Torque-driven steering of magnetic micro/nanobots in fluids is one of the most promising platforms of controlled propulsion at the small scales, and it has been the focus of modern biomedical applications. The propulsion is a result of rotation–translation coupling and it requires non-trivial (e.g. chiral) geometry of the nanobot and the weak (millitesla) rotating magnetic field. At submicron scale, nanobots are subjected to intrinsic thermal fluctuations that may become comparable to the magnetic driving. We investigate the effect of Brownian fluctuations on the actuation and steering of magnetized nanohelices in a viscous fluid numerically, using Langevin simulations. First, we assume force-free propulsion and study the effect of thermal fluctuations on driven rotation and steering of the nanohelix. We demonstrate that the random Brownian torque dramatically impedes the nanobot’s propulsion via (i) hindering the rate of the forced rotation; (ii) altering its orientation, i.e. increasing the precession angle of the forced rotations. We further demonstrate that even for fairly low thermal noise (rotational Péclet number, $ \textit{Pe} \approx 10$), the angular velocity of the forced rotation drops by $2$–$3$ times, while the precession angle increases two fold as compared with the non-Brownian limit. Both these factors contribute to an approximately $2.5$-fold reduction of the propulsion velocity. Furthermore, when the magnitude of thermal fluctuations is comparable to magnetic driving ($ \textit{Pe} \approx 1$), we find an order-of-magnitude reduction of the propulsion speed. Although inclusion of a stochastic thermal force does not alter the propulsion velocity on average, it considerably increases its variance and further impedes the propeller’s steerability.

Dense arrays of soft hair-like structures protruding from surfaces are ubiquitous in living systems. Fluid flows can easily deform these soft hairs, which in turn impacts the flow properties. At the microscale, flows are often confined, which exacerbates this feedback loop: the hair deformation strongly affects the flow geometry. Here, I investigate experimentally and theoretically pressure-driven flows in laminar channels obstructed by a dense array of elastic fibres or ‘hairs’. I show that the system displays a nonlinear hydraulic resistance that I model by treating the hair bed as a deformable porous medium whose height results from the deflection of individual fibres. This fluid–structure interaction model encompassing flow in porous media, confinement and elasticity is then leveraged to identify the key dimensionless parameter governing the problem: $\hat {f}_0$, a dimensionless drag that combines fluid, solid and geometrical properties. Finally, I demonstrate how these results can be harnessed to design passive flow control elements for microfluidic networks.

The recirculation zone is critical for flame stabilization in combustion processes, yet a quantitative, mechanistic understanding of its inherently complex mixing state remains a challenge. To address this gap, we introduce a novel characteristic parameter, the characteristic mixture fraction ($Z_u$), defined from the observation of localized mixture uniformity within the zone. Using validated large-eddy simulation combined with the flamelet/progress-variable approach, we systematically examine the relationship between $Z_u$ and the momentum flux ratio ($J$). The results reveal that a dual-power-law scaling relationship between $Z_u$ and $J$ is a fundamental characteristic of bluff-body stabilized flows, persisting with and without chemical reactions. This scaling, however, is profoundly modified by combustion. Compared with non-reacting flows, reacting flows exhibit a shift in the transition point between power-law regimes to a higher $J$ and a shallower scaling exponent (e.g. approximately −0.15 for reacting versus −0.5 for non-reacting flows in the jet-envelopment regime). These quantitative distinctions are decisively attributed to thermophysical effects induced by heat release, interpreted through two synergistic mechanisms: at the macroscale, thermal expansion reduces density, weakening the recirculation zone’s momentum resistance; at the microscale, increased viscosity suppresses turbulent mixing efficiency. Thus, a predictive mechanistic framework centred on the parameter $Z_u$ is established, providing not only a robust metric for quantifying complex mixing states but also fundamental insights into how heat release acts on turbulent mixing. Consequently, it offers new perspectives for combustor optimization and understanding of complex mixing–combustion coupling.

The present study experimentally investigates the onset of ventilation of surface-piercing hydrofoils. Under steady-state conditions, the depth-based Froude number $\textit{Fr}$ and the angle of attack $\alpha$ define regions in which distinct flow regimes are either locally or globally stable. To map the boundary between these stability regions, the parameter space $(\alpha , \textit{Fr})$ was systematically surveyed by increasing $\alpha$ until the onset of ventilation while maintaining a constant $\textit{Fr}$. Two simplified model hydrofoils were examined: a semi-ogive with a blunt trailing edge and a modified NACA 0010-34. Tests were conducted in a towing tank under quasi-steady-state conditions for aspect ratios of $1.0$ and $1.5$, and for $\textit{Fr}$ ranging from $0.5$ to $2.5$. Ventilation occurred spontaneously for all test conditions as $\alpha$ increased. Three distinct trigger mechanisms were identified: nose, tail and base ventilation. Nose ventilation is prevalent at $\textit{Fr} \lt 1.0$ and $\textit{Fr} \lt 1.25$ for aspect ratios of $1.0$ and $1.5$, respectively, and is associated with an increase in the inception angle of attack. Tail ventilation becomes prevalent at higher $\textit{Fr}$, and the inception angle of attack exhibits a negative trend. Base ventilation was only observed for the semi-ogive profile, but it did not lead to the development of a stable ventilated cavity. Notably, the measurements indicate that the boundary between bistable and globally stable regions is not uniform and extends to significantly higher $\alpha$ than previously estimated. A revised stability map is proposed to reconcile previously published and current data, demonstrating how two alternative paths to a steady-state condition can lead to different flow regimes.

A low-density jet is known to exhibit global self-excited axisymmetric oscillations at a discrete natural frequency. This global mode manifests as large-scale periodic vortex ring structures in the near field. We experimentally investigate the effectiveness of axial and transverse forcing in controlling such global vortical structures. We apply acoustic forcing at a frequency ($f_{\!f}$) around the natural global frequency of the jet ($f_n$) leading up to and beyond lock-in. Using time-resolved stereoscopic particle image velocimetry, we find that the jet synchronises to $f_{\!f}$ when forced sufficiently strongly. When forced purely axially, the jet exhibits in-phase roll-up of the shear layers, producing axisymmetric vortex ring structures. When forced purely transversely, the jet exhibits anti-phase roll-up of the shear layers, producing tilted vortex ring structures. We find that the former produces relatively strong oscillations, while the latter produces oscillations that are even weaker than those of the unforced case due to asynchronous quenching. We show that the transverse forcing breaks the jet axisymmetry by altering the topology of the coherent structures in the near field, leading to global instability suppression. We also find that the wavelength of the applied forcing has a notable influence on the evolution of vortical structures, thereby modifying the forced response of the jet. The efficacy of transverse forcing and the influence of the forcing wavelength in suppressing the global mode of a self-excited low-density jet present new possibilities for the open-loop control of a variety of globally unstable flows.

The cell body of flagellated microalgae is commonly considered to act merely as a passive load during swimming, and a larger body size would simply reduce the speed. In this work, we use numerical simulations based on a boundary element method to investigate the effect of body–flagella hydrodynamic interactions (HIs) on the swimming performance of the biflagellate Chlamydomonas reinhardtii. We find that body–flagella HIs significantly enhance swimming speed and efficiency. As body size increases, the competition between the enhanced HIs and the increased viscous drag leads to an optimal body size for swimming. Based on the simplified three-sphere model, we further demonstrate that the enhancement by body–flagella HIs arises from an effective non-reciprocity: the body affects the flagella more strongly during the power stroke, while the flagella affect the body more strongly during the recovery stroke. Our results have implications for both microalgal swimming and laboratory designs of biohybrid microrobots.

In the present study, we introduce a new temperature transformation for compressible turbulent boundary layers with adiabatic and isothermal walls. Unlike existing transformations that rely on a single invariant function for the non-dimensional temperature gradient across the entire inner layer, a composite transformation strategy is proposed by leveraging two newly proposed Mach-number and wall-temperature invariant functions for the mean temperature field. This approach not only deploys appropriate Mach-number invariant functions in the viscous sublayer and the logarithmic region, but also introduces an improved solution to the long-standing singularity challenge inherent in single invariant function models. The performance of this composite transformation is verified by extensive direct numerical simulation (DNS) datasets (26 cases) of compressible turbulent boundary-layer flows. The results demonstrate that the proposed transformation maps the mean temperature profiles to the incompressible reference without case-specific parameter tuning, exhibiting significantly reduced scatter when compared with the existing temperature transformations.

This study conducted theoretical analysis and direct numerical simulations (DNS) of vertical natural convection in a two-dimensional cavity filled with porous media, where the imposed temperature gradient is oriented perpendicular to the direction of gravity. Three regimes characterised by distinct flow states and the angle $\theta$ of the isothermal layer are identified. In the steady regime I with $\theta \approx \pi /2$, the flow is weak and heat transfer is dominated by conduction. In the transitional regime II with rapidly increasing $\theta$, kinetic and thermal boundary layers gradually develop. In the turbulent regime III with $\theta \approx 0$, clear boundary layers arise and turbulent thermal convection prevails. Corresponding to these flow states, theoretical analysis is performed to derive the scaling laws of the Nusselt number $\textit{Nu}-1\sim Ra_{D}^{\gamma _1 }\textit{Pr}^{\eta _1}$ and Reynolds number $\textit{Re}\sim Ra_{D}^{\gamma _2 }\textit{Pr}^{\eta _2}$ with respect to Rayleigh–Darcy number $Ra_D$ and Prandtl number $\textit{Pr}$. We derive $(\gamma _1,\gamma _2,\eta _1,\eta _2)=(2,1,0,-1)$ for the steady regime and $(1/3,4/9,0,-2/3)$ for the turbulent regime. All theoretical scaling exponents in these two regimes are validated by DNS results. Furthermore, we find that the influence of the Darcy number $Da$ becomes almost negligible when it is sufficiently small. Unified models for $\textit{Pr}=1$ are proposed to integrate the three regimes and are applicable across a broad range of $\phi$ and $Ra_D$, which are satisfactorily verified by DNS results. The unified models provide a predictive framework for heat transport and flow intensity in porous-medium thermal convection, thereby offering practical values for thermal engineering applications.

In many electrochemical systems, variations in fluid density due to salinity gradients are unavoidable, leading to solutally driven Rayleigh–Bénard convection (RBC). In this study, we perform direct numerical simulations and theoretical analyses of two-dimensional solutal convection near perfectly cation-selective membranes by incorporating buoyancy and electrostatic forces into the Navier–Stokes and Poisson–Nernst–Planck equations. When electroconvection (EC) is negligible, we observe a flow reversal of large-scale circulation (LSC) in salt-driven RBC within a square-cavity electrochemical system, triggered by the periodic reconfiguration of corner vortices. Furthermore, we found that the competition between RBC and EC determines the dominant flow pattern. The buoyancy-driven convection and the LSC are suppressed at sufficiently strong EC flow, leading to a transition from buoyancy-driven flow to electrically driven flow. Consequently, the flow structures into a pair of EC vortices, driven by strong electric field forces within the extended space charge layer. Using Grossmann–Lohse theory, we derive a critical scaling law that describes the flow pattern selection, governed by the combined effects of the Rayleigh number, voltage difference and hydrodynamic coupling coefficient. Our work presents a novel approach to controlling flow patterns, distinct from existing strategies in thermally driven RBC.

Recent work (Raufaste et al. 2022 Soft Matter, vol. 18, p. 4944) studied the dynamics of a soap film in the shape of an unstable minimal surface whose evolution is governed in part by the frictional forces associated with surface Plateau border (SPB) motion. In this note, we study a variant of this problem in which a half-catenoid bounded by a wire loop and a fluid bath axisymmetrically surrounds a cylindrical rod with a radius equal to the neck of the critical catenoid given by the wire loop. When the half-catenoid is brought just beyond the point of instability, the film touches the cylinder and separates from the bath, creating an SPB that is dragged upwards along the rod by the now unstable soap film, and asymptotically relaxes to a new stable annular minimal surface. For this free-boundary problem involving an unstable initial condition, we find the dynamics by balancing the capillary force of successive unstable minimal surfaces spanning the SPB and the wire loop with the frictional force associated with the moving SPB. We find good agreement between theory and experiment using the frictional force $f\sim \textit{Ca}^{2/3}$ given by Bretherton’s law, where $ \textit{Ca} $ is the capillary number.

The acoustically excited vibrations of a micrometric object in a viscous liquid induce a net fluid flow known as microstreaming. This phenomenon can be harnessed for a variety of microscale applications, including particle transport, fluid mixing and the propulsion of micro-swimmers. Acoustic propulsion holds significant promise for in vivo manipulation due to its inherent biocompatibility and remote actuation capability, eliminating the need for an onboard energy source. However, designing steerable swimmers powered by vibrating tails requires a detailed understanding of the relationship between the input acoustic signal and the resulting streaming flow. In this paper, we characterise experimentally and model the microstreaming generated by a vertically standing micro-cantilever attached to a vibrating plate, as a function of the excitation frequency. Significant streaming is observed only at specific frequencies corresponding to the vibration modes of the support, which both translate and bend the cantilever. Computations based on a two-dimensional semi-analytical model enable quantitative predictions of the in-plane streaming flow structure and velocity magnitude, using as input the cantilever’s vibration profile, fully characterised by laser Doppler vibrometry. In particular, comparison between experiments and simulations allows us to rationalise the frequency-dependent emergence of dipolar, circular and elliptical streaming patterns, which are respectively induced by rectilinear, circular and elliptical translations of the cantilever. This analysis also explains the prevalence of elliptical streaming structures observed in our system. Beyond advancing our fundamental understanding of streaming generated by vibrating slender bodies, these results highlight the potential for frequency-based control of micro-swimmers through predictable, mode-specific flow responses.

We study the behaviour of a thin fluid filament (a rivulet) flowing in an air-filled Hele-Shaw cell. Transverse and longitudinal deformations can propagate on this rivulet, although both are linearly attenuated in the parameter range we use. On this seemingly simple system, we impose an external acoustic forcing, homogeneous in space and harmonic in time. When the forcing amplitude exceeds a given threshold, the rivulet responds nonlinearly, adopting a peculiar pattern. We investigate the dance’ of the rivulet both experimentally using spatiotemporal measurements, and theoretically using a model based on depth-averaged Navier–Stokes equations. The instability is due to a three-wave resonant interaction between waves along the rivulet, the resonance condition fixing the pattern wavelength. Although the forcing is additive, the amplification of transverse and longitudinal waves is effectively parametric, being mediated by the linear response of the system to the homogeneous forcing. Our model successfully explains the mode selection and phase-locking between the waves, it notably allows us to predict the frequency dependence of the instability threshold. The dominant spatiotemporal features of the generated pattern are understood through a multiple-scale analysis.

In this work we present a framework to explain the prediction of the velocity fluctuation at a certain wall-normal distance from wall measurements with a deep-learning model. For this purpose, we apply the deep-SHAP (deep Shapley additive explanations) method to explain the velocity fluctuation prediction in wall-parallel planes in a turbulent open channel at a friction Reynolds number ${\textit{Re}}_\tau =180$. The explainable-deep-learning methodology comprises two stages. The first stage consists of training the estimator. In this case, the velocity fluctuation at a wall-normal distance of 15 wall units is predicted from the wall-shear stress and wall-pressure. In the second stage, the deep-SHAP algorithm is applied to estimate the impact each single grid point has on the output. This analysis calculates an importance field, and then, correlates the high-importance regions calculated through the deep-SHAP algorithm with the wall-pressure and wall-shear stress distributions. The grid points are then clustered to define structures according to their importance. We find that the high-importance clusters exhibit large pressure and shear-stress fluctuations, although generally not corresponding to the highest intensities in the input datasets. Their typical values averaged among these clusters are equal to one to two times their standard deviation and are associated with streak-like regions. These high-importance clusters present a size between 20 and 120 wall units, corresponding to approximately 100 and 600 $\unicode{x03BC} \textrm {m}$ for the case of a commercial aircraft.