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 present a mathematical framework to include quantum interfacial interactions, provided by Keldysh nonequilibrium quantum transport formalism, bottom-up coupled to a nanoscale lattice Boltzmann method. As an applicative scenario, we simulate a two-dimensional water flow between two parallel solid plates hosting electrons and phonons in the solid bottom wall. The corresponding tool may prove useful for the computational design of quantum-engineered nanofluidic devices, showing its capability to explore the effects of the interfacial quantum transport phenomena at scales of experimental relevance.

In this work, we present accLB, a high-performance Fortran-based lattice Boltzmann (LB) solver tailored to multiphase turbulent flows on multi-GPU architectures. The code couples a conservative phase-field formulation of the Allen–Cahn equation with a thread-safe, regularized LB method to capture complex interface dynamics. Designed from the ground up for HPC environments, accLB employs MPI for distributed memory parallelism and OpenACC for GPU acceleration, achieving excellent portability and scalability on leading pre-exascale systems such as Leonardo and LUMI. Benchmark tests demonstrate strong and weak scaling efficiencies on multiple GPUs. Physical validation includes direct numerical simulations of homogeneous isotropic turbulence (HIT). Further, we examine bubble-laden HIT and observe a transition to a -3 energy scaling, as in experiments and theoretical predictions, due to bubble-induced dissipation, along with enhanced small-scale intermittency. These results highlight accLB as a robust and scalable platform for the simulation of multiphase turbulence in extreme computational regimes.

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.

Accurate prediction of rarefied gas dynamics is crucial for optimizing flows through microelectromechanical systems, air filtration devices, and shale gas extraction. Traditional methods, such as discrete velocity and direct simulation Monte Carlo (DSMC), demand intensive memory and computation, especially for microflows in non-convex domains. Recently, physics-informed neural networks (PINNs) emerged as a meshless and adaptable alternative for solving non-linear partial differential equations. We trained a PINN using a limited number of DSMC-generated rarefied gas microflows in the transition regime (0.1<3), incorporating continuity and Cauchy momentum exchange equations in the loss function. The PINN achieved under 2 % error on these residuals and effectively filtered DSMC's intrinsic statistical noise. Predictions remained strong for a tested flow field with Kn=0.7, and showed limited extrapolation performance on a flow field with Kn=5 with a local overshoot of about 20 %, while maintaining physical consistency. Notably, each DSMC field required ∼20 hours on 4 graphics processing units (GPU), while the PINN training took <2 hours on one GPU, with evaluations under 2 seconds.

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.

We report new dynamical modes in confined soft granular flows, such as stochastic jetting and dripping, with no counterpart in continuum viscous fluids. The new modes emerge as a result of the propagation of the chaotic behavior of individual grains - here, monodisperse emulsion droplets - to the level of the entire system as the emulsion is focused into a narrow orifice by an external viscous flow. We observe avalanching dynamics and the formation of remarkably stable jets - single-file granular chains - which occasionally break, resulting in a non-Gaussian distribution of cluster sizes. We find that the sequences of droplet rearrangements that lead to the formation of such chains resemble unfolding of cancer cell clusters in narrow capillaries, overall demonstrating that microfluidic emulsion systems could serve to model various aspects of soft granular flows, including also tissue dynamics at the mesoscale.

We present LBcuda, a GPU accelerated version of LBsoft, our open-source MPI-based software for the simulation of multi-component colloidal flows. We describe the design principles, the optimization and the resulting performance as compared to the CPU version, using both an average cost GPU and high-end NVidia GPU cards (V100 and the latest A100). The results show a substantial acceleration for the fluid solver reaching up to 200 GLUPS (Giga Lattice Updates Per Second) on a cluster made of 512 A100 NVIDIA cards simulating a grid of eight billion lattice points. These results open attractive prospects for the computational design of new materials based on colloidal particles. Program summary: Program Title: LBcuda CPC Library link to program files: https://doi.org/10.17632/v6fvmzpcrn.1 Developer's repository link: https://github.com/copmat/LBcuda Licensing provisions: 3-Clause BSD License Programming language: CUDA Fortran Nature of problem: Hydro-dynamics of colloidal multi-component systems and Pickering emulsions. Solution method: Lattice-Boltzmann method solving the Navier-Stokes equations for the fluid dynamics within an Eulerian description. Particle solver describing colloidal particles within a Lagrangian representation coupled to the fluid solver. The numerical solution of the coupling algorithm includes the back reaction effects for each force terms according to a fluid-particle multi-scale paradigm.

Deep neural networks are rapidly emerging as data analysis tools, often outperforming the conventional techniques used in complex microfluidic systems. One fundamental analysis frequently desired in microfluidic experiments is counting and tracking the droplets. Specifically, droplet tracking in dense emulsions is challenging due to inherently small droplets moving in tightly packed configurations. Sometimes, the individual droplets in these dense clusters are hard to resolve, even for a human observer. Here, two deep learning-based cutting-edge algorithms for object detection [you only look once (YOLO)] and object tracking (DeepSORT) are combined into a single image analysis tool, DropTrack, to track droplets in the microfluidic experiments. DropTrack analyzes input microfluidic experimental videos, extracts droplets' trajectories, and infers other observables of interest, such as droplet numbers. Training an object detector network for droplet recognition with manually annotated images is a labor-intensive task and a persistent bottleneck. In this work, this problem is partly resolved by training many object detector networks (YOLOv5) with several hybrid datasets containing real and synthetic images. We present an analysis of a double emulsion experiment as a case study to measure DropTrack's performance. For our test case, the YOLO network trained by combining 40% real images and 60% synthetic images yields the best accuracy in droplet detection and droplet counting in real experimental videos. Also, this strategy reduces labor-intensive image annotation work by 60%. DropTrack's performance is measured in terms of mean average precision of droplet detection, mean squared error in counting the droplets, and image analysis speed for inferring droplets' trajectories. The fastest configuration of DropTrack can detect and track the droplets at approximately 30 frames per second, well within the standards for a real-time image analysis.

This work analyzes trajectories obtained by YOLO and DeepSORT algorithms of dense emulsion systems simulated via lattice Boltzmann methods. The results indicate that the individual droplet's moving direction is influenced more by the droplets immediately behind it than the droplets in front of it. The analysis also provide hints on constraints of a dynamical model of droplets for the dense emulsion in narrow channels.

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.

We present a numerical investigation of the airflow dynamics and particle transport through an averaged human nasal cavity. The effect of particle size and breathing rate on the deposition patterns are explored. The simulations reveal that smaller particles penetrate deeper into the airway, whereas larger particles agglomerate near the anterior portion of the nasal cavity. Increasing the flow rate augmented the penetration of the particles. The complex interplay of the finite particle size and the flow inertia decided the spatial deposition of the particles. The findings from this study demonstrate the efficacy of state-of-art simulation frameworks for targeting respiratory disorders.

A recently proposed mesoscale approach for the simulation of multicomponent flows with near-contact interactions is employed to investigate the early stage formation and clustering statistics of soft flowing crystals in microfluidic channels. Specifically, we first demonstrate the ability of the aforementioned mesoscale model to accurately reproduce main mechanisms leading to the formation of two basic droplet patterns (triangular and hexagonal), in close agreement with experimental evidence. Next, we quantitatively evaluate the device-scale clustering efficiency of the crystal formation process by introducing a new orientational order parameter, based on the Delaunay triangulation and Voronoi diagrams analysis of the droplet patterns. The mesoscale computational approach employed in this work proves to be an efficient tool to shed new light on the complex dynamics of dense emulsions, from short-scale thin-film hydrodynamics, all the way up to global structure formation and statistics of the resulting droplets ensembles.