As fine templates to prepare microcapsules, multiple emulsions with complex internal structures have been generated through microfluidics. To study effects of layers, inner droplets and asymmetry of internal structures on rheology of multiple emulsions, a generalized boundary integral method is developed to investigate multiple emulsions with orderly structures up to n layers and up to mi droplets in the i-th layer. Under a modest extensional flow, the complication of internal structures and the collision among inner droplets will subject the particle to stronger shears. However, the particle will ease the added tension through the simplification of internal structures (destabilization) such as coalescence or release of inner droplets. Since the rheology of multiple emulsions is sensitive to internal structures and their change, modelling them as the core-shell droplets to obtain viscosity equation should be modified by introducing the variable "time". Asymmetric internal structures will induce oriented contact and merging of the outer and inner interface. The start time of the interface merging can be controlled by adjusting the viscosity ratio and enhancing the asymmetry, which is promising in the controlled release of inner droplets for targeted drug delivery.
A generalized boundary integral method is developed to investigate the rheology of multiple emulsions with orderly structures up to n layers and up to mi droplets in the i-th layer in microchannels with various geometries. Recently, as fine templates to prepare microcapsules for targeted drug delivery, multiple emulsions with complex structures have been generated through microfluidics. The deformation and breakup of multiple emulsions are critical to the transport and release of their inclusion. However, the numerical investigation of the rheology of multiple emulsions is only limited to a si…
We study the rheology of monodisperse and bidisperse emulsions with various droplet sizes (1 $μ$m -- 2 $μ$m diameter). Above a critical volume fraction $ϕ_c$, these systems exhibit solid-like behavior and a yield stress can be detected. Previous experiments suggest that for small thermal particles, rheology will see a glass transition at $ϕ_c = ϕ_g =0.58$; for large athermal systems, rheology will see a jamming transition at $ϕ_c = ϕ_J =0.64$. However, simulations point out that at the crossover of thermal and athermal regimes, the glass and jamming transitions may both be observed in the same…
Adhesion differentials control the rheology of biomimetic emulsions
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Laboratoire Jean Perrin（让·佩兰实验室）；Inserm（法国国家健康与医学研究院）；Institut de Biologie Paris-Seine（巴黎塞纳生物学研究所）；Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CPT (UMR 7332)（复杂系统物理中心（UMR 7332））；Turing Center for Living Systems（图灵生命系统中心）
We numerically study by lattice Boltzmann simulations the rheological properties of an active emulsion made of a suspension of an active polar gel embedded in an isotropic passive background. We find that the hexatic equilibrium configuration of polar droplets is highly sensitive to both active injection and external forcing and may either lead to asymmetric unidirectional states which break top-bottom symmetry or symmetric ones. In this latter case, for large enough activity, the system develops a shear-thickening regime at low shear rates. Importantly, for larger external forcing a regime wi…
The rheological behaviour of an emulsion made of an active polar component and an isotropic passive fluid is studied by lattice Boltzmann methods. Different flow regimes are found by varying the values of shear rate and extensile activity (occurring, e.g., in microtubule-motor suspensions). By increasing activity, a first transition occurs from linear flow regime to spontaneous persistent unidirectional macro-scale flow, followed by another transition either to (low shear) intermittent flow regime with coexistence of states with positive, negative, and vanishing apparent viscosity, or to (high…
We show how attractive interactions dramatically influence emulsion rheology. Unlike the repulsive case, attractive emulsions below random close packing, RCP, can form soft gel-like elastic solids. However, above RCP, attractive and repulsive emulsions have similar elasticities. Such compressed attractive emulsions undergo an additional shear-driven relaxation process during yielding. Our results suggest that attractive emulsions begin to yield at weak points through the breakage of bonds, and, above RCP, also undergo droplet configurational rearrangements.
We present local velocity measurements in emulsions under shear using heterodyne Dynamic Light Scattering. Two emulsions are studied: a dilute system of volume fraction $ϕ=20$ % and a concentrated system with $ϕ=75$ %. Velocity profiles in both systems clearly show the presence of wall slip. We investigate the evolution of slip velocities as a function of shear stress and discuss the validity of the corrections for wall slip classically used in rheology. Focussing on the bulk flow, we show that the dilute system is Newtonian and that the concentrated emulsion is shear-thinning. In the latter c…
The aggregation of protein-stabilised emulsions leads to the formation of emulsion gels. These soft solids are classically envisioned as droplet-filled matrices. Here however, it is assumed that protein-coated sub-micron droplets contribute to the network formation in a similar way to proteins. Emulsion gels are thus envisioned as composite networks made of proteins and droplets. Emulsion gels with a wide range of composition are prepared and their viscoelasticity and frequency dependence are measured. Their rheological behaviours are then analysed and compared with the properties of pure gels…
We discuss the linear and non-linear rheology of concentrated (sub)microscale emulsions, amorphous disordered solids composed of repulsive and deformable soft colloidal spheres. Based on recent results from simulation and theory, we derive quantitative predictions for the dependences of the elastic shear modulus and the yield stress on the droplet volume fraction. The remarkable agreement with experiments we observe supports the scenario that the repulsive glass and the jammed state can be clearly identified in the rheology of soft spheres at finite temperature while crossing continuously from…
We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fraction and viscosity ratio under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for about 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To sing…
The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a non-magnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets extra stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The …
Protein-stabilised emulsion gels can be studied in the theoretical framework of colloidal gels, because both protein assemblies and droplets may be considered as soft colloids. These particles differ in their nature, size and softness, and these differences may have an influence on the rheological properties of the gels they form. Pure gels made of milk proteins (sodium caseinate), or of sub-micron protein-stabilised droplets, were prepared by slow acidification of suspensions at various concentrations. Their microstructure was characterised, their viscoelasticity, both in the linear and non-l…
Polyelectrolyte-surfactant complexes (PESCs) have long been employed as oil-in-water (o/w) emulsions stabilizers, but never in the structure of colloidal complex coacervates providing a Pickering effect. The complexed state of PESCs could make them unsuitable o/w Pickering emulsifiers, which instead require a balance between colloidal structure and stability, amphiphilicity and wettability. Here we hypothesize that PESCs coacervates are efficient Pickering stabilizers. Instead of classical surfactants, we employ sophorolipid (SL) biosurfactants, atypical anionic/neutral stimuli-responsive bios…
We study the Poiseuille flow of a soft-glassy material above the jamming point, where the material flows like a complex fluid with Herschel- Bulkley rheology. Microscopic plastic rearrangements and the emergence of their spatial correlations induce cooperativity flow behavior whose effect is pronounced in presence of confinement. With the help of lattice Boltzmann numerical simulations of confined dense emulsions, we explore the role of geometrical roughness in providing activation of plastic events close to the boundaries. We probe also the spatial configuration of the fluidity field, a conti…
Emulsions are a central component of many modern formulations in food, pharmaceuticals, agrichemicals and personal care products. The droplets in these formulations are limited to being spherical as a consequence of the interfacial tension between the dispersed phase and continuous phase. The ability to control emulsion droplet morphology and stabilise non-spherical droplets would enable the modification of emulsion properties such as stability, substrate binding, delivery rate and rheology. One way of controlling droplet microstructure is to apply an elastic film around the droplet to prevent…
We present mesoscale numerical simulations of Rayleigh-Bénard convection in a two-dimensional concentrated emulsion, confined between two parallel walls, heated from below and cooled from above, under the effect of buoyancy forces. The systems under study comprise finite-size droplets, whose concentration $Φ_0$ is varied, ranging from the dilute limit up to the point where the emulsion starts to be packed and exhibits non-Newtonian rheology. We focus on the characterisation of the convective heat transfer properties close to the transition from conductive to convective states. The convective f…
High internal phase emulsions (HIPEs) are considered as an important functional material and have been the focus of intense development effort, but it has not been possible to alter their fundamental attributes at either the microcosmic or macroscopic level, which severely limits their practical applications in various areas. In this work, we report a general strategy for creating complex HIPEs and we additionally show a route to forming HIPE films at liquid interfaces. Double HIPEs and Janus HIPEs are both realized for the first time. They feature complex microscopic patterns with a short-ran…
It is well known that jammed soft materials will flow if sheared above their yield stress - think mayonnaise spread on bread - but a complete microscopic description of this seemingly sim- ple process has yet to emerge. What remains elusive is a microscopic framework that explains the macroscopic flow, derived from a 3-D spatially resolved analysis of the dynamics of the droplets or particles that compose the soft material. By combining confocal-rheology experiments on compressed emulsions and numerical simulations, we unravel that the primary microscopic mechanisms for flow are strongly influ…
We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration Phi_0 is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit a non-steady dyna…
Particle-stabilized emulsions are commonly used in various industrial applications. These emulsions can present in different forms, such as Pickering emulsions or bijels, which can be distinguished by their different topologies and rheology. We numerically investigate the effect of the volume fraction and the uniform wettability of the stabilizing spherical particles in mixtures of two fluids. For this, we use the well-established three-dimensional lattice Boltzmann method, extended to allow for the added colloidal particles with non-neutral wetting properties. We obtain data on the domain siz…
We have discovered the existence of extremely polydisperse High Internal-Phase-Ratio Emulsions (HIPE) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to Apollonian packing rules. Such Apollonian emulsions are obtained from dispersing oil dropwise in water in the presence of very little surfactant, and allowing them to evolve at rest for a week. The packing structure of the droplets was confirmed through size distribution measurements that evolved spontaneously towards power laws with the known Apoll…
The issue of the stability of Pickering emulsions is tackled at a mesoscopic level using dissipative particle dynamics simulations within the Adiabatic Biased Molecular Dynamics framework. We consider the early stage of the coalescence process between two spherical water droplets in decane solvent. The droplets are stabilized by Janus nanoparticles of different shapes (spherical and ellipsoidal) with different three-phase contact angles. Given a sufficiently dense layer of particles on the droplets, we show that the stabilization mechanism strongly depends on the collision speed. This is consi…
As a main structural level in colloidal food materials, extended colloidal networks are important for texture and rheology. By obtaining the 3D microstructure of the network, macroscopic mechanical properties of the material can be inferred. However, this approach is hampered by the lack of suitable non-destructive 3D imaging techniques with submicron resolution. We present results of quantitative ptychographic X-ray computed tomography applied to a palm kernel oil based oil-in-water emulsion. The measurements were carried out at ambient pressure and temperature. The 3D structure of the extend…
Protein-based high internal phase emulsions (HIPEs) have gained tremendous attention in diverse fields, but their mechanism in the emulsification process remains elusive. In this article, HIPEs were stabilized directly by food-grade proteins, depending on a self-organized process featuring a fluid laminarization. We elucidated that the emulsification with the rotor-stator mixer is a typical non-equilibrium process. The crucial factor for the process is related to the irreversible energy dissipation, while the internal phase volume fraction is the threshold determining the laminarization. The f…
We numerically study the Rayleigh-Bénard (RB) convection in two-dimensional model emulsions confined between two parallel walls at fixed temperatures. The systems under study are heterogeneous, with finite-size droplets dispersed in a continuous phase. The droplet concentration is chosen to explore the convective heat transfer of both Newtonian (low droplet concentration) and non-Newtonian (high droplet concentration) emulsions, the latter exhibiting shear-thinning rheology, with a noticeable increase of viscosity at low shear rates. It is well known that the transition to convection of a homo…
We study water-in-oil emulsion droplets, running the Belousov-Zhabotinsky reaction, that form a new type of active matter unit. These droplets, stabilised by surfactants dispersed in the oil medium, are capable of internal chemical oscillations and also self-propulsion due to dynamic interfacial instabilities that result from the chemical reactions. The chemical oscillations can couple via the exchange of activator and inhibitor type of reaction intermediates across the droplets under precise conditions of surfactant bilayer formation between the droplets. Here we present the synchronization b…
Stabilized dense emulsions display a rich phenomenology connecting microstructure and rheology. In this work we study how an emulsion with a finite yield stress can be built via large-scale stirring. By gradually increasing the volume fraction of the dispersed minority phase, under the constant action of a stirring force, we are able to achieve volume fractions close to $80\%$. Despite the fact that our system is highly concentrated and not yet turbulent we observe a droplet size distribution consistent with the $-10/3$ scaling, often associated to inertial range droplets breakup. We report th…
The rheology of pressure-driven flows of two-dimensional dense monodisperse emulsions in neutral wetting microchannels is investigated by means of mesoscopic lattice simulations, capable of handling large collections of droplets, in the order of several hundreds. The simulations reveal that the fluidization of the emulsion proceeds through a sequence of discrete steps, characterized by yielding events whereby layers of droplets start rolling over each other, thus leading to sudden drops of the relative effective viscosity. It is shown that such discrete fluidization is robust against loss of c…
By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor-Couette (TC) turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviors, i.e., the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction neither for O/W nor for W/O. However, for W/O it is…
We investigate the rheology of strain-hardening spherical capsules, from the dilute to the concentrated regime under a confined shear flow using three-dimensional numerical simulations. We consider the effect of capillary number, volume fraction and membrane inextensibility on the particle deformation and on the effective suspension viscosity and normal stress differences of the suspension. The suspension displays a shear-thinning behaviour which is a characteristic of soft particles such as emulsion droplets, vesicles, strain-softening capsules, and red blood cells. We find that the membrane …
We have discovered the existence of polydisperse High Internal-Phase-Ratio Emulsions (HIPE) in which the internal-phase droplets, present at 95% volume fraction, remain spherical and organize themselves in the available space according to Apollonian packing rules. These polydisperse HIPE are formed during emulsification of surfactant-poor compositions of oil-surfactant-water two-phase systems. Their droplet size-distributions evolve spontaneously towards power laws with the Apollonian exponent. Small-Angle X-Ray Scattering performed on aged HIPEs demonstrated that the droplet packing structure…
Multi-phase flows encountered in nature or in industry, exhibit non trivial rheological properties, that can be understood better thanks to model materials and appropriate rheometers. Here, we use model unsaturated granular materials: assemblies of frictional spherical particles bonded by a small quantity of a wetting liquid, over a rough inclined plane. Our results show steady uniform flows for a wide range of parameters (the inclination angle and the mass flow-rate). A theoretical model, based on the Mohr-Coulomb yield criterion extended to inertial flows: $τ$ = $τ$c + $μ$(I)P, in which $τ$c…
Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary condition, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the later is selected from among 6 walls with various roughness, local concavity, and compliance. W…
We study numerically the behaviour of a mixture of a passive isotropic fluid and an active polar gel, in the presence of a surfactant favouring emulsification. Focussing on parameters for which the underlying free energy favours the lamellar phase in the passive limit, we show that the interplay between nonequilibrium and thermodynamic forces creates a range of multifarious exotic emulsions. When the active component is contractile (e.g., an actomyosin solution), moderate activity enhances the efficiency of lamellar ordering, whereas strong activity favours the creation of passive droplets wit…
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 micro…
In nature, structural colour generation is based on discriminative light propagation associated with physical structures in the range of the wavelengths of light1. These iridescent structural colours are of immense significance2 but not easy to control experimentally and therefore difficult to exploit for applications. In this work, we employ microfluidics to produce polymerizable double emulsions that can not only induce the already known lensing effect3 but also result in the spectral separation of white light. Here, liquids of varying refractive in-dex that constitute the emulsions resulted…
We numerically investigate the rheological response of a non-coalescing multiple emulsion under a symmetric shear flow. We find that the dynamics significantly depends on the magnitude of the shear rate and on the number of the encapsulated droplets, two key parameters whose control is fundamental to accurately select the resulting non-equilibrium steady states. The double emulsion, for instance, attains a static steady state in which the external droplet stretches under flow and achieves an elliptical shape (closely resembling the one observed in a sheared isolated fluid droplet), while the i…
We present and analyze a thermodynamical theory of rheology with single internal variable. The universality of the model is ensured as long as the mesoscopic and/or microscopic background processes satisfy the applied thermodynamical principles, which are the second law, the basic balances and the existence of an additional-tensorial-state variable. The resulting model, which we suggest to call the Kluitenberg-Verhás body, is the Poynting-Thomson-Zener body with an additional inertial element, or, in other words, is the extension of Jeffreys model to solids. We argue that this Kluitenberg-Verh…
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 sta…
In this work, we present two types of microfluidic chips involving magnetic nanoparticles dispersed in cyclohexane with oleic acid. In the first case, the hydrophobically coated nanoparticles are self-assembled with an amphiphilic diblock copolymer by a double-emulsion process in order to prepare giant magnetic vesicles (polymersomes) in one step and at a high throughput. It was shown in literature that such diblock copolymer W/O/W emulsion droplets can evolve into polymersomes made of a thin (nanometric) magnetic membrane through a dewetting transition of the oil phase from the aqueous intern…
The influence of the internal structure of a biological cell (e.g., a leukocyte) on its dynamics and rheology is not yet fully understood. By using 2D numerical simulations of a bilamellar vesicle (BLV) consisting of two vesicles as a cell model, we find that increasing the size of the inner vesicle (mimicking the nucleus) triggers a tank-treading-to-tumbling transition. A new dynamical state is observed, the undulating motion: the BLV inclination with respect to the imposed flow oscillates while the outer vesicle develops rotating lobes. The BLV exhibits a non-Newtonian behavior with a time-d…
We explore the shape and internal structure of diblock copolymer (di-BCP) nanoparticles (NPs) by using the Ginzburg-Landau free-energy expansion. The self-assembly of di-BCP lamellae confined in emulsion droplets can form either ellipsoidal or onion-like NPs. The corresponding inner structure is a lamellar phase that is either perpendicular to the long axis of the ellipsoids (L$_\perp$) or forms a multi-layer concentric shell (C$_\parallel$), respectively. We focus on the effects of the interaction parameter between the A/B monomers $τ$, and the polymer/solvent $χ$, as well as the NP size on t…
