Metastable and unstable hydrodynamics in multiphase lattice Boltzmann

Metastability in liquids is at the foundation of complex phase transformation dynamics such as nucleation and cavitation. Intermolecular interaction details, beyond the equation of state, and thermal hydrodynamic fluctuations play a crucial role. However, most numerical approaches suffer from a slow time and space convergence, thus hindering the convergence to the hydrodynamic limit. This work shows that the Shan-Chen lattice Boltzmann model has the unique capability of simulating the hydrodynamics of the metastable state. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave vectors, reduced temperatures, and pressures, deep into the metastable region. Such remarkable agreement between the theory and simulations leverages the exact implementation at the lattice level of the mechanical equilibrium condition. The static structure factor is found to consistently diverge as the temperature approaches the critical point or the density approaches the spinodal line at a subcritical temperature. Theoretically predicted critical exponents are observed in both cases. Finally, the phase separation in the unstable branch follows the same pattern, i.e., the generation of interfaces with different topology, as observed in molecular dynamics simulations.

Mesoscale perspective on the Tolman length

We demonstrate that the multiphase Shan-Chen lattice Boltzmann method (LBM) yields a curvature dependent surface tension σ as computed from three-dimensional hydrostatic droplets and bubbles simulations. Such curvature dependence is routinely characterized, at first order, by the so-called Tolman length δ. LBM allows one to precisely compute σ at the surface of tension R_{s} and determine the Tolman length from the coefficient of the first order correction. The corresponding values of δ display universality for different equations of state, following a power-law scaling near the critical temperature. The Tolman length has been studied so far mainly via computationally demanding Molecular Dynamics simulations or by means of Density Functional Theory approaches playing a pivotal role in extending Classical Nucleation Theory. The present results open a hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled. All the results can be independently reproduced through the "idea.deploy" framework.

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio [Formula: see text] (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate [Formula: see text] applied to the RBC. However, the membrane viscosity [Formula: see text] plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity [Formula: see text] on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios [Formula: see text], larger values of [Formula: see text] lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing [Formula: see text] or increasing [Formula: see text] results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

Extreme flow simulations reveal skeletal adaptations of deep-sea sponges

Since its discovery^1,2, the deep-sea glass sponge Euplectella aspergillum has attracted interest in its mechanical properties and beauty. Its skeletal system is composed of amorphous hydrated silica and is arranged in a highly regular and hierarchical cylindrical lattice that begets exceptional flexibility and resilience to damage^3-6. Structural analyses dominate the literature, but hydrodynamic fields that surround and penetrate the sponge have remained largely unexplored. Here we address an unanswered question: whether, besides improving its mechanical properties, the skeletal motifs of E. aspergillum underlie the optimization of the flow physics within and beyond its body cavity. We use extreme flow simulations based on the 'lattice Boltzmann' method⁷, featuring over fifty billion grid points and spanning four spatial decades. These in silico experiments reproduce the hydrodynamic conditions on the deep-sea floor where E. aspergillum lives^8-10. Our results indicate that the skeletal motifs reduce the overall hydrodynamic stress and support coherent internal recirculation patterns at low flow velocity. These patterns are arguably beneficial to the organism for selective filter feeding and sexual reproduction^11,12. The present study reveals mechanisms of extraordinary adaptation to live in the abyss, paving the way towards further studies of this type at the intersection between fluid mechanics, organism biology and functional ecology.

Structure and isotropy of lattice pressure tensors for multirange potentials

We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multiphase lattice Boltzmann models (LBM) with multirange interactions. Due to lattice discrete effects, we show that the built-in isotropy properties of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multirange potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of nonideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of nonideal interfaces.

Loading and relaxation dynamics of a red blood cell

We use mesoscale numerical simulations to investigate the unsteady dynamics of a single red blood cell (RBC) subjected to an external mechanical load. We carry out a detailed comparison between the loading (L) dynamics, following the imposition of the mechanical load on the RBC at rest, and the relaxation (R) dynamics, allowing the RBC to relax to its original shape after the sudden arrest of the mechanical load. Such a comparison is carried out by analyzing the characteristic times of the two corresponding dynamics, i.e., t_L and t_R. When the intensity of the mechanical load is small enough, the two kinds of dynamics are symmetrical (t_L≈t_R) and independent of the typology of mechanical load (intrinsic dynamics); otherwise, in marked contrast, an asymmetry is found, wherein the loading dynamics is typically faster than the relaxation one. This asymmetry manifests itself with non-universal characteristics, e.g., dependency on the applied load and/or on the viscoelastic properties of the RBC membrane. To deepen such a non-universal behaviour, we consider the viscosity of the erythrocyte membrane as a variable parameter and focus on three different typologies of mechanical load (mechanical stretching, shear flow, elongational flow): this allows to clarify how non-universality builds up in terms of the deformation and rotational contributions induced by the mechanical load on the membrane. Finally, we also investigate the effect of the elastic shear modulus on the characteristic times t_L and t_R. Our results provide crucial and quantitative information on the unsteady dynamics of RBC and its membrane response to the imposition/cessation of external mechanical loads.

On the effects of membrane viscosity on transient red blood cell dynamics

Computational Fluid Dynamics (CFD) is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of red blood cells (RBCs) at the mesoscale. In many practical instances, biomedical devices work on time-scales comparable to the intrinsic relaxation time of RBCs: thus, a systematic understanding of the time-dependent response of erythrocyte membranes is crucial for the effective design of such devices. So far, this information has been deduced from experimental data, which do not necessarily adapt to the broad variety of fluid dynamic conditions that can be encountered in practice. This work explores the novel possibility of studying the time-dependent response of an erythrocyte membrane to external mechanical loads via mesoscale numerical simulations, with a primary focus on the detailed characterisation of the RBC relaxation time tc following the arrest of the external mechanical load. The adopted mesoscale model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM), coupled with the Standard Linear Solid (SLS) model to account for the RBC membrane viscosity. We underscore the key importance of the 2D membrane viscosity μm to correctly reproduce the relaxation time of the RBC membrane. A detailed assessment of the dependencies on the typology and strength of the applied mechanical loads is also provided. Overall, our findings open interesting future perspectives for the study of the non-linear response of RBCs immersed in time-dependent strain fields.

Hydrodynamic behavior of the pseudopotential lattice Boltzmann method for interfacial flows

The lattice Boltzmann method (LBM) is routinely employed in the simulation of complex multiphase flows comprising bulk phases separated by nonideal interfaces. The LBM is intrinsically mesoscale with a hydrodynamic equivalence popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary in space and time. The latter assumptions become questionable close to interfaces where the method is also known to be affected by spurious nonhydrodynamical contributions. This calls for quantitative hydrodynamical checks. In this paper, we analyze the hydrodynamic behavior of the LBM pseudopotential models for the problem of the breakup of a liquid ligament triggered by the Plateau-Rayleigh instability. Simulations are performed at fixed interface thickness, while increasing the ligament radius, i.e., in the "sharp interface" limit. The influence of different LBM collision operators is also assessed. We find that different distributions of spurious currents along the interface may change the outcome of the pseudopotential model simulations quite sensibly, which suggests that a proper fine-tuning of pseudopotential models in time-dependent problems is needed before the utilization in concrete applications. Taken all together, we argue that the results of the proposed paper provide a valuable insight for engineering pseudopotential model applications involving the hydrodynamics of liquid jets.

On the effects of surface corrugation on the hydrodynamic performance of cylindrical rigid structures

In this work, we perform fully three-dimensional numerical simulations of the flow field surrounding cylindrical structures characterized by different types of corrugated surface. The simulations are carried out using the Lattice Boltzmann Method (LBM), considering a flow regime with a Reynolds number [Formula: see text]. The fluid-dynamic wake structure and stability are investigated by means of PSD analyses of the velocity components and by visual inspection of the vortical coherent structure evolution. Moreover, the energy dissipation of the flow is assessed by considering an equivalent discharge coefficient [Formula: see text], which measures the total pressure losses of the flow moving around the various layout under investigation. Outcomes from our study demonstrate that the helical ridges augment energy dissipation, but might also have a role in the passive control of the characteristic frequencies of the unsteady wake flow.

Effect of nanoscale flows on the surface structure of nanoporous catalysts

The surface structure and composition of a multi-component catalyst are critical factors in determining its catalytic performance. The surface composition can depend on the local pressure of the reacting species, leading to the possibility that the flow through a nanoporous catalyst can affect its structure and reactivity. Here, we explore this possibility for oxidation reactions on nanoporous gold, an AgAu bimetallic catalyst. We use microscopy and digital reconstruction to obtain the morphology of a two-dimensional slice of a nanoporous gold sample. Using lattice Boltzmann fluid dynamics simulations along with thermodynamic models based on first-principles total-energy calculations, we show that some sections of this sample have low local O₂ partial pressures when exposed to reaction conditions, which leads to a pure Au surface in these regions, instead of the active bimetallic AgAu phase. We also explore the effect of temperature on the surface structure and find that moderate temperatures (≈300-450 K) should result in the highest intrinsic catalytic performance, in apparent agreement with experimental results.

Regularized lattice Bhatnagar-Gross-Krook model for two- and three-dimensional cavity flow simulations

We investigate the accuracy and performance of the regularized version of the single-relaxation-time lattice Boltzmann equation for the case of two- and three-dimensional lid-driven cavities. The regularized version is shown to provide a significant gain in stability over the standard single-relaxation time, at a moderate computational overhead.

Transverse harmonic oscillations of laminae in viscous fluids: a lattice Boltzmann study

In this paper, we use the lattice Boltzmann method with the Bhatnagar-Gross-Krook linear collision operator to study the flow physics induced by a rigid lamina undergoing moderately large harmonic oscillations in a viscous fluid. We propose a refill procedure for the hydrodynamic quantities in the lattice sites that are in the vicinity of the oscillating lamina. The numerically estimated flow field is used to compute the complex hydrodynamic function that describes the added mass and hydrodynamic damping experienced by the lamina. Results of the numerical simulations are validated against theoretical predictions for small amplitude vibrations and experimental and numerical findings for moderately large oscillations.

Rupture of a ferrofluid droplet in external magnetic fields using a single-component lattice Boltzmann model for nonideal fluids

A nonisotropic tensorial extension of the single-component Shan-Chen pseudopotential Lattice Boltzmann method for nonideal fluids is presented. Direct comparison with experimental data shows that this extension is able to capture relevant features of ferrofluid behavior, such as the deformation and subsequent rupture of a liquid droplet as a function of an externally applied magnetic field. The present model offers an economic lattice-kinetic pathway to the simulation of complex ferrofluid hydrodynamics.

Lattice Boltzmann models for nonideal fluids with arrested phase-separation

The effects of midrange repulsion in lattice Boltzmann models on the coalescence and/or breakup behavior of single-component, nonideal fluids are investigated. It is found that midrange repulsive interactions allow the formation of spraylike, multidroplet configurations, with droplet size directly related to the strength of the repulsive interaction. The simulations show that just a tiny 10% of midrange repulsive pseudoenergy can boost the surface:volume ratio of the phase-separated fluid by nearly two orders of magnitude. Drawing upon a formal analogy with magnetic Ising systems, a pseudopotential energy is defined, which is found to behave similar to a quasiconserved quantity for most of the time evolution. This offers a useful quantitative indicator of the stability of the various configurations, thus helping the task of their interpretation and classification. The present approach appears to be a promising tool for the computational modeling of complex flow phenomena, such as atomization, spray formation, microemulsions, breakup phenomena, and possibly glassylike systems as well.