We numerically investigate the rheological response of a noncoalescing 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 nonequiibrium 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 internal one remains essentially unaffected. Novel nonequiibrium steady states arise in a multiple emulsion. Under low/moderate shear rates, for instance, the encapsulated droplets display a nontrivial planetarylike motion that considerably affects the shape of the external droplet. Some features of this dynamic behavior are partially captured by the Taylor deformation parameter and the stress tensor. Besides a theoretical interest on its own, our results can potentially stimulate further experiments, as most of the predictions could be tested in the lab by monitoring droplets' shapes and position over time. Published under license by AIP Publishing.

The study of the underlying physics of soft flowing materials depends heavily on numerical simulations, due to the complex structure of the governing equations reflecting the competition of concurrent mechanisms acting at widely disparate scales in space and time. A full-scale computational modelling remains a formidable challenge since it amounts to simultaneously handling six or more spatial decades in space and twice as many in time. Coarse-grained methods often provide a viable strategy to significantly mitigate this issue, through the implementation of mesoscale supramolecular forces designed to capture the essential physics at a fraction of the computational cost of a full-detail description. Here, we review some recent advances in the design of a lattice Boltzmann mesoscale approach for soft flowing materials, inclusive of near-contact interactions (NCIs) between dynamic interfaces, as they occur in high packing-fraction soft flowing crystals. The method proves capable of capturing several aspects of the rheology of soft flowing crystals, namely, (i) a 3/2 power-law dependence of the dispersed phase flow rate on the applied pressure gradient, (ii) the structural transition between an ex-two and ex-one (bamboo) configurations with the associated drop of the flow rate, (iii) the onset of interfacial waves once NCI is sufficiently intense. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

A new class of multiscale scheme is presented for micro-hydrodynamic problems based on a dual representation of the fluid observables. The hybrid model is first tested against the classical flow between two parallel plates and then applied to a plug flow within a micrometer-sized striction and a shear flow within a microcavity. Both cases demonstrate the capability of the multiscale approach to reproduce the correct macroscopic hydrodynamics also in the presence of refined grids (one and two levels), while retaining the correct thermal fluctuations, embedded in the multiparticle collision method. This provides the first step toward a novel class of fully mesoscale hybrid approaches able to capture the physics of fluids at the micro- and nanoscales whenever a continuum representation of the fluid falls short of providing the complete physical information, due to a lack of resolution and thermal fluctuations.

We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation, and (iii) different pattern formation during spinodal decomposition of binary mixtures.

Bicontinuous interfacially jammed emulsion gels ("bijels") represent a new class of soft materials made of a densely packed monolayer of solid particles sequestered at the interface of a bicontinuous fluid. Their mechanical properties are relevant to many applications, such as catalysis, energy conversion, soft robotics, and scaffolds for tissue engineering. While their stationary bulk properties have been covered in depth, much less is known about their behavior in the presence of an external shear. In this paper, we numerically study the dynamics of a bijel confined within a three-dimensional rectangular domain and subject to a symmetric shear flow sufficiently intense to break the material. Extensive numerical simulations reveal that the shear flow generally promotes the detachment of a sizable amount of particles from the fluid interface and their accumulation in the bulk. Fluid interfaces undergo large stretching and deformations along the flow direction, an effect that reduces their capability of entrapping particles. These results are supported by a series of quantitative indicators such as (i) curvature of the fluid interface, (ii) spatial distribution of the colloidal particles, and (iii) fluid flow structure within the microchannel. (c) 2020 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

We use computer simulations to study the morphology and rheological properties of a bidimensional emulsion resulting from a mixture of a passive isotropic fluid and an active contractile polar gel, in the presence of a surfactant that favours the emulsification of the two phases. By varying the intensity of the contractile activity and of an externally imposed shear flow, we find three possible morphologies. For low shear rates, a simple lamellar state is obtained. For intermediate activity and shear rate, an asymmetric state emerges, which is characterized by shear and concentration banding at the polar/isotropic interface. A further increment in the active forcing leads to the self-assembly of a soft channel where an isotropic fluid flows between two layers of active material. We characterize the stability of this state by performing a dynamical test varying the intensity of the active forcing and shear rate. Finally, we address the rheological properties of the system by measuring the effective shear viscosity, finding that this increases as active forcing is increased-so that the fluid thickens with activity.

We provide a brief survey of our current developments in the simulation-based design of novel families of mesoscale porous materials using computational kinetic theory. Prospective applications on exascale computers are also briefly discussed and commented on, with reference to two specific examples of soft mesoscale materials: microfluid crystals and bi-continuous jels.

We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multicore morphology confined within a microfluidic channel. A variety of nonequilibrium steady states is reported. Under low shear rates, the emulsion is found to exhibit a solidlike behavior, in which cores display a periodic planetarylike motion with approximately equal angular velocity. At higher shear rates, two steady states emerge, one in which all inner cores align along the flow and become essentially motionless and a further one in which some cores accumulate near the outer interface and produce a dynamical elliptical-shaped ring chain, reminiscent of a treadmillinglike structure, while others occupy the center of the emulsion. A quantitative description in terms of the (i) motion of the cores, (ii) rate of deformation of the emulsion, and (iii) structure of the fluid flow within the channel is also provided.

We study numerically the behaviour of a two-dimensional 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 within an active matrix. For extensile activity (occurring, e.g., in microtubule-motor suspensions), instead, we observe an emulsion of spontaneously rotating droplets of different size. By tuning the overall composition, we can create high internal phase emulsions, which undergo sudden phase inversion when activity is switched off. Therefore, we find that activity provides a single control parameter to design composite materials with a strikingly rich range of morphologies.

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 the shear rate and extensile activity (occurring, e.g., in microtubule-motor suspensions). By increasing the activity, a first transition occurs from the linear flow regime to spontaneous persistent unidirectional macro-scale flow, followed by another transition either to a (low shear) intermittent flow regime with the coexistence of states with positive, negative, and vanishing apparent viscosity, or to a (high shear) symmetric shear thinning regime. The different behaviours can be explained in terms of the dynamics of the polarization field close to the walls. A maximum entropy production principle selects the most likely states in the intermittent regime.

Drug releasing capsules and droplets are largely used in biomedical applications. Such vehicles consist of a drug-loaded core surrounded by a thin semi-permeable layer. Diffusion is by far the dominant mechanism in drug delivery, beside other physico-chemical factors, such as osmosis, drug dissolution, polymer swelling and degradation. We upgrade existing mechanistic models by extending their applications to the composite structures, and characterize the kinetics of the drug eluted from the vehicle into the external targeted medium. We develop a theoretical and computational study aimed at modelling the drug release from a composite spherical core-shell capsule or a double emulsion having either a protective coating or a surfactant, under the assumption of radial symmetry. The problem of release from such a layer-by-layer composite systems is described by a system of coupled partial differential equations, which we solve analytically in terms of Fourier series or using numerical solutions. In addition to the conventional partitioning and interlayer conditions, we consider a finite mass transfer coefficient, to model the resistance at the surface. Expressions for the concentration and the cumulative mass in all layers are given to show the dependence and sensitivity to parameters, such as diffusivity, permeability and partition coefficients. The release curve characterizes the drug transport mechanism and suggests how to guarantee a controlled release. The proposed model constitutes a simple tool to predict the release from composite materials that, measuring their performance or comparing different configurations, can help in designing novel drug delivery systems.

We review the state of the art of active fluids with particular attention to hydrodynamic continuous models and to the use of Lattice Boltzmann Methods (LBM) in this field. We present the thermodynamics of active fluids, in terms of liquid crystals modelling adapted to describe large-scale organization of active systems, as well as other effective phenomenological models. We discuss how LBM can be implemented to solve the hydrodynamics of active matter, starting from the case of a simple fluid, for which we explicitly recover the continuous equations by means of Chapman-Enskog expansion. Going beyond this simple case, we summarize how LBM can be used to treat complex and active fluids. We then review recent developments concerning some relevant topics in active matter that have been studied by means of LBM: spontaneous flow, self-propelled droplets, active emulsions, rheology, active turbulence, and active colloids.

We investigate the dynamics of a phase-separating binary fluid, containing colloidal dumbbells anchored to the fluid-fluid interface. Extensive lattice Boltzmann-immersed boundary method simulations reveal that the presence of soft dumbbells can significantly affect the curvature dynamics of the interface between phase-separating fluids, even though the coarsening dynamics is left nearly unchanged. In addition, our results show that the curvature dynamics exhibits distinct non-local effects, which might be exploited for the design of new soft mesoscale materials. We point out that the inspection of the statistical dynamics of the curvature can disclose new insights into local inhomogeneities of the binary fluid configuration, as a function of the volume fraction and aspect ratio of the dumbbells.

Computer simulations of bi-continuous two-phase fluids with interspersed dumbbells show that, unlike rigid colloids, soft dumbbells do not lead to arrested coarsening. However, they significantly alter the curvature dynamics of the fluid-fluid interface, whose probability density distributions are shown to exhibit (i) a universal spontaneous transition (observed even in the absence of colloids) from an initial broad-shape distribution towards a highly localized one and (ii) super-diffusive dynamics with long-range effects. Both features may prove useful for the design of novel families of soft porous materials.

We present a mesoscale representation of near-contact interactions between colliding droplets which permits one to reach up to the scale of full microfluidic devices, where such droplets are produced. The method is demonstrated for the case of colliding droplets and the formation of soft flowing crystals in flow-focusing microfluidic devices. This model may open up the possibility of multiscale simulation of microfluidic devices for the production of new droplet and bubble-based mesoscale porous materials.

The dynamic interaction of complex fluid interfaces is highly sensitive to near-contact interactions occurring at the scale of ten of nanometers. Such interactions are difficult to analyze because they couple self-consistently to the dynamic morphology of the evolving interface, as well as to the hydrodynamics of the interstitial fluid film. In this work, we show that, above a given magnitude threshold, near-contact interactions trigger nontrivial microvorticity patterns, which in turn affect the effective near-contact interactions, giving rise to persistent fluctuating ripples at the fluid interface. In such a regime, near-contact interactions may significantly affect the macroscopic arrangement of emulsion configurations, such as those arising in soft-flowing microfluidic crystals.

We systematically investigate the role of different swimming patterns on the concentration distribution of bacterial suspensions confined between two flat walls, by considering wild-type motility Escherichia coli and Pseudomonas aeruginosa, which perform Run and Tumble and Run and Reverse patterns, respectively. The experiments count motile bacteria at different distances from the bottom wall. In agreement with previous studies, an accumulation of motile bacteria close to the walls is observed. Different wall separations, ranging from 100 to 250?m, are tested. The concentration profiles result to be independent on the motility pattern and on the walls' separation. These results are confirmed by numerical simulations, based on a collection of self-propelled dumbbells-like particles interacting only through steric interactions. The good agreement with the simulations suggests that the behavior of the investigated bacterial suspensions is determined mainly by steric collisions and self-propulsion, as well as hydrodynamic interactions.

The dynamics of a quasi two-dimensional isotropic droplet in a cholesteric liquid crystal medium under symmetric shear flow is studied by lattice Boltzmann simulations. We consider a geometry in which the flow direction is along the axis of the cholesteric, as this setup exhibits a significant viscoelastic response to external stress. We find that the dynamics depends on the magnitude of the shear rate, the anchoring strength of the liquid crystal at the droplet interface and the chirality. While low shear rate and weak interface anchoring the system shows a non-Newtonian behavior, a Newtonian-like response is observed at high shear rate and strong interface anchoring. This is investigated both by estimating the secondary flow profile, namely a flow emerging along the out-of-plane direction (absent in fully-Newtonian fluids, such as water) and by monitoring defect formation and dynamics, which significantly alter the rheological response of the system.

We describe the basic properties and consequences of introducing active stresses, with principal direction along the local director, in cholesteric liquid crystals. The helical ground state is found to be linearly unstable to extensile stresses, without threshold in the limit of infinite system size, whereas contractile stresses are hydrodynamically screened by the cholesteric elasticity to give a finite threshold. This is confirmed numerically and the non-linear consequences of instability, in both extensile and contractile cases, are studied. We also consider the stresses associated to defects in the cholesteric pitch (? lines) and show how the geometry near to the defect generates threshold-less flows reminiscent of those for defects in active nematics. At large extensile activity ? lines are spontaneously created and can form steady-state patterns sustained by constant active flows.

In this work we numerically study the switching dynamics of a 2D cholesteric emulsion droplet immersed in an isotropic fluid under an electric field, which is either uniform or rotating with constant speed. The overall dynamics depend strongly on the magnitude and on the direction (with respect to the cholesteric axis) of the applied field, on the anchoring of the director at the droplet surface and on the elasticity. If the surface anchoring is homeotropic and a uniform field is parallel to the cholesteric axis, the director undergoes deep elastic deformations and the droplet typically gets stuck into metastable states which are rich in topological defects. When the surface anchoring is tangential, the effects due to the electric field are overall less dramatic, as a small number of topological defects form at equilibrium. The application of the field perpendicular to the cholesteric axis usually has negligible effects on the defect dynamics. The presence of a rotating electric field of varying frequency fosters the rotation of the defects and of the droplet as well, typically at a lower speed than that of the field, due to the inertia of the liquid crystal. If the surface anchoring is homeotropic, a periodic motion is found. Our results represent a first step to understand the dynamical response of a cholesteric droplet under an electric field and its possible application in designing novel liquid crystal-based devices.