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.

Droplet microfluidics has emerged as highly relevant technology in diverse fields such as nanomaterials synthesis, photonics, drug delivery, regenerative medicine, food science, cosmetics, and agriculture. While significant progress has been made in understanding the fundamental mechanisms underlying droplet generation in microchannels and in fabricating devices to produce droplets with varied functionality and high throughput, challenges persist along two important directions. On one side, the generalization of numerical results obtained by computational fluid dynamics would be important to deepen the comprehension of complex physical phenomena in droplet microfluidics, as well as the capability of predicting the device behavior. Conversely, truly three-dimensional architectures would enhance microfluidic platforms in terms of tailoring and enhancing droplet and flow properties. Recent advancements in artificial intelligence (AI) and additive manufacturing (AM) promise unequaled opportunities for simulating fluid behavior, precisely tracking individual droplets, and exploring innovative device designs. This review provides a comprehensive overview of recent progress in applying AI and AM to droplet microfluidics. The basic physical properties of multiphase flows and mechanisms for droplet production are discussed, and the current fabrication methods of related devices are introduced, together with their applications. Delving into the use of AI and AM technologies in droplet microfluidics, topics covered include AI-assisted simulations of droplet behavior, real-time tracking of droplets within microfluidic systems, and AM-fabrication of three-dimensional systems. The synergistic combination of AI and AM is expected to deepen the understanding of complex fluid dynamics and active matter behavior, expediting the transition toward fully digital microfluidic systems.

We introduce a regularized fluctuating lattice Boltzmann model (Reg-FLBM) for the D3Q27 lattice, which incorporates thermal fluctuations through Hermite-based projections to ensure compliance with the fluctuation-dissipation theorem. By leveraging the recursive regularization framework, the model achieves thermodynamic consistency for both hydrodynamic and ghost modes. Compared to the conventional single-relaxation-time BGK-FLBM, the Reg-FLBM provides improved stability and a more accurate description of thermal fluctuations. The implementation is optimized for large-scale parallel simulations on graphics processing unit-accelerated architectures, enabling systematic investigation of fluctuation-driven phenomena in mesoscale and nanoscale fluid systems.

This study presents a high-order, thread-safe version of the lattice Boltzmann method, incorporating an interface-capturing equation, based on the conservative Allen-Cahn equation, to simulate incompressible two-component systems with high-density and viscosity contrasts. The method utilizes a recently proposed thread-safe implementation optimized for shared-memory architectures, and it is employed to reproduce the dynamics of droplets and bubbles in several test cases with results in agreement with experiments and other numerical simulations from the literature. The proposed approach offers promising opportunities for high-performance computing simulations of realistic fluid systems with high-density and viscosity contrasts for advanced applications in environmental, atmospheric, and meteorological flows, all the way down to microfluidic and biological systems, particularly on graphic processing unit-based architectures.

Recent experiments of fluid transport in nano-channels have shown evidence of a coupling between charge-fluctuations in polar fluids and electronic excitations in graphene solids, which may lead to a significant reduction of friction a phenomenon dubbed “negative quantum friction.” In this paper, we present a semi-classical mesoscale Boltzmann-Wigner lattice kinetic model of quantum-nanoscale transport and perform a numerical study of the effects of the quantum interactions on the evolution of a one-dimensional nano-fluid subject to a periodic external potential. It is shown that the effects of quantum fluctuations become visible once the quantum length scale (Fermi wavelength) of the quasiparticles becomes comparable to the lengthscale of the external potential. Under such conditions, quantum fluctuations are mostly felt on the odd kinetic moments, while the even ones remain nearly unaffected because they are “protected” by thermal fluctuations. It is hoped that the present Boltzmann-Wigner lattice model and extensions thereof may offer a useful tool for the computer simulation of quantum-nanofluidic transport phenomena at scales of engineering relevance.

In microfluidic systems, droplets undergo intricate deformations as they traverse flow-focusing junctions, posing a challenging task for accurate measurement, especially during short transit times. This study investigates the physical behavior of droplets within dense emulsions in diverse microchannel geometries, specifically focusing on the impact of varying opening angles within the primary channel and injection rates of fluid components. Employing a sophisticated droplet tracking tool based on deep-learning techniques, we analyze multiple frames from flow-focusing experiments to quantitatively characterize droplet deformation in terms of ratio between maximum width and height and propensity to form liquid with hexagonal spatial arrangement. Our findings reveal the existence of an optimal opening angle where shape deformations are minimal and hexagonal arrangement is maximal. Variations of fluid injection rates are also found to affect size and packing fraction of the emulsion in the exit channel. This paper offers insight into deformations, size, and structure of fluid emulsions relative to microchannel geometry and other flow-related parameters captured through machine learning, with potential implications for the design of microchips utilized in cellular transport and tissue engineering applications.

We present a mapping between a Schrödinger equation with a shifted nonlinear potential and the Navier–Stokes equation. Following a generalization of the Madelung transformations, we show that the inclusion of the Bohm quantum potential plus the laplacian of the phase field in the nonlinear term leads to continuity and momentum equations for a dissipative incompressible Navier–Stokes fluid. An alternative solution, built using a complex quantum diffusion, is also discussed. The present models may capture dissipative effects in quantum fluids, such as Bose–Einstein condensates, as well as facilitate the formulation of quantum algorithms for classical dissipative fluids.

The shape of liquid droplets in air plays an important role in the aerodynamic behavior and combustion dynamics of miniaturized propulsion systems such as microsatellites and small drones. Their precise manipulation can yield optimal efficiency in such systems. It is desired to have a minimal representation of droplet shapes using as few parameters as possible to automate shape manipulation using self-learning algorithms, such as reinforcement learning. In this paper, we use a neural compression algorithm to represent, with only two parameters, elliptical and bullet-shaped droplets initially represented with 200 points (400 real numbers) at the droplet boundary. The mapping of many to two points is achieved in two stages. Initially, a Fourier series is formulated to approximate the contour of the droplet. Subsequently, the coefficients of this Fourier series are condensed to lower dimensions utilizing a neural network with a bottleneck architecture. Finally, 5000 synthetically generated droplet shapes were used to train the neural network. With a two-real-number representation, the recovered droplet shapes had excellent overlap with the original ones, with a mean square error of ∼10−3 . Hence, this method compresses the droplet contour to merely two numerical parameters via a fully reversible process, a crucial feature for rendering learning algorithms computationally tractable.

We introduce a two-step, fully reversible process designed to project the outer shape of a generic droplet onto a lower-dimensional space. The initial step involves representing the droplet's shape as a Fourier series. Subsequently, the Fourier coefficients are reduced to lower-dimensional vectors by using autoencoder models. The exploitation of the domain knowledge of the droplet shapes allows us to map generic droplet shapes to just two-dimensional (2D) space in contrast to previous direct methods involving autoencoders that could map it on minimum eight-dimensional (8D) space. This six-dimensional (6D) reduction in the dimensionality of the droplet's description opens new possibilities for applications, such as automated droplet generation via reinforcement learning, the analysis of droplet shape evolution dynamics, and the prediction of droplet breakup. Our findings underscore the benefits of incorporating domain knowledge into autoencoder models, highlighting the potential for increased accuracy in various other scientific disciplines.

We present a highly optimized thread-safe lattice Boltzmann model in which the non-equilibrium part of the distribution function is locally reconstructed via recursivity of Hermite polynomials. Such a procedure allows the explicit incorporation of non-equilibrium moments of the distribution up to the order supported by the lattice. Thus, the proposed approach increases accuracy and stability at low viscosities without compromising performance and amenability to parallelization with respect to standard lattice Boltzmann models. The high-order thread-safe lattice Boltzmann is tested on two types of turbulent flows, namely, the turbulent channel flow at R e τ = 180 and the axisymmetric turbulent jet at Re = 7000; it delivers results in excellent agreement with reference data [direct numerical simulations (DNS), theory, and experiments] and (a) achieves peak performance [ ∼ 5 × 10 12 floating point operations (FLOP) per second and an arithmetic intensity of ∼ 7 FLOP / byte on a single graphic processing unit] by significantly reducing the memory footprint, (b) retains the algorithmic simplicity of standard lattice Boltzmann computing, and (c) allows to perform stable simulations at vanishingly low viscosities. Our findings open attractive prospects for high-performance simulations of realistic turbulent flows on GPU-based architectures. Such expectations are confirmed by excellent agreement among lattice Boltzmann, experimental, and DNS reference data.

Quasiparticles are low-energy excitations with important roles in condensed matter physics. An intriguing example is provided by Majorana quasiparticles, which are equivalent to their antiparticles. Despite being implicated in neutrino oscillations and topological superconductivity, their experimental realizations remain very rare. Here, we propose a purely classical realization of Majorana fermions in terms of three-dimensional disclination lines in active nematics. The underlying reason is the well-known equivalence, in 3D, between a + 1 / 2 local defect profile and a - 1 / 2 profile, which acts as its antiparticle. The mapping also requires proving that defect profiles transform as spinors, and activity is needed to overcome the elastic cost associated with these excitations, so they spontaneously appear in steady state. We combine topological considerations and numerics to show that active nematics under confinement spontaneously create in their interior topologically charged disclination lines and loops, akin to Majorana quasiparticles with finite momentum. Within a long channel, the phenomenology we observe resembles that of the Kitaev chain, as Majorana-like states appear near the boundaries, while a delocalized topological excitation arises in the form of a chiral disclination line. The analogy between 3D nematic defects and topological quasiparticles further suggests that active turbulence can be viewed as a topological phase, where defects percolate to form delocalized topological quasiparticles similar to those observed in the channel. We propose that three-dimensional active disclinations can be used to probe the physics of Majorana spinors at much larger scale than that for which they were originally introduced, potentially facilitating their experimental study.

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. In contrast, 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.

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.

A regularized version of the lattice Boltzmann method for efficient simulation of soft materials is introduced. Unlike standard approaches, this method reconstructs the distribution functions from available hydrodynamic variables (density, momentum, and pressure tensor) without storing the full set of discrete populations. This scheme shows significantly lower memory requirements and data access costs. A series of benchmark tests of relevance to soft matter, such as collisions of fluid droplets, is discussed to validate the method. The results can be of particular interest for high-performance simulations of soft matter systems on future exascale computers.

We present thread-safe, highly-optimized lattice Boltzmann implementations, specifically aimed at exploiting the high memory bandwidth of GPU-based architectures. At variance with standard approaches to LB coding, the proposed strategy, based on the reconstruction of the post-collision distribution via Hermite projection, enforces data locality and avoids the onset of memory dependencies, which may arise during the propagation step, with no need to resort to more complex streaming strategies. The thread-safe lattice Boltzmann achieves peak performances, both in two and three dimensions and it allows to reduce significantly the memory footprint (tens of GigaBytes for order billions lattice nodes simulations) by retaining the algorithmic simplicity of standard LB computing. Our findings open attractive prospects for high-performance simulations of complex flows on GPU-based architectures.

Physiological solvent flows surround biological structures triggering therein collective motions. Notable examples are virus/host-cell interactions and solvent-mediated allosteric regulation. The present work describes a multiscale approach joining the Lattice Boltzmann fluid dynamics (for solvent flows) with the all-atom atomistic molecular dynamics (for proteins) to model functional interactions between flows and molecules. We present, as an applicative scenario, the study of the SARS-CoV-2 virus spike glycoprotein protein interacting with the surrounding solvent, modeled as a mesoscopic fluid. The equilibrium properties of the wild-type spike and of the Alpha variant in implicit solvent are described by suitable observables. The mesoscopic solvent description is critically compared to the all-atom solvent model, to quantify the advantages and limitations of the mesoscopic fluid description.

In the last decades kinetic theory has developed into a very elegant and effective framework to handle a broad spectrum of problems involving complex states of flowing matter, far beyond the original realm of rarefied gas dynamics. In this paper, we present recent applications of the lattice Boltzmann method to the computational design of soft mesoscale materials, including soft flowing crystals, dense multicore emulsions, as well as Petascale simulations of deep-sea glassy sponges. This manuscript is a tribute to the groundbreaking work of Carlo Cercignani and his undiminished impact on modern non-equilibrium statistical physics.

Active droplets are artificial microswimmers built from a liquid dispersion by microfluidic tools and showing self-propelled motion. These systems hold particular interest for mimicking biological phenomena, such as some aspects of cell locomotion and collective behaviors of bacterial colonies, as well as for the design of droplet-based biologically inspired materials, such as engineered tissues. Growing evidence suggests that geometrical confinement crucially affects their morphology and motility, but the driving physical mechanisms are still poorly understood. Here, we study the effect of activity on a droplet containing a contractile polar fluid confined within microfluidic channels of various sizes. We find a surprising wealth of shapes and dynamic regimes, whose mechanics is regulated by a subtle interplay between contractile stress, droplet elasticity, and microchannel width. They range from worm-like and cell-like shaped droplets displaying an oscillating behavior within wider channels to bullet-shaped droplets exhibiting rectilinear motion in narrower slits. Our findings support the view that geometrical confinement can provide a viable strategy to control and predict the propulsion direction of active droplets. It would be of interest to look for analogs of these motility modes in biological cells or in synthetic active matter.

We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at the droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates coherently triggering a concurrent orbital motion of both droplets around each other, an effect due to the momentum transfer to the surrounding fluid. In addition the topological defects, resulting from the conflict orientation of the liquid crystal within the drops, exhibit a chaotic-like motion in cholesterics with a high pitch, in contrast with a regular one occurring along circular trajectories observed in nematics drops. Such behavior is found to depend on magnitude and frequency of the applied field as well as on the anchoring of the liquid crystal at the droplet interface. These findings are quantitatively evaluated by measuring the angular velocity of fluid and drops for various frequencies of the applied field.

Tracking droplets in microfluidics is a challenging task. The difficulty arises in choosing a tool to analyze general microfluidic videos to infer physical quantities. The state-of-the-art object detector algorithm You Only Look Once (YOLO) and the object tracking algorithm Simple Online and Realtime Tracking with a Deep Association Metric (DeepSORT) are customizable for droplet identification and tracking. The customization includes training YOLO and DeepSORT networks to identify and track the objects of interest. We trained several YOLOv5 and YOLOv7 models and the DeepSORT network for droplet identification and tracking from microfluidic experimental videos. We compare the performance of the droplet tracking applications with YOLOv5 and YOLOv7 in terms of training time and time to analyze a given video across various hardware configurations. Despite the latest YOLOv7 being 10% faster, the real-time tracking is only achieved by lighter YOLO models on RTX 3070 Ti GPU machine due to additional significant droplet tracking costs arising from the DeepSORT algorithm. This work is a benchmark study for the YOLOv5 and YOLOv7 networks with DeepSORT in terms of the training time and inference time for a custom dataset of microfluidic droplets.