Bubble nucleation at catalyst surfaces plays a critical role in the operation of electrolyzers. However, achieving controlled bubble nucleation remains challenging due to limited understanding of the underlying mechanisms. Here, we present a free-energy model that quantitatively predicts both the activation energy and critical nucleus size of bubbles at given supersaturation, temperature, pressure, and surface wettability. We find that the activation energy ΔG_max decreases with increasing supersaturation ζ, following a power-law scaling of ΔG_max∼ ζ^-2, while the critical nucleus radius R_c scales as R_c∼ ζ^-1. Our theoretical predictions for the critical nucleus radius of hydrogen, oxygen and nitrogen bubbles are in quantitative agreement with experimental measurements. Finally, we present a simple model that couples gas diffusion and electrochemical reaction kinetics to determine the maximum gas supersaturation at a given current density. Our results advance the fundamental understanding of bubble nucleation at catalyst surfaces and provide practical guidelines for catalyst layer design to improve the performance of electrolyzers.

Pulsatile flow in corrugated tubes arises in hemodynamics and microfluidics, where oscillatory forcing and geometric constrictions jointly determine transport and wall loading. We extend Womersley's classical solution for oscillatory flow in a rigid circular tube to rigid axisymmetric tubes of slowly varying radius. Within the lubrication approximation, we derive closed-form expressions for the axial velocity profile, volumetric flow rate, phase lag, and wall shear stress at an arbitrary Womersley number. Three-dimensional lattice Boltzmann simulations are used to assess the regime of validity of the theory. The analysis shows that the local velocity profile varies strongly along the tube, ranging from plug-like in wide sections to more parabolic near bottlenecks. The cycle-maximum flow rate decreases with increasing corrugation, but this reduction weakens as pulsatility increases, reflecting a crossover from the quasi-steady scaling ⟨ R^-4⟩^-1 to the high-frequency scaling ⟨ R^-2⟩^-1. The wall shear stress is maximal at the bottleneck and decreases with Womersley number. For sinusoidal corrugations, the bottleneck wall shear stress depends non-monotonically on the corrugation because of the competition between local shear amplification and global hydraulic resistance. Closed-form expressions for the time-averaged wall shear stress and oscillatory shear index further connect the theory to standard hemodynamic metrics.

We propose a reaction-limited evaporation model within the color-gradient lattice Boltzmann (LB) multicomponent framework to address the lack of intrinsic evaporation mechanisms. Unlike diffusion-driven approaches, our method directly enforces mass removal at the fluid interface in a reaction-limited manner while maintaining numerical stability. Using the inherent color-gradient magnitude and a single adjustable parameter, evaporation sites are chosen in a computationally efficient way with seamless mass exchange between the components, with no change to the core algorithm. Extensive validation across diverse interface geometries and evaporation flux magnitudes demonstrates high accuracy, with errors below 5% for unit density ratios. For density contrasts, the method remains robust in the limit of smaller evaporation flux magnitudes and density ratios. Our approach extends the applicability of the color-gradient LB model to scenarios involving reaction-limited evaporation, such as droplet evaporation on heated substrates, vacuum evaporation of molten metals, and drying processes in porous media.

Despite decades of research on blood flow, an analogue of Navier-Stokes equations that accurately describe blood flow properties has not been established yet. The reason behind this is that the properties of blood flow seem à priori non universal as they depend on various factors such as global concentration of red blood cells (RBCs) and channel width. Here, we have discovered a universal law when the stress and strain rate are measured at a given local RBCs concentration. However, the local concentration must be determined in order to close the problem. We propose a non-local diffusion equation of RBCs concentration that agrees with the full simulation. The universal law is exemplified for both shear and pressure driven flows. While the theory is restricted to a simplistic geometry (straight channel) it provides a fundamental basis for future research on blood flow dynamics and could lead to the development of a new theory that accurately describes blood flow properties under various conditions, such as in complex vascular networks.

Margination, a fundamental process in which leukocytes migrate from the flowing blood to the vessel wall, is well-documented in physiology. However, it is still an open question on how the differences in cell size and stiffness of white and red cells contribute to this phenomenon. To investigate the specific influence of cell stiffness, we conduct experimental and numerical studies on the segregation of a binary mixture of artificially stiffened red blood cells within a suspension of healthy cells. The resulting distribution of stiffened cells within the channel is found to depend on the channel geometry, as demonstrated with slit, rectangular, and cylindrical cross sections. Notably, an unexpected central peak in the distribution of stiffened red blood cells, accompanied by fourfold peaks at the corners, emerges in agreement with simulations. Our results unveil a nonmonotonic variation in segregation/margination concerning hematocrit and flow rate, challenging the prevailing belief that higher flow rates lead to enhanced margination.

We present a method to achieve reaction-limited evaporation for the color-gradient lattice Boltzmann multicomponent model. Our approach involves a systematic way to remove fluid mass from the interface region in order to achieve evaporation rates similar to those in a reaction-limited regime. Through various tests, our method demonstrates accurate and consistent results for different interface shapes across a wide range of evaporation flux magnitudes. A single free parameter is required to choose the evaporation sites where fluid mass is exchanged between the components. We find that at unit density ratio, this single parameter allows for the correct description of an arbitrarily shaped interface with an error of less than 5 contrasts, accurate results are observed for lower evaporation flux magnitudes and density ratios. Our proposed method can be applied to isothermal reaction-limited scenarios, such as evaporation in pure vapor or under a gas draft. It can also handle weakly space-time-dependent fluxes, making it suitable for specific non-isothermal applications such as drop evaporation from heated substrates.

The wetting dynamics of liquid particles, from coated droplets to soft capsules, holds significant technological interest. Motivated by the need to simulate liquid metal droplet with an oxidize surface layer, in this work we introduce a computational scheme that allows to simulate droplet dynamics with general surface properties and model different levels of interface stiffness, describing also cases that are intermediate between pure droplets and capsules. Our approach is based on a combination of the immersed boundary (IB) and the lattice Boltzmann (LB) methods. Here, we validate our approach against the theoretical predictions in the context of shear flow and static wetting properties and we show its effectiveness in accessing the wetting dynamics, exploring the ability of the scheme to address a broad phenomenology.

Membrane viscosity is known to play a central role in the transient dynamics of isolated viscoelastic capsules by decreasing their deformation, inducing shape oscillations and reducing the loading time, that is, the time required to reach the steady-state deformation. However, for dense suspensions of capsules, our understanding of the influence of the membrane viscosity is minimal. In this work, we perform a systematic numerical investigation based on coupled immersed boundary–lattice Boltzmann (IB-LB) simulations of viscoelastic spherical capsule suspensions in the non-inertial regime. We show the effect of the membrane viscosity on the transient dynamics as a function of volume fraction and capillary number. Our results indicate that the influence of membrane viscosity on both deformation and loading time strongly depends on the volume fraction in a non-trivial manner: dense suspensions with large surface viscosity are more resistant to deformation but attain loading times that are characteristic of capsules with no surface viscosity, thus opening the possibility to obtain richer combinations of mechanical features.

The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves. We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method (LBM) simulations. Our numerical algorithm consists of two separable parts. Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid. The two components couple via an immersed boundary method. We present data for a single swimmer system and our data also show the onset of collective effects and, in particular, an overall velocity increment of clusters of swimmers.

Bifurcations and branches in the microcirculation dramatically affect blood flow as they determine the spatiotemporal organization of red blood cells (RBCs). Such changes in vessel geometries can further influence the formation of a cell-free layer (CFL) close to the vessel walls. Biophysical cell properties, such as their deformability, which is impaired in various diseases, are often thought to impact blood flow and affect the distribution of flowing RBCs. This study investigates the flow behavior of healthy and artificially hardened RBCs in a bifurcating microfluidic T-junction. We determine the RBC distribution across the channel width at multiple positions before and after the bifurcation. Thus, we reveal distinct focusing profiles in the feeding mother channel for rigid and healthy RBCs that dramatically impact the cell organization in the successive daughter channels. Moreover, we experimentally show how the characteristic asymmetric CFLs in the daughter vessels develop along their flow direction. Complimentary numerical simulations indicate that the buildup of the CFL is faster for healthy than for rigid RBCs. Our results provide fundamental knowledge to understand the partitioning of rigid RBC as a model of cells with pathologically impaired deformability in complex in vitro networks.

The dynamics of rigid particle suspensions in a wall-bounded laminar flow present several nontrivial and intriguing features, including particle ordering, lateral transport, and the appearance of stable, preferential locations like the Segré-Silberberg annulus. The formation of more than one annulus is a particularly puzzling phenomenon that is still not fully explained. Here, we present numerical simulation results of a dilute suspension of particles in (periodic) pipe flow based on the lattice Boltzmann and the discrete element methods (DEM). Our simulations provide access to the full radial position history of the particles while traveling downstream. This allows to accurately quantify the transient and steady states. We observe the formation of the secondary, inner annulus and show that its position invariably shifts toward the Segré-Silberberg one if the channel is sufficiently long, proving that it is, in fact, a transient feature for Reynolds numbers ($Re$) up to $600$. We quantify the variation of the channel focusing length ($L_s/2R$) with $Re$. Interestingly and unlike the theoretical prediction for a point-like particle, we observe that $L_s/2R$ increases with $Re$ for both the single particle and the suspension.

We investigate the rheology of strain-hardening spherical capsules, from the dilute to the concentrated regime under a confined shear flow using three-dimensional numerical simulations. We consider the effect of capillary number, volume fraction and membrane inextensibility on the particle deformation and on the effective suspension viscosity and normal stress differences of the suspension. The suspension displays a shear-thinning behaviour which is a characteristic of soft particles such as emulsion droplets, vesicles, strain-softening capsules, and red blood cells. We find that the membrane inextensibility plays a significant role on the rheology and can almost suppress the shear-thinning. For concentrated suspensions a non-monotonic dependence of the normal stress differences on the membrane inextensibility is observed, reflecting a similar behaviour in the particle shape. The effective suspension viscosity, instead, grows and eventually saturates, for very large inextensibilities, approaching the solid particle limit. In essence, our results reveal that strain-hardening capsules share rheological features with both soft and solid particles depending on the ratio of the area dilatation to shear elastic modulus. Furthermore, the suspension viscosity exhibits a universal behaviour for the parameter space defined by the capillary number and the membrane inextensibility, when introducing the particle geometrical changes at the steady-state in the definition of the volume fraction.

The ordering of particles in the drying process of a colloidal suspension is crucial in determining the properties of the resulting film. For example, microscopic inhomogeneities can lead to the formation of cracks and defects that can deteriorate the quality of the film considerably. This type of problem is inherently multiscale and here we study it numerically, using our recently developed method for the simulation of soft polymeric capsules in multicomponent fluids. We focus on the effect of the particle softness on the film microstructure during the drying phase and how it relates to the formation of defects. We quantify the order of the particles by measuring both the Voronoi entropy and the isotropic order parameter. Surprisingly, both observables exhibit a non-monotonic behaviour when the softness of the particles is increased. We further investigate the correlation between the interparticle interaction and the change in the microstructure during the evaporation phase. We observe that the rigid particles form chain-like structures that tend to scatter into small clusters when the particle softness is increased. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

When a suspension dries, the suspending fluid evaporates, leaving behind a dry film composed of the suspended particles. During the final stages of drying, the height of the fluid film on the substrate drops below the particle size, inducing local interface deformations that lead to strong capillary interactions among the particles. Although capillary interactions between rigid particles are well studied, much is still to be understood about the behaviour of soft particles and the role of their softness during the final stages of film drying. Here, we use our recently-introduced numerical method that couples a fluid described using the lattice Boltzmann approach to a finite element description of deformable objects to investigate the drying process of a film with suspended soft particles. Our measured menisci deformations and lateral capillary forces, which agree well with previous theoretical and experimental works in case of rigid particles, show that the deformations become smaller with increasing particle softness, resulting in weaker lateral interaction forces. At large interparticle distances, the force approaches that of rigid particles. Finally, we investigate the time dependent formation of particle clusters at the late stages of the film drying.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

Complex fluids are common in our daily life and play an important role in many industrial applications. The understanding of the dynamical properties of these fluids and interfacial effects is still lacking. Computer simulations pose an attractive way to gain insight into the underlying physics. In this report we restrict ourselves to two examples of complex fluids and their simulation by means of numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem. First, we study Janus particles at a fluid-fluid interface using the Shan-Chen pseudopotential approach for multicomponent fluids in combination with a discrete element algorithm. Second, we study the dense suspension of deformable capsules in a Kolmogorov flow by combining the lattice Boltzmann method with the immersed boundary method.

Widely regarded as an interesting model system for studying flow properties of blood, vesicles are closed membranes of phospholipids that mimic the cytoplasmic membranes of red blood cells. In this study we analyze the rheology of a suspension of vesicles in a confined geometry: the suspension, bound by two planar rigid walls on each side, is subject to a shear flow. Flow properties are then analyzed as a function of shear rate γ[over ̇], the concentration of the suspension ϕ, and the viscosity contrast λ=η_{in}/η_{out}, where η_{in} and η_{out} are the fluid viscosities of the inner and outer fluids, respectively. We find that the apparent (or effective viscosity) of the suspension exhibits both shear thinning (decreasing viscosity with shear rate) or shear thickening (increasing viscosity with shear rate) in the same concentration range. The shear thinning or thickening behaviors appear as subtle phenomena, dependant on viscosity contrast λ. We provide physical arguments on the origins of these behaviors.

Plasma proteins such as fibrinogen induce the aggregation of red blood cells (RBC) into rouleaux, which are responsible for the pronounced shear thinning behavior of blood, control the erythrocyte sedimentation rate (ESR) - a common hematological test - and are involved in many situations of physiological relevance such as structuration of blood in the microcirculation or clot formation in pathological situations. Confocal microscopy is used to characterize the shape of RBCs within rouleaux at equilibrium as a function of macromolecular concentration, revealing the diversity of contact zone morphology. Three different configurations that have only been partly predicted before are identified, namely parachute, male-female and sigmoid shapes, and quantitatively recovered by numerical simulations. A detailed experimental and theoretical analysis of clusters of two cells shows that the deformation increases nonlinearly with the interaction energy. Models indicate a forward bifurcation in which the contacting membrane undergoes a buckling instability from a flat to a deformed contact zone at a critical value of the interaction energy. These results are not only relevant for the understanding of the morphology and stability of RBC aggregates, but also for a whole class of interacting soft deformable objects such as vesicles, capsules or cells in tissues.

The mechanism of hydrodynamics-induced pairing of soft particles, namely closed bilayer membranes (vesicles, a model system for red blood cells) and drops, is studied numerically with a special attention paid to the role of the confinement (the particles are within two rigid walls). This study unveils the complexity of the pairing mechanism due to hydrodynamic interactions. We find both for vesicles and for drops that two particles attract each other and form a stable pair at weak confinement if their initial separation is below a certain value. If the initial separation is beyond that distance, the particles repel each other and adopt a longer stable interdistance. This means that for the same confinement we have (at least) two stable branches. To which branch a pair of particles relaxes with time depends only on the initial configuration. An unstable branch is found between these two stable branches. At a critical confinement the stable branch corresponding to the shortest interdistance merges with the unstable branch in the form of a saddle-node bifurcation. At this critical confinement we have a finite jump from a solution corresponding to the continuation of the unbounded case to a solution which is induced by the presence of walls. The results are summarized in a phase diagram, which proves to be of a complex nature. The fact that both vesicles and drops have the same qualitative phase diagram points to the existence of a universal behavior, highlighting the fact that with regard to pairing the details of mechanical properties of the deformable particles are unimportant. This offers an interesting perspective for simple analytical modeling.