In this study, we investigate the sedimentation of spheroidal particles in an initially quiescent fluid by means of particle-resolved direct numerical simulations. Settling particles with three different shapes – oblate spheroid, sphere and prolate spheroid – but fixed Galileo number $Ga=80$ and density ratio $\gamma =2$ at volume fraction $\phi =1\%$ are considered. Oblate and prolate particles are found to form column-like clusters as a consequence of the wake-induced hydrodynamic interactions in the suspension. This effect, together with the change of particle orientation, enhances the mean settling velocity of the dispersed phase. In contrast, spherical particles do not exhibit clustering, and settle with hindered velocity in the suspension. Furthermore, we focus on the pseudo-turbulence induced by the settling particles. We report a non-Gaussian distribution of the fluid velocity and a robust $-3$ power law of the energy spectra. By scrutinizing the scale-by-scale budget, we find that the anisotropy of the particle-induced pseudo-turbulence is manifested not only by the uneven allocation of turbulence kinetic energy among the different velocity components, but also by the anisotropic distribution of energy in spectral space. The fluid–particle interactions inject energy into the vertical velocity component, thus sustaining the turbulence, while pressure redistributes the kinetic energy among the different velocity components. The clustering of oblate/prolate particles significantly increases the energy input at large scales, forcing elongated flow structures. Moreover, the redistribution and nonlinear transfer of the energy are also intensified in the presence of particle clustering, which reduces the anisotropy of the particle-induced pseudo-turbulence.

This study employs volume-of-fluid-based computational fluid dynamics modelling to investigate the coupled effects of surface wettability and inflow vapour velocity on R134a ($p/p_{cri}=0.25$) condensation heat transfer in horizontal tubes. The results demonstrate that both the condensation heat transfer coefficient (HTC) and Nusselt number consistently increase with rising vapour velocity, indicating enhanced convective heat transfer at higher flow rates. Within this overall trend, the influence of surface wettability varies significantly across different velocity regimes. At moderate inlet velocities (10 m s−1), surface wettability demonstrates maximum impact, with the HTC enhancement exceeding 19.1% between peak and minimum values, optimising at contact angles of 120$^\circ$–140$^\circ$. As velocity increases to 20 m s−1, while surface wettability effects persist with $\gt$11.7 % enhancement, convective heat transfer becomes increasingly dominant, showing $\gt$38.8 % improvement in the maximum HTC compared with the 10 m s−1 case. At higher velocities (40 m s−1), the influence of surface wettability diminishes substantially, with the HTC variation reducing to $\gt$1.04 %. At extreme velocities (80 m s−1), surface tension effects become negligible compared with vapour shear forces, resulting in minimal (0.53 %) variation across different contact angles. The equivalent Reynolds number peaks at 20 m s−1, indicating optimal conditions for condensate formation and flow characteristics. These findings provide crucial insights for condensation system design, suggesting that while increasing velocity generally enhances heat transfer performance, surface wettability modifications are most effective at moderate velocities, while high-velocity applications should prioritise flow dynamics and system geometry optimisation.

While we now have a relatively good understanding of low-Reynolds-number hydrodynamics, and elegant techniques to dissect it, one cannot truly say the same for yield-stress fluids. For these materials, the nonlinearity associated with the yield stress complicates analysis and prevents the use of many of the techniques used for slow viscous flow. Simultaneously, the presence of a yield stress introduces a range of new features into the problem beyond those of traditional Stokes flow. Accordingly, in this essay, we discuss the impact of a yield stress in the relatively simple setting of two-dimensional, steady, inertialess flow. The main goals are to establish intuition for the dramatically different features that can be introduced to the flow by the yield stress, and to outline the various tools available to the modeller to construct and interpret these flows.

Direct numerical simulations are performed for turbulent forced convection in a half-channel flow with a wall oscillating either as a spanwise plane oscillation or to generate a streamwise travelling wave. The friction Reynolds number is fixed at $Re_{\tau _0} = 590$, but the Prandtl number $Pr$ is varied from 0.71 to 20. For $Pr\gt 1$, the heat transfer is reduced by more than the drag, 40 % compared with 30 % at $Pr=7.5$. This outcome is related to the different responses of the velocity and thermal fields to the Stokes layer. It is shown that the Stokes layer near the wall attenuates the large-scale energy of the turbulent heat flux and the turbulent shear stress, but amplifies their small-scale energy. At higher Prandtl numbers, the thinning of the conductive sublayer means that the energetic scales of the turbulent heat flux move closer to the wall, where they are exposed to a stronger Stokes layer production, increasing the contribution of the small-scale energy amplification. A predictive model is derived for the Reynolds and Prandtl number dependence of the heat-transfer reduction based on the scaling of the thermal statistics. The model agrees well with the computations for Prandtl numbers up to 20.

In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in under- and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023) J. Fluid Mech. 975, R3, by taking into account modified gas fluxes across the bubble interface, that result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nano-bubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a) Phys. Rev. E 91 (3), 031003(R), by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nano-bubbles and for micro-bubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

Turbulent emulsions are ubiquitous in chemical engineering, food processing, pharmaceuticals and other fields. However, our experimental understanding of this area remains limited due to the multiscale nature of turbulent flow and the presence of extensive interfaces, which pose significant challenges to optical measurements. In this study, we address these challenges by precisely matching the refractive indices of the continuous and dispersed phases, enabling us to measure local velocity information at high volume fractions. The emulsion is generated in a turbulent Taylor–Couette flow, with velocity measured at two radial locations: near the inner cylinder (boundary layer) and in the middle gap (bulk region). Near the inner cylinder, the presence of droplets suppresses the emission of angular velocity plumes, which reduces the mean azimuthal velocity and its root mean squared fluctuation. The former effect leads to a higher angular velocity gradient in the boundary layer, resulting in greater global drag on the system. In the bulk region, although droplets suppress turbulence fluctuations, they enhance the cross-correlation between azimuthal and radial velocities, leaving the angular velocity flux contributed by the turbulent flow nearly unchanged. In both locations, droplets suppress turbulence at scales larger than the average droplet diameter and increase the intermittency of velocity increments. However, the effects of the droplets are more pronounced near the inner cylinder than in the bulk, likely because droplets fragment in the boundary layer but are less prone to break up in the bulk. Our study provides experimental insights into how dispersed droplets modulate global drag, coherent structures and the multiscale characteristics of turbulent flow.

Combined theoretical and quantitative experimental study of resonant internal standing waves in a pycnocline between two miscible liquids in a narrow rectangular basin is presented. The waves are excited by a cylinder that harmonically oscillates in the vertical direction. A linear theoretical model describing the internal wave structure that accounts for pycnocline thickness, the finite wavemaker size and dissipation is developed. Separate series of measurements were performed using shadowgraphy and time-resolved particle image velocimetry. Accurate density profile measurements were carried out to monitor the variation of the pycnocline parameters in the course of the experiments; these measurements were used as the input parameters for the model simulations. The detected broadening of the pycnocline is attributed mainly to the presence of the waves and leads to the variation of the wave structure. The complex spatio-temporal structure of the observed internal wavefield was elucidated by carrying band-pass filtering in the temporal domain. The experiments demonstrate the coexistence of multiple spatial modes at the forcing frequency as well as the presence of the internal wave system at the second harmonic of the forcing frequency. The results of the theoretical model are in good agreement with the experiments.

A spherical vesicle is made up of a liquid core bounded by a semi-permeable membrane that is impermeable to solute molecules. When placed in an externally imposed gradient of solute concentration, the osmotic pressure jump across the membrane results in an inward trans-membrane solvent flux at the solute-depleted side of the vesicle, and and outward flux in its solute-enriched side. As a result, a freely suspended vesicle drifts down the concentration gradient, a phenomenon known as osmophoresis. An experimental study of lipid vesicles observed drift velocities that are more than three orders of magnitude larger than the linearised non-equilibrium prediction (Nardi et al., Phys. Rev. Lett., vol. 82, 1999, pp. 5168–5171). Inspired by this study, we analyse osmophoresis of a vesicle in close proximity to an impermeable wall, where the vesicle–wall separation $a\delta$ is small compared with the vesicle radius $a$. Due to intensification of the solute concentration gradient in the narrow gap between the membrane and the wall, the ‘osmophoretic’ force and torque on a stationary vesicle scale as an irrational power, $1/\sqrt {2}-1\ (\approx -0.29289\ldots )$, of $\delta$. Both the rectilinear velocity $\mathcal V$ and the angular velocity $\unicode {x1D6FA}$ of a freely suspended vesicle scale as the ratio of that power to $\ln \delta$. In contrast to the classical problem of sedimentation parallel to a wall, where the ratio $a\unicode {x1D6FA}/\mathcal V$ approaches $1/4$ as $\delta \to 0$, here the ratio approaches unity, as though the vesicle performs pure rigid-body rolling without slippage. Our approximations are in excellent agreement with hitherto unexplained numerical computations in the literature.

The attached-eddy model (AEM) predicts that the mean streamwise velocity and streamwise velocity variance profiles follow a logarithmic shape, while the vertical velocity variance remains invariant with height in the overlap region of high Reynolds number wall-bounded turbulent flows. Moreover, the AEM coefficients are presumed to attain asymptotically constant values at very high Reynolds numbers. Here, the AEM predictions are examined using sonic anemometer measurements in the near-neutral atmospheric surface layer, with a focus on the logarithmic behaviour of the streamwise velocity variance. Utilizing an extensive 210-day dataset collected from a 62 m meteorological tower located in the Eastern Snake River Plain, Idaho, USA, the inertial sublayer is first identified by analysing the measured momentum flux and mean velocity profiles. The logarithmic behaviour of the streamwise velocity variance and the associated ‘$-1$’ scaling of the streamwise velocity energy spectra are then investigated. The findings indicate that the Townsend–Perry coefficient ($A_1$) is influenced by mild non-stationarity that manifests itself as a Reynolds number dependence. After excluding non-stationary runs, and requiring the bulk Reynolds number defined using the atmospheric boundary layer height to be larger than $4 \times 10^{7}$, the inferred $A_1$ converges to values ranging between 1 and 1.25, consistent with laboratory experiments. Furthermore, nine benchmark cases selected through a restrictive quality control reveal a close relation between the ‘$-1$’ scaling in the streamwise velocity energy spectrum and the logarithmic behaviour of streamwise velocity variance. However, additional data are required to determine whether the plateau value of the pre-multiplied streamwise velocity energy spectrum is identical to $A_1$.

This study presents a novel investigation into the vortex dynamics of flow around a near-wall rectangular cylinder based on direct numerical simulation at $Re=1000$, marking the first in-depth exploration of these phenomena. By varying aspect ratios ($L/D = 5$, $10$, $15$) and gap ratios ($G/D = 0.1$, $0.3$, $0.9$), the study reveals the vortex dynamics influenced by the near-wall effect, considering the incoming laminar boundary layer flow. Both $L/D$ and $G/D$ significantly influence vortex dynamics, leading to behaviours not observed in previous bluff body flows. As $G/D$ increases, the streamwise scale of the upper leading edge (ULE) recirculation grows, delaying flow reattachment. At smaller $G/D$, lower leading edge (LLE) recirculation is suppressed, with upper Kelvin–Helmholtz vortices merging to form the ULE vortex, followed by instability, differing from conventional flow dynamics. Larger $G/D$ promotes the formation of an LLE shear layer. An intriguing finding at $L/D = 5$ and $G/D = 0.1$ is the backward flow of fluid from the downstream region to the upper side of the cylinder. At $G/D = 0.3$, double-trailing-edge vortices emerge for larger $L/D$, with two distinct flow behaviours associated with two interactions between gap flow and wall recirculation. These interactions lead to different multiple flow separations. For $G/D = 0.9$, the secondary vortex (SV) from the plate wall induces the formation of a tertiary vortex from the lower side of the cylinder. Double-SVs are observed at $L/D = 5$. Frequency locking is observed in most cases, but is suppressed at $L/D = 10$ and $G/D = 0.9$, where competing shedding modes lead to two distinct evolutions of the SV.

The transition to chaos in the subcritical regime of counter-rotating Taylor–Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics is found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier–Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs.

Undulatory swimming is among the most common swimming forms found in nature across various length scales. In this study, we analyse the inertial effects of both the fluid and the swimmer on the transient motion of undulatory swimming using Taylor’s waving sheet model. We derive the transient velocity of the sheet for combined longitudinal and transverse waves in the Laplace domain, identifying three contributions to the velocity: the ‘slip’ velocity, fluid convection and a hydrodynamic force contribution. By numerically inverting the Laplace transform, we obtain the time history of the velocity for swimmers with varying swimming parameters and initial configurations. The acceleration performance of two types of swimmers is analysed by considering three dimensionless parameters: the acceleration rate $1/T$, sheet mass $M$, and Reynolds number $Re$, representing the effects of unsteady, convective and swimmer inertia, respectively. Under a relatively strong inertia effect, the start-up time scales as $\sim TM^2\,Re$ and $\sim TM^2$ for longitudinal and transverse waving sheets, respectively. Under weak inertia effects, the start-up time approximately reaches a constant for longitudinal waves, while it scales as $\sim T$ for transverse waves. Additionally, the transverse waving may induce a velocity overshoot, and enhances the burst swimming performance.

In rotating convection, analysis of heat transfer reveals a distinct shift in behaviour as the system transitions from a steep scaling regime near the onset of convection to a shallower scaling at higher Rayleigh numbers ($Ra$), irrespective of whether the top and bottom plates have stress-free, no-slip or no boundaries (homogeneous convection). However, while most research on this transition focuses on no-slip boundary conditions, geophysical and astrophysical flows commonly involve stress-free and homogeneous convection models as well. This study delves into the transition from the rapidly rotating regime to the non-rotating one with both stress-free and homogeneous models, leveraging direct numerical simulations (DNS) and existing literature data. Our findings unveil that for stress-free boundary conditions, the transitional Rayleigh number ($Ra_T$) exhibits a relationship $Ra_T\sim Ek^{-12/7}$, whereas for homogeneous rotating convection, $Ra_T\sim Ek^{-2}\, Pr$, where $Ek$ denotes the Ekman number, and $Pr$ denotes the Prandtl number. Both of these relationships align with the data obtained through DNS.

Head-on collisions between elliptic vortex rings (EVRs) and walls were studied experimentally using planar laser-induced fluorescence visualisations and time-resolved particle image velocimetry. Aspect ratios of $AR=2$ and 4 EVRs at a Reynolds number of $Re=4000$ were used. Collision locations were based on four key axis-switching stages of freely translating EVRs, which would shed light upon how axis-switching behaviour and aspect ratio variations affect the collision outcomes. Results show that non-uniform circumferential induced velocities in both colliding EVRs produce different behaviours along major and minor planes, where vortex-stretching/compression and hence circumferential flows play key roles in the vortex dynamics. Non-uniform formations of secondary/tertiary EVRs also lead to varied entanglements around the primary EVRs. As such, secondary vortex rings form vortex loops that may congregate along the collision axis, depending on the exact collision location. Vortex-core trajectories show the net primary/secondary vortex-core movements result from a balance between EVR diameter expansion due to collision and EVR segment motions associated with the axis-switching stage at the point of collision. Confinement effects are also observed to dominate over aspect ratio effects when the collision occurs closest to the orifice. While increasing the aspect ratio leads to different vortex-stretching/compression behaviour and more varied vortex-core trajectories due to the greater non-uniform induced velocities, they could still be understood by the preceding interpretations. Finally, three-dimensional vortex flows are reconstructed based on the experimental results to further explain the flow mechanisms.

A reactive control strategy is implemented to attenuate the streaks formed on a wing boundary layer due to free-stream turbulence (FST). Numerical simulations are performed on a section of a NACA0008 profile, considering its leading edge, while forced by FST with turbulence intensities of 0.5 % and 2.5 %. The controller is composed of localised sensors and actuators, with the control law consisting of a linear quadratic Gaussian regulator designed on a reduced-order model based only on the impulse responses of the system. Three configurations are evaluated by considering three different numbers of sensors/actuators along the spanwise direction. It is found that all configurations are effective in damping the streaks inside the boundary layer, whose effect is sustained downstream of the objective function location. However, distinct behaviours are observed when comparing the capability of the controllers with delay transition, where the best performance is attained for the case with larger number of sensors/actuators. This is attributed to the effectiveness of the controller in damping the streaks that will later break down, which in this case are associated with relatively short spanwise wavelength. This observation is confirmed by analysing the stability of the flow before the appearance of turbulent spots. Our results suggest that for an effective transition delay, efforts should not only be put into control of streaks with average spanwise wavelength, but also in the short spanwise wavelength associated with breakdown.

We investigate the deformation, dynamics and rheology of a single and a suspension of elastic capsules in inertial shear flow using high-fidelity particle-resolved simulations. For a single capsule in the shear flow, we elucidate the interplay of flow inertia and viscosity ratio, revealing the mechanism behind the stretching of capsule surface during tank-treading motion and the sign changes in normal stress differences with increasing inertia. When examining capsule suspensions, we thoroughly discuss the impact of volume fraction on average deformation, diffusion and rheology. Notably, we observe the formation of bridge structures due to hydrodynamic interactions, which enhance the inhomogeneity of the microstructure and alter the surface stress distribution within the suspension. We identify a critical Reynolds number range that marks the transition of capsule diffusion from non-inertial to inertial regimes. Furthermore, we reveal close connections between the behaviour of individual capsules and dense suspensions, particularly regarding capsule deformation and dynamics. Additionally, we propose multiple new empirical correlations for predicting the deformation factor of a single capsule and the relative viscosity of the suspension. These findings provide valuable insights into the complex behaviour of elastic capsules in inertial flows, informing the design of more accurate and efficient inertial microfluidic systems.