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

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.

Machine learning acceleration of simulations of Stokesian suspensions

Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such flows are challenging and expensive. Here, we propose a generic machine-learning-augmented reduced model for these flows. Our model replaces expensive parts of a numerical scheme with regression functions. Given the physical parameters of the particle, our model generalizes to arbitrary geometries and boundary conditions without the need to retrain the regression functions. It is approximately an order of magnitude faster than a state-of-the-art numerical scheme using the same number of degrees of freedom and can reproduce several features of the flow accurately. We illustrate the performance of our model on integral equation formulation of vesicle suspensions in two dimensions.

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.

Stagnation point flows in analytical chemistry and life sciences

Isolated microfluidic stagnation points – formed within microfluidic interfaces – have come a long way as a tool for characterizing materials, manipulating micro particles, and generating confined flows and localized chemistries.

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.

Commensurability-driven structural defects in double emulsions produced with two-step microfluidic techniques

The combination of two drop makers such as flow focusing geometries or ┬ junctions is commonly used in microfluidics to fabricate monodisperse double emulsions and novel fluid-based materials. Here we investigate the physics of the encapsulation of small droplets inside large drops that is at the core of such processes. The number of droplets per drop studied over time for large sequences of consecutive drops reveals that the dynamics of these systems are complex: we find a succession of well-defined elementary patterns and defects. We present a simple model based on a discrete approach that predicts the nature of these patterns and their non-trivial scheme of arrangement in a sequence as a function of the ratio of the two timescales of the problem, the production times of droplets and drops. Experiments validate our model as they concur very well with predictions.

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.