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Over the last decade, the Lattice Boltzmann method has found major scope for the simulation of a large spectrum of problems in soft matter, from multiphase and multi-component microfluidic flows, to foams, emulsions, colloidal flows, to name but a few. Crucial to many such applications is the role of supramolecular interactions which occur whenever mesoscale structures, such as bubbles or droplets, come in close contact, say of the order of tens of nanometers. Regardless of their specific physico-chemical origin, such near-contact interactions are vital to preserve the coherence of the mesoscale structures against coalescence phenomena promoted by capillarity and surface tension, hence the need of including them in Lattice Boltzmann schemes. Strictly speaking, this entails a complex multiscale problem, covering about six spatial decades, from centimeters down to tens of nanometers, and almost twice as many in time. Such a multiscale problem can hardly be taken by a single computational method, hence the need for coarse-grained models for the near-contact interactions. In this review, we shall discuss such coarse-grained models and illustrate their application to a variety of soft flowing matter problems, such as soft flowing crystals, strongly confined dense emulsions, flowing hierarchical emulsions, soft granular flows, as well as the transmigration of active droplets across constrictions. Finally, we conclude with a few considerations on future developments in the direction of quantum-nanofluidics, machine learning, and quantum computing for soft flows applications., Comment: 43 pages, 26 figures

We numerically study the dynamics of a passive fluid droplet confined within a microchannel whose walls are covered with a thin layer of active gel. The latter represents a fluid of extensile material modelling, for example, a suspension of cytoskeletal filaments and molecular motors. Our results show that the layer is capable of producing a spontaneous flow triggering a rectilinear motion of the passive droplet. For a hybrid design (a single wall covered by the active layer), at the steady state the droplet attains an elliptical shape, resulting from an asymmetric saw-toothed structure of the velocity field. On the contrary, if the active gel covers both walls, the velocity field exhibits a fully symmetric pattern considerably mitigating morphological deformations. We further show that the structure of the spontaneous flow in the microchannel can be controlled by the anchoring conditions of the active gel at the wall. These findings are also confirmed by selected 3D simulations. Our results may stimulate further research addressed to design novel microfludic devices whose functioning relies on the collective properties of active gels., Comment: Accepted on Soft Matter

Active fluid droplets are a class of soft materials exhibiting autonomous motion sustained by an energy supply. Such systems have been shown to capture motility regimes typical of biological cells and are ideal candidates as building-block for the fabrication of soft biomimetic materials of interest in pharmacology, tissue engineering and lab on chip devices. While their behavior is well established in unconstrained environments, much less is known about their dynamics under strong confinement. Here, we numerically study the physics of a droplet of active polar fluid migrating within a microchannel hosting a constriction with adhesive properties, and report evidence of a striking variety of dynamic regimes and morphological features, whose properties crucially depend upon droplet speed and elasticity, degree of confinement within the constriction and adhesiveness to the pore. Our results suggest that non-uniform adhesion forces are instrumental in enabling the crossing through narrow orifices, in contrast to larger gaps where a careful balance between speed and elasticity is sufficient to guarantee the transition. These observations may be useful for improving the design of artificial micro-swimmers, of interest in material science and pharmaceutics, and potentially for cell sorting in microfluidic devices., Comment: Post-peer-review version of an article published in Nature Communications

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., Comment: 15 pages, 14 figures

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., Comment: Post peer-review version. 11 pages, 6 figures. Movies upon request

We numerically study the dynamics of a polydisperse double emulsion under a symmetric shear flow. We show that both dispersity and shear rate crucially affect the behavior of the innermost drops and of the surrounding shell. While at low/moderate values of shear rates the inner drops rotate periodically around a common center of mass triggered by the fluid vortex formed within the emulsion generally regardless of their polydispersity, at higher values such dynamics occurs only at increasing polydispersity, since monodisperse drops are found to align along the shear flow and become approximately motionless at late times. Our simulations also suggest that increasing polydispersity favours close-range contacts among cores and persistent collisions, while hindering shape deformations of the external droplet. A quantitative evaluation of these effects is also provided., Comment: 10 pages, 7 figures. Post peer-reviewed version accepted for publication on Physics of Fluids. Movies upon request

We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multi-core morphology confined within a microfluidic channel. A variety of new nonequilibrium steady states is reported. Under low shear rates, the emulsion is found to exhibit a solid-like behavior, in which cores display a periodic planetary-like 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 treadmilling-like structure, while others occupy the center of the emulsion. A quantitative description in terms of 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., Comment: 11 pages, 15 figures

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 analyse 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 non-trivial micro-vorticity patterns, which in turn affect the effective near-contact interactions, giving rise to persistent fluctuating ripples at the fluid interface. In such regime, near-contact interactions may significantly affect the macroscopic arrangement of emulsion configurations, such as those arising in soft-flowing microfluidic crystals.

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., Comment: Post-peer-review version of an article published in Nature Communications. Movies upon request

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 internal one remains essentially unaffected. Novel non-equilibrium steady states arise in a multiple emulsion. Under a low/moderate shear rates, for instance, the encapsulated droplets display a non-trivial planetary-like 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., Comment: 12 pages, 11 figures