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.

In this work an optimized multicomponent lattice Boltzmann (LB) model is deployed to simulate axisymmetric turbulent jets of a fluid evolving in a quiescent, immiscible environment over a wide range of dynamic regimes. The implementation of the multicomponent LB code achieves peak performance on graphic processing units (GPUs) with a significant reduction of the memory footprint, retains the algorithmic simplicity inherent to standard LB computing, and, being based on a high-order extension of the thread-safe LB algorithm, allows us to perform stable simulations at vanishingly low viscosities. The proposed approach opens attractive prospects for high-performance computing simulations of realistic turbulent flows with interfaces on GPU-based architectures.

Cyclic nucleotide-gated (CNG) ion channels are crucial to the intracellular calcium dynamics in neurons and other sensory cells, in several organisms. Mutations in CNG genes are linked to various dysfunctions and diseases. In this work, we propose a theoretical investigation of the structural and functional properties of wild-type TAX-4, a non-selective CNG ion channel, expressed in various sensory neurons of Caenorhabditis elegans, and involved in the permeation of monovalent and multivalent cations. Using a recent cryo-electron microscopy structure of the open state of the channel as the starting conformation, we conduct all-atom molecular dynamics simulations of the full-length channel in a membrane/water/ions system, both in the cGMP-bound and unbound conformations. Several channel structural descriptors are examined and a first-level functional annotation is carried out, on the microsecond time scale. A comparison with the available experimental data on TAX-4 and human homologues allows us to assign the simulated bound and unbound models as the pre-open and closed conformations of TAX-4, respectively. Comparisons between the bound and unbound conformations enable us to suggest key conformational changes underlying the binding-to-gating transition.

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.

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.

Nucleation and growth of methane clathrate hydrates is an exceptional playground to study crystallisation of multi-component, host-guest crystallites when one of the species forming the crystal, the guest, has a higher concentration in the solid than in the liquid phase. This adds problems related to the transport of the low concentration species, here methane. A key aspect in the modelling of clathrates is the water model employed in the simulation. In previous articles, we compared an all-atom force model, TIP4P/Ewald, with a coarse grain one, which is highly appreciated for its computational efficiency. Here, we perform a complementary analysis considering three all-atoms water models: TIP4P/Ewald, TIP4P/ice and TIP5P. A key difference between these models is that the former predicts a much lower freezing temperature. Intuitively, one expects that to lower freezing temperatures of water correspond to lower water/methane-methane gas-clathrate coexistence ones, which determines the degree of supercooling and the degree of supersaturation. Hence, in the simulation conditions, 250 K (500 atm, and fixed methane molar fraction), one expects computational samples made of TIP4P-ice and TIP5P, with a similar freezing temperature (T-f similar to 273 K), to be more supersaturated with respect to the case of TIP4P-Ew (T-f similar to 245 K), and crystallisation to be faster. Surprisingly, we find that while the nucleation rate is consistent with this prediction, growth rate with TIP4P-ice and TIP5P is much slower than with TIP4P-Ew. The latter was attributed to the slower reorientation of water molecules in strong supercooled conditions, resulting in a lower growth rate. This suggests that the freezing temperature is not a suitable parameter to evaluate the adequacy of a water model.[GRAPHICS]

The book is interwoven according to the intrinsic logics of modern most important applications of electrospun nanofibers. It discusses such application-oriented nanofibers as self-healing vascular nanotextured materials, biopolymer nanofibers, soft robots and actuators based on nanofibers, biopolymer nanofiber-based triboelectric nanogenerators, metallized nanofibers, and heaters and sensors based on them. It also includes such topics as the injectable nanofibrous biomaterials, fibrous hemostatic agents and their interaction with blood, as well as electrospun nanofibers for face-mask applications. The book also details polyelectrolytes-based complex nanofibers and their use as actuators. It also covers drug release facilitated by polyelectrolytes-based complex nanofibers. The fundamental aspects of electrospinning of polymer nanofibers discussed in the final part of the book link them to the applications described in the preceding chapters. Such topics as polymer solution preparation and their rheological properties, e.g., viscoelasticity and the related spinnability, the electrical conductivity of polymer solutions, and the cascade of the physical phenomena resulting in formation of nanofibers encompass the experimental aspects. Also, the general quasi-1D equations used for modeling of formation of electrospun polymer nanofibers, and the numerical aspects of their solution are discussed in detail, including such modeling-driven applications as nanofiber alignment by electric focusing fields.

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.