Many suspensions contain particles with complex shapes that are affected not only by hydrodynamics but also by thermal fluctuations, internal activity, kinematic constraints, and other long-range nonhydrodynamic interactions. Modeling these systems represents a significant numerical challenge due to the interplay between different effects and the need to accurately capture multiscale phenomena. In this article we review recent developments to model large suspensions of particles of arbitrary shapes and multiple couplings with controllable accuracy within the rigid multiblob framework. We discuss the governing equations, highlight key numerical developments, and illustrate applications ranging from microswimmers to complex colloidal suspensions. This review illustrates the effectiveness and versatility of the rigid multiblob method in tackling a wide range of physical problems in fluid mechanics, soft matter physics, biophysics, materials, and colloidal science.

The interaction of microswimmers with solid surfaces in heterogeneous viscous environments is prevalent in various natural and engineering settings, which motivates efforts to unravel the underlying hydrodynamics. In this work, we semi-analytically investigate the influence of an imposed spatially linearly varying viscosity field on near-wall motion of a model microswimmer (squirmer). We explore its associated phase portraits and swimming trajectories for different swimming gaits and compare them with their constant-viscosity analogs. The observations are validated with stability analysis and finite-element-based numerical simulations. We find that even a slight transverse (wall-perpendicular) viscosity gradient disrupts the typical leading-order wall-escaping behavior of neutral squirmers, resulting in its near-wall periodic oscillations regardless of the initial conditions. Similarly, the gradient also modifies behavior of obliquely oriented puller and pusher squirmers (not initialized perpendicular to the wall) from their usual constant-viscosity patterns, leading to its near-wall stabilization with damped temporal oscillations (orientation towards wall). These swimming trends persist across all viscosity-gradient strengths and squirmer parameters tested. In longitudinal (wall-parallel) gradient, although squirmers predominantly exhibit viscophobic motility; we show that depending on initial conditions, pullers and pushers can also display viscophilic tendencies. Moreover, while transverse gradient preserves the puller-pusher duality, in longitudinal gradient it breaks. To elucidate underlying mechanisms behind these observations, we decompose the problem into its corresponding drag and thrust counterparts and observe that apart from leading-order effects and bulk viscotactic responses, the gradient-induced hydrodynamic couplings in drag components play a significant role in modifying these near-wall trajectories. We further extend these findings to arbitrarily oriented viscosity gradients. The results reveal that neutral squirmers either escape wall or settle near it, depending on the relative strength of the gradient's longitudinal and transverse components. For pullers and pushers, the phase portraits remain qualitatively similar; however, a critical gradient direction induces Hopf bifurcations and stable limit cycles, with the onset increasing with swimmer strength. This indicates that strong pullers and pushers require a more transverse-aligned gradient to maintain stable near-wall swimming. Overall, this study demonstrates the substantial role of even simplistic ambient viscosity profile on near-wall squirmer motility, which provides valuable insights for understanding and controlling microswimmer motion in heterogeneous biological and microfluidic systems.

Tidal stream turbines were widely deployed at tidal energy sites with high turbulence levels. The harsh environment can significantly affect the wake dynamics, which in turn affects the overall efficiency of tidal turbine arrays/farms. Current studies have demonstrated a faster wake recovery and increased fatigue loads perceived by rotors prompted by incoming turbulence. However, the wake dynamics and recovery mechanism in turbulence were not fully understood. This paper presents a detailed analysis of the near-wake characteristics of a three-bladed, horizontal-axis tidal turbine. The results revealed a strong correlation between the wake recovery process and the tip vortex instability. Specifically, the onset of the instability was greatly accelerated by incoming turbulence, speeding up the wake expansion, shear layer development, and production of turbulence kinetic energy. The momentum recovery process was further quantified using the streamwise momentum equation, which manifests the important role of turbulence transport and vertical advection in the near wake region. The entire measurements and analysis provided a comprehensive insight into the wake recovery process of axial-flow hydrokinetic turbines, especially in turbulent environments.

Understanding collective evaporation of micron-sized breath droplets can enhance modeling of clouds and inform strategies to limit virus transmission. In this work, we analyze thousands of micron-sized droplets within human and pure water breath figures, identifying two regimes. First, during coarsening, whilst the entire array is evaporating, larger droplets grow at the expense of smaller ones, driven by differences in equilibrium vapor concentration as low as 0.02%, arising from varying interfacial curvature. In this regime, the temporal distribution of droplet radii behaves according to classic Ostwald ripening theory, a mechanism which is usually considered only for submicron droplets. We then use a mean field model to connect droplet evaporation theory with Ostwald ripening, and predict individual droplet dynamics, showing how the accuracy depends on droplet coverage fraction. Finally, we show how the Coarsening regime is terminated by an edge regime, in which all remaining droplets evaporate rapidly.

Accurate reconstruction of directional wave spectra is essential for a wide range of oceanographic and engineering applications. Conventional wave data processing methods rely on potential theory, assuming irrotational flow and can account only for vertically uniform currents. These assumptions neglect the effects of ambient vertically shearing currents, which are often present in the ocean. This may lead to inaccurate wave parameter estimations, such as wave heights, periods and direction. This study presents a rotational data processing methodology incorporating the influence of shearing currents by solving the Rayleigh boundary value problem and deriving frequency- and direction-dependent numerical transfer functions. The method was validated through controlled numerical simulations and applied to in situ dataset obtained by an acoustic Doppler current profiler. Simulation results show that the rotational approach substantially improves the accuracy of directional wave spectrum estimations, compared to potential theory methods which were found to overestimate wave height up to 80% and to introduce directional errors exceeding ${10}^{\circ }$, especially when using pressure sensors near the seabed. The study highlights the sensitivity of wave estimates to current shear gradients and underscores the need for robust numerical approaches when interpreting field measurements. These findings have direct implications for coastal engineering, where small directional errors can critically impact sediment transport modeling and infrastructure design.

Many lipid-membrane-mediated transport processes—such as mechanically gated channel activation and solute transport—involve structural and dynamical features on membrane thickness length scales. Most existing membrane models, however, tend to adopt (quasi-)two-dimensional descriptions that neglect thickness-dependent phenomena relevant to internal membrane mechanics and thus do not fully account for the complex coupling of lipid membranes with their surrounding fluid media. Therefore, explicitly incorporating membrane thickness effects in lipid-membrane models enables a more accurate description of the influence of membrane-fluid coupling on transport phenomena in the vicinity of the bilayer surfaces. Here, we present a continuum model for membrane fluctuations that accounts for finite membrane thickness and resolves hydrodynamic interactions between the bilayer and its surrounding fluid. By applying linear response analysis, we observe that membrane-thickness-mediated effects, such as bending-induced lipid reorientations, can generate shear flows close to the membrane surface that slow down the relaxation of nanometer-scale shape fluctuations. Additionally, we reveal the emergence of pressure inversion and flow reversal near the membrane interfaces, accompanied by localized stagnation points. Among these, extensional stagnation points give rise to a novel mode of bulk dissipation originating from bending-induced compression and expansion of the membrane surfaces and their coupling to shear stresses in the fluid. Our findings identify membrane thickness as a key factor in nanoscale hydrodynamics and suggest that its effects may be detectable in fluctuation spectra and can be relevant to interfacial processes such as solute permeability and contact with solid boundaries or other membranes.

We study the dynamics of collisions between a pair of uncharged conducting droplets under the influence of a uniaxial compressional flow and an external electric field. The near-field asymptotic expression for the electric-field-induced attractive force demonstrates that surface-to-surface contact in finite time is facilitated by overcoming lubrication resistance. We demonstrate the significant role of the external electric field on the relative trajectories of two droplets in a compressional flow and provide estimates of the correlation between collision efficiency and the forces induced by the electric field. For droplet collisions in clouds, continuum lubrication approximations become inadequate to capture collision dynamics, and thus we incorporate noncontinuum lubrication interactions into our analysis to address this complexity. Our findings reveal the dependence of collision efficiency on the strength of the electric field, geometry of the two interacting droplets, noncontinuum effects, and van der Waals forces. We show that the electric fields typical of strongly electrified clouds substantially enhance the efficiency of droplet collisions. In contrast, the electric fields typical of fair-weather conditions have a negligible influence on the dynamics of droplet collisions.

We conducted an experiment on water exit with an air jet, using a cylinder with an ogival nose moving at a preset velocity. The air jet opens the water and forms a cavity that allows the cylinder to move within the air jet-induced cavity. We investigated the evolutionary patterns, morphological, and geometric characteristics of the cavity formed by the air jet, varying exit velocities, nozzle diameters, and air injection rates. For underwater cavity formation, three distinct cavity flow patterns were observed across all of our experiments: Bubbly flow (BF), unstable cavity (UC), and jet cavity (JC). Moreover, UC can be further divided into unstable partial cavity (UPC) and unstable continuous cavity (UCC), depending on the relative geometry between the cavity and the cylinder. During free surface penetration in the JC regime, two distinct cavity flow patterns arising from the interaction between the cavities and the cylinder have been identified: attached ventilated cavity (AVC) and collapsed ventilated cavity (CVC), corresponding to different momentum ratio ranges. The AVC is proposed as a potential solution for achieving a stable water exit without cavity collapse. Furthermore, the geometry of the ventilated cavity in the JC regime follows a power-law relationship with the momentum ratio.

A computational study using a three-dimensional fully coupled fluid-structure interaction model is presented on the flow of deformable capsules in a compliant, inflating tube at small but finite inertia. Flow of single capsules and single-file flow of multiple capsules are considered, and the effects of deformability, size, and constitutive models on the capsule-vessel interaction are studied. Results in terms of transient capsule deformation, velocity, and tube flow rate are presented and compared against those in a rigid tube under similar transient flow conditions of the inflating tube. Vessel inflation is shown to significantly affect the deformation of capsules with large transient variations in their shape that are absent in the rigid tube. The rapidly increasing flow in the inflating tube causes an axial contraction of the capsules that increases with increasing tube deformability. The instantaneous capsule velocity also strongly varies as it traverses the inflating tube, with the peak velocity higher than that seen in the rigid tube. The mean capsule velocity is maximal at an intermediate tube deformability, unlike in the rigid tube where it increases with increasing flow rate. A notable interaction between the capsules and inflating vessel is observed in the form of oscillations in the flow rate, which are absent in the rigid tube. For the single-file flow of multiple capsules, the tube inflation causes an increased capsule density near the vessel inlet. The axial contraction is also much greater in this case than that of a single capsule.

Fluid-fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. The hydrodynamic instability of fluid interfaces has long centered on the pressure gradient-driven long-wavelength Rayleigh-Taylor instability and the resonance-induced short-wavelength Faraday instability. However, neither instability alone can explain the dynamics when both mechanisms are present. We identify a previously unseen multi-modal instability emerging from their coexistence. When the denser fluid is polydimethylsiloxane, the mixed region at a high density contrast (Atwood number = 0.9) spans a vibration amplitude range approximately twice the gravitational acceleration. Using Floquet stability analysis, we show how vibrations govern transitions between the RT and Faraday instabilities, leading to contention between these instabilities rather than resonant enhancement. The initial transient growth is represented by the exponential modal growth of the most unstable Floquet exponent, along with its accompanying periodic behavior. Direct numerical simulations validate these findings and track interface breakup into the multiscale and nonlinear regimes. Specifically, we show that growing RT modes nonlinearly suppresses Faraday responses even when the initial growth rate of the Faraday instability is 3.63 times that of RT, so a bidirectional competition hinders their sustained coexistence.

The flow of a highly viscous film lining the interior of a tube with time-dependent radius is studied using a long-wave asymptotic model. The base flow, arising due to pressure-driven core flow and/or gravity, is studied first. The impact of tube expansion and contraction in time on net transport is explored mathematically through prescribing the tube radius and air volume flow rate as a function of time. First-order model corrections—which incorporate the growth (and its saturation) of long-wave disturbances arising due to the Plateau-Rayleigh instability—are then added to the model. Linear stability analysis of this periodically forced model show that tube contractions and expansions enhance instability growth compared to a rigid tube. Simulations of the full nonlinear model equation highlight the role of free-surface waves in enhancing transport. Parameter values used here are motivated by the human lung and airway system.

A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived by volume averaging. The self-similar solution proposed by Tsiberkin [Transp. Porous Media 121, 109 (2018)] for streamwise-growing permeability is extended to include compressibility, heat conduction, and a nonlinear drag. The velocity profile shows an inflection point at the free fluid-porous interfacial layer, below which it decreases to zero. A marked reduction of the adiabatic recovery temperature of the fluid and the velocity gradient at the interface is observed for high porosity, large grains, and relatively high Mach numbers. The temperature imposed at the bottom of the porous substrate has a negligible influence on the shear stresses.

The present study numerically investigates the two-dimensional mixed convective flow of air past a square cylinder placed at an angle of incidence $\alpha ={45}^{\circ }$ to the free stream. We perform direct numerical simulations for a Reynolds number of 100, a range of Richardson numbers (Ri) between 0.0 and 1.0, and a Prandtl number of 0.7. The critical Richardson number at which the near field becomes a steady flow from an unsteady one lies between $0.65$ and $0.7$, along with a simultaneous emergence of the far field unsteadiness. There is no range of Ri for which the entire flow field is seen to be steady. At a relatively moderate Ri, the flow field reveals the presence of vorticity inversion through the momentum addition in the downstream region. We discuss the dual wake-plume nature of the flow behind the cylinder. The wake exhibits characteristics similar to those of a plume, revealing a self-similar behavior in the far field at increased buoyancy. We explore the cause of the far field unsteadiness and discuss the mechanism of the observed flow physics using instantaneous and time-averaged flow fields. The important flow quantities, such as force coefficients, vortex shedding frequency, and Nusselt number, are discussed at various Richardson numbers.

Mixing and spreading of fluids during viscous fingering in the presence of a continuous injection source boundary is an open question in energy and environment applications such as ${\mathrm{CO}}_2$ injection into oil reservoirs and groundwater remediation. Direct numerical simulation (DNS) of viscous fingering is computationally prohibitive at high viscosity contrasts (e.g., a displaced-to-displacing fluid viscosity ratio greater than 50) due to tip-splitting, merging, and channeling mechanisms that rapidly generate and eliminate large gradients in the concentration field. Recent advances in deep learning offer promise in overcoming the limitations of DNS. However, this promise has not been realized due to the formidable challenge posed by the multiscale dynamics of viscous fingering. Here, we present a novel deep learning framework that combines spatial embedding to extract the fingering mechanisms at multiple scales with Koopman-based temporal dynamics to learn the evolution of fingering-driven mixing. We demonstrate the framework using two models: a baseline autoencoder coupled with a transformer model (BAE-GPT2), which was recently proposed for the turbulent flow problem, and a new densely connected convolutional network autoencoder coupled with a long-short-term memory model (DAE-LSTM). Our DAE-LSTM model outperforms the BAE-GPT2 model in predicting concentration variance and mean scalar dissipation rate in the domain and the concentration breakthrough profile at the outlet. We derive the evolution equation for the degree of mixing, defined in terms of the concentration variance, in the context of continuous injection of the less viscous fluid—a problem that has remained unsolved until now due to challenges related to source/sink boundaries. Finally, we demonstrate that the DAE-LSTM model can forecast local-scale features, such as the number and size of fingers, as well as global-scale metrics, such as the degree and rate of mixing, for fluid-fluid displacement processes with high viscosity contrasts—a goal that has eluded many DNS methods.

Gravity currents are horizontal flows that occur due to density differences between two fluids. In porous media, gravity currents have been extensively studied, typically focusing on two-dimensional rectilinear geometry and assuming a sharp interface between the ambient fluid and the gravity current. In this study, we examine gravity currents in an axisymmetric geometry and develop a theoretical model to account for the mixing effects caused by the dispersive entrainment of ambient fluid into the gravity current. Our analysis reveals that with continuous injection flux, the buoyancy and radius of the gravity current evolve in a self-similar manner, with the radius increasing over time as $t^{1/2}$. However, unlike sharp-interface gravity currents, the height and concentration of the dispersive gravity currents do not display self-similar behavior. Due to the dispersive entrainment, the gravity current mixes with the ambient fluid, resulting in a monotonic dilution. We find that this dilution significantly thickens the current over time and leads to a blunt nose, which contradicts the assumption of a long and thin current at later times. Additionally, we provide estimates of the total volume of entrained fluid over time and the associated mean concentration of the gravity current. We also present results from numerical simulations conducted in comsol to validate some of our assumptions and findings from the theoretical model.

Inspired by bouncing drop experiments that revealed how macroscopic systems can exhibit wave-particle properties previously thought to be exclusive to quantum systems, we introduce here a wave-particle system based on internal gravity waves propagating in density-stratified fluids. Recent experiments on particles (called ludions) oscillating in such a fluid medium suggest that wave-particle interactions can induce symmetry breaking, leading to spontaneous self-propulsion of the particle in the horizontal plane. Here, we propose a minimal hydrodynamic theory showing that this instability can be explained by a Doppler force emerging from interactions between the ludion and its own wave field. We validate our theoretical predictions using direct numerical simulations, which confirm that the growth of the instability is determined by the particle oscillation amplitude. In wall-bounded domains, reflections of the internal waves create a Casimir-like potential that rapidly develops and constrains the particle motion. Despite the presence of the Doppler force, this potential governs the ludion long-term dynamics, leading to capture in fixed points or chaotic attractors near the potential wells. We show that the essential features of this behavior are well captured by a minimal dynamical model. Our findings establish the ludion as a hydrodynamic pilot-wave system, offering a platform for exploring macroscopic wave-particle behaviors, particularly in three-dimensional configurations.

The mechanism underlying the stability of bulk nanobubbles has been a long-standing and contentious topic, with recent studies emphasizing the role of external pressure in nanobubble dynamics. However, there remains a lack of experimental evidence to unravel the complexities of bulk nanobubble behavior under elevated external pressures. In this study, we investigated the effect of external pressure on the stability of bulk hydrogen nanobubbles in both water and methanol liquid media using a nanobubble experimental system, with the external pressure up to 0.9 MPa. Our results show that nanobubble concentration increases linearly with pressure, and the nanobubbles exhibit longer lifetimes under high-pressure storage conditions, indicating enhanced stability. Notably, the effect of external pressure on surface charge is negligible, ruling out the hypothesis that surface charge dominates nanobubble stability. All-atom molecular dynamics (MD) simulations were conducted to elucidate the nanobubble evolution under varying external pressures. It demonstrates that elevated external pressure does not diminish the internal-external pressure differential. Increased supersaturation, reduced gas molecular diffusion, and reinforced hydrogen bond network were identified as primary factors for the stability enhancement at high external pressures. This study provides insights and experimental findings regarding the impact of external pressure on the dynamic behaviors of bulk nanobubbles.

A capillary jet plunging into a quasi-2D slab of monodisperse foam of the same solution is studied experimentally. We show that the jet can have a drastic impact on the foam. At small speeds it inflates the channels separating the bubbles. At intermediate speeds, impact with channels creates very small bubbles. At higher speeds the jet action reverses: it now thins the liquid film up to the point of rupture, which can induce bubble coalescence. We study the mechanisms behind these processes using an elementary foam made of three soap films in contact through a Plateau border. We obtain scaling laws ruling the jet-foam interaction which transfer quantitatively from the elementary foam to the 2D foam.

Opposition control (OC), which suppresses drag-inducing motions near the wall by local blowing and suction, has been shown to be effective in reducing drag in wall-bounded turbulence at low Reynolds numbers ($\text{Re}$). However, its performance at high $\text{Re}$ remains an open question. Here we investigate OC at high $\text{Re}$ using direct numerical simulations of turbulent channel flow at friction Reynolds numbers (${\text{Re}}_{\tau }$) ranging from 200 to 2000, delineating its limitations and identifying the physical mechanisms responsible. The principal finding is that drag reduction ($\mathcal{DR}$) decreases with increasing ${\text{Re}}_{\tau }$, consistent with similar low $\text{Re}$ results reported in the literature. For the detection plane at $y_d^{+}=15, \mathcal{DR}$ decreases from $22.3\%$ at ${\text{Re}}_{\tau }=200$ to $18.1\%$ at ${\text{Re}}_{\tau }=2000$. In addition, the optimal $y_d^{+}$ moves slightly inward as ${\text{Re}}_{\tau }$ increases, in line with the inward shift of the near-wall peak of the streamwise vorticity fluctuation. Using previously proposed models, we predict that an approximately $15\%$ drag reduction can be obtained at high Reynolds numbers, say, ${\text{Re}}_{\tau }\ge {10}^4$. Interestingly, the root-mean-square wall-normal velocity fluctuation at the wall ($v_{\mathrm{rms},w}^{\prime +}$) to achieve the maximum $\mathcal{DR}$ is around 0.25 for all ${\text{Re}}_{\tau }$ cases. Further statistical analysis reveals that the decrease in $\mathcal{DR}$ at high ${\text{Re}}_{\tau }$ is due to a reduced ability to suppress large-scale turbulence near the wall, whose contribution continuously increases due to the enhanced modulation and penetration effect of the outer large-scale and very large-scale motions. Coherent structure analysis confirms the inability of OC to control outer large-scale structures and shows the strengthening of near-wall streamwise vortices with increasing ${\text{Re}}_{\tau }$. These findings suggest that future efforts should explore advanced approaches such as hybrid control strategies incorporating phase-lag formulations or complementary actuation targeting outer-layer motions, to extend the effectiveness of OC at high $\text{Re}$.

In fluid dynamics experiments, flake-based flow visualization captures flow structures through light reflection from suspended flat tracers. However, the correspondence between visualization patterns and underlying flow physics remains unclear when the flows are unknown a priori. Inspired by the introduction of spin variable in quantum mechanics, we introduced the orientation variable into fluid dynamics and adapted the time-dependent Fokker-Planck framework to reveal the connection between experimental flake visualization patterns and virtual orientation probability fields from an Eulerian perspective. As a first example in which a dimensionless parameter distinguishes the dependency on the initial condition, we illustrated an analytical solution of the orientation probability in a rotating wave flow. With the inclusion of the diffusion term in the governing equation, the probability converges, beyond simple isotropization, to the flow-determined state with spatially varying anisotropy, eliminating dependency on initial conditions. As a second example, we solved the orientation probability field in the axisymmetric state in spherical Couette flow, demonstrating independence from initial conditions consistent with experimental reproducibility. An asymmetric pattern in experimental images, unexplained by the dynamics of the tracer orientation, was successfully recovered from the unique solution of the proposed equation.