We developed a two-phase lattice Boltzmann model by coupling the entropic multiple-relaxation-time (EMRT or KBC) collision operator enabling low fluid viscosity, with a source term (Wang et al. 2022, Phys. Rev. E vol. 105, no 4) to independently adjust surface tension. The coupling is implemented via the exact difference method (EDM), which allows full consideration of external-force effects on the entropic stabiliser in KBC, in contrast to the recent work of Wang et al. (2022 Phys. Rev. E vol. 105) and Xu et al. (2024 Comput. Math. Appl. vol. 159, 92–101). More importantly, we address a major drawback of the EDM by explicitly demonstrating how its high-order error terms influence the pressure tensor and surface tension. Using the developed model, we investigated droplet impact and splashing on a thin liquid film at a remarkably high Weber number of ${\textit{We}} = 5000$ and Reynolds number of ${\textit{Re}} = 5000$. Droplet impact and splashing on flat surfaces and mesh structures at very high ${\textit{Re}}$ (15 200) and ${\textit{We}}$ (1020) are also studied after validating four representative cases against experiments. For droplet impact on flat surfaces, hydrophobicity promotes the growth of peripheral instabilities, leading to fingering splashing. Corona splashing transitions to fingering splashing as the liquid–gas viscosity ratio increases. For droplet impact on mesh structures, large openings promote liquid penetration, whereas small openings enhance spreading. As the solid ratio increases, the maximum spreading ratio increases monotonically but nonlinearly, whereas the maximum penetrated liquid pillar length first rises and then drops. These simulations demonstrate the proposed model offers significant advantages for accurately capturing and elucidating complex droplet impact and splashing dynamics at high ${\textit{Re}}$ and ${\textit{We}}$.

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.