclet number (Pe), the surfactant concentration at the outer interface increases with an increase in capillary number (Ca); however, such a tendency is difficult to identify at the inner interface. Next, the Pe effects are analyzed. With an increase in Pe, the deformation of the inner droplet decreases significantly. The local distribution of the surfactant considerably affects the double emulsion stabilization, which is analyzed in terms of internal flow. The interfacial tension gradient induced by the surfactant generates vortices internally, which is verified by applying the surfactant to each interface independently. The radius ratio affects droplet deformation and surfactant transport. The compression of the inner flow region increases the viscous force and decreases the interface velocity. Therefore, with an increase in radius ratio, the deformation increases, and the surfactant transport becomes slow.

Modeling drug delivery from multiple emulsions

We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multilayer droplet where the drug kinetics are described by a pure diffusive process through different liquid shells. The multilayer problem is described by a system of diffusion equations coupled via interlayer conditions imposing continuity of drug concentration and flux. Mass resistance is imposed at the outer boundary through the application of a surfactant at the external surface of the droplet. The two-dimensional problem is solved numerically by finite volume discretization. Concentration profiles and drug release curves are presented for three typical round-shaped (circle, ellipse, and bullet) droplets and the dependency of the solution on the mass transfer coefficient at the surface analyzed. The main result shows a reduced release time for an increased elongation of the droplets.

Effect of interactions between multiple interfaces on the rheological characteristics of double emulsions

In this study, we analyzed the rheological characteristics of double emulsions by using a three-dimensional lattice Boltzmann model. Numerical simulations indicate that interactions between multiple interfaces play a vital role in determining the shear stress on interfaces and affect deformations, which influence the relative viscosity of double emulsions. The large shear stress induced by droplets in contact increases the relative viscosity for high volume fractions. The double emulsions also show shear-thinning behavior, which corresponds with the Carreau model. The interfacial interference between the core and the deforming shell cause the relative viscosity to increase with increasing core-droplet radius. Finally, we investigated the dependence of the double-emulsion viscosity on the core-droplet viscosity. At high shear rates, the relative viscosity increases with increasing core-droplet viscosity. However, the trend is opposite at low shear rates, which results from the high inward flow (Marangoni flow) at low core-droplet viscosity.

Dynamics of deformation and pinch-off of a migrating compound droplet in a tube

A computational fluid dynamic investigation has been carried out to study the dynamics of a moving compound droplet inside a tube. The motions associated with such a droplet is uncovered by solving the axisymmetric Navier-Stokes equations in which the spatiotemporal evolution of a pair of twin-deformable interfaces has been tracked employing the volume-of-fluid approach. The deformations at the interfaces and their subsequent dynamics are found to be stimulated by the subtle interplay between the capillary and viscous forces. The simulations uncover that when a compound drop composed of concentric inner and outer interfaces migrates inside a tube, initially in the unsteady domain of evolution, the inner drop shifts away from the concentric position to reach a morphology of constant eccentricity at the steady state. The coupled motions of the droplets in the unsteady regime causes a continuous deformation of the inner and outer interfaces to obtain a configuration with a (an) prolate (oblate) shaped outer (inner) interface. The magnitudes of capillary number and viscosity ratio are found to have significant influence on the temporal evolution of the interfacial deformations as well as the eccentricity of the droplets. Further, the simulations uncover that, following the asymmetric deformation of the interfaces, the migrating compound droplet can undergo an uncommon breakup stimulated by a rather irregular pinch-off of the outer shell. The breakup is found to initiate with the thinning of the outer shell followed by the pinch-off. Interestingly, the kinetics of the thinning of outer shell is found to follow two distinct power-law regimes-a swiftly thinning stage at the onset followed by a rate limiting stage before pinch-off, which eventually leads to the uncommon breakup of the migrating compound droplets.

Drop Encapsulated in Bubble: A New Encapsulation Structure

A new fluid encapsulation structure, which is characterized by a bubble encapsulating a drop, is reported. It is stably generated from the breakup of a liquid column inside a bubble, which is achieved via the injection of Taylor flow into liquid. A model is constructed to explain the liquid column breakup mechanism. A dimensionless control guidance, which enables the possibility to create different-scale capsules, is provided. The encapsulation stability in external flows is verified, and a method to trigger the release of the encapsulated drop is provided, which supports potential applications with great advantages such as fluid transport.

Bifurcation Dynamics of a Particle-Encapsulating Droplet in Shear Flow

To understand the behavior of composite fluid particles such as nucleated cells and double emulsions in flow, we study a finite-size particle encapsulated in a deforming droplet under shear flow as a model system. In addition to its concentric particle-droplet configuration, we numerically explore other eccentric and time-periodic equilibrium solutions, which emerge spontaneously via supercritical pitchfork and Hopf bifurcations. We present the loci of these solutions around the codimension-two point. We adopt a dynamic system approach to model and characterize the coupled behavior of the two bifurcations. By exploring the flow fields and hydrodynamic forces in detail, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.

Steady-state deformation behavior of confined composite droplets under shear flow

The shear-induced dynamics of two-dimensional composite droplets in a narrow channel is investigated numerically. The droplets consist of a viscous inner droplet (core) and shell immersed in a continuous Newtonian fluid. Attention is focused on studying the effects of confinement at different core-to-shell radii ratios, relative viscosities of the medium components, and interfacial tensions on the steady-state deformation and orientation of a composite droplet. The role of the "sustaining" effect due to the internal core and competition between the near-wall shear flow and downward and upward secondary streams is discussed.

Enhancing and suppressing effects of an inner droplet on deformation of a double emulsion droplet under shear

We combine experimental investigation with numerical simulation to explore fundamental hydrodynamic effects of an inner droplet on deformation of a double emulsion droplet under shear. The transient deformation oscillation is found to be intensified by the inner droplet. Especially, we demonstrate that the double emulsion droplet can exhibit both larger and smaller steady deformation than the single-phase droplet, which arises from the competition between the coexisting enhancing and suppressing effects by the inner droplet on the deformation. We further provide a regime diagram to quantitatively recognize the respective dominant regime of these two effects, depending on the capillary number and radius ratio of the inner droplet to the outer one.

Possible oriented transition of multiple-emulsion globules with asymmetric internal structures in a microfluidic constriction

When a globule with a complete symmetry (such as simple spherical droplets and concentric double emulsions) is transiting in a constriction tube, there is only one pattern of the transition. However, for a multiple-emulsion globule with asymmetric internal structures, there are many possible patterns with different pressure drops Δp due to various initial orientations of the inner droplets. In this paper, a boundary integral method developed recently is employed to investigate numerically the possible oriented transition of a globule with two unequal inner droplets in an axisymmetric microfluidic constriction. The transition is driven by an axisymmetric Poiseuille flow with a fixed volume flow rate, and the rheological behaviors of the globule are observed carefully. When the big inner droplet is initially located in the front of the globule, the maximum pressure drop during the transition is always lower than that when it is initially placed in the rear. Thus, a tropism-whereby a globule more easily gets through the constriction when its bigger inner droplet locates in its front initially-might exist, in which the orientating stimulus is the required pressure drops. The physical explanation of this phenomenon has also been analyzed in this paper.

Three-phase interactions and interfacial transport phenomena in coacervate/oil/water systems

Complex coacervation is an associative liquid/liquid phase separation resulting in the formation of two liquid phases: a polymer-rich coacervate phase and a dilute continuous solvent phase. In the presence of a third liquid phase in the form of disperse oil droplets, the coacervate phase tends to wet the oil/water interface. This affinity has long been known and used for the formation of core/shell capsules. However, while encapsulation by simple or complex coacervation has been used empirically for decades, there is a lack of a thorough understanding of the three-phase wetting phenomena that control the formation of encapsulated, compound droplets and the role of the viscoelasticity of the biopolymers involved. In this contribution, we review and discuss the interplay of wetting phenomena and fluid viscoelasticity in coacervate/oil/water systems from the perspective of colloid chemistry and fluid dynamics, focusing on aspects of rheology, interfacial tension measurements at the coacervate/solvent interface, and on the formation and fragmentation of three-phase compound drops.

Formation and dynamics of core–shell droplets in immiscible polymer blends

Two mechanisms of generating core–shell droplets, namely the rupture of blend films and the disintegration of compound threads, were identified.

Effects of complex internal structures on rheology of multiple emulsions particles in 2D from a boundary integral method

A boundary integral method is developed to investigate the effects of inner droplets and asymmetry of internal structures on rheology of two-dimensional multiple emulsion particles with arbitrary numbers of layers and droplets within each layer. Under a modest extensional flow, the number increment of layers and inner droplets, and the collision among inner droplets subject the particle to stronger shears. In addition, the coalescence or release of inner droplets changes the internal structure of the multiple emulsion particles. Since the rheology of such particles is sensitive to internal structures and their change, modeling them as the core-shell particles to obtain the viscosity equation of a single particle should be modified by introducing the time-dependable volume fraction Φ(t) of the core instead of the fixed Φ. An asymmetric internal structure induces an oriented contact and merging of the outer and inner interface. The start time of the interface merging is controlled by adjusting the viscosity ratio and enhancing the asymmetry, which is promising in the controlled release of inner droplets through hydrodynamics for targeted drug delivery.

Breakup of double emulsion droplets in a tapered nozzle

When double emulsion droplets flow through a tapered nozzle, the droplets may break up and cause the core to be released. We model the system on the basis of the capillary instability and show that a droplet will not break up when the tilt angle of the nozzle is larger than 9°. For smaller tilt angles, whether the droplet breaks up also depends on the diameter ratio of the core of the droplet to the orifice of the nozzle. We verified this mechanism by experiments. The ideas are useful for the design of nozzles not only to break droplets for controlled release but also to prevent the droplet from rupturing in applications requiring the reinjection of an emulsion.

Impact of a compound droplet on a flat surface: A model for single cell epitaxy

The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We=2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing.