This paper presents a theoretical model for the electro-osmotic flow (EOF) of semi-dilute polyelectrolyte (PE) solutions in nanochannels. We use mean-field theories to describe the properties of electric double layer and viscosity of PE solutions that are prerequisites for constructing the EOF model. The EOF model is validated via a good match to the existing experimental results. Based on the validated EOF model, we conduct a comprehensive analysis of EOF of semi-dilute PE solutions in nanochannels. First, we observe considerable EOF of PE solutions in the uncharged nanochannels, which is in stark contrast to EOF of simple electrolyte solutions. The analyses show that the EOF of PE solutions in uncharged nanochannels is triggered by the external electric field acting on the near-wall non-electroneutral regions resulting from the confinement-induced inhomogeneous distribution of PE monomers. Although the solutions are electroneutral as a whole, the presence of local non-electroneutral regions and the mismatch between non-electroneutral regions and high-viscosity regions lead to the net EOF in uncharged nanochannels. Furthermore, we reveal that the EOF mobility $\mu _{{eof}}$ in uncharged nanochannels exhibits a scaling law $\mu _{{eof}} \propto a^{-0.44}$ (wherein $a$ denotes monomer Kuhn length) and is inversely proportional to the PE chain length, while it decreases nonlinearly with the charge fraction of the PE chains. Moreover, the EOF mobility reaches its maximum at specific bulk monomer concentration, and increases with the nanochannel height before converging to that under no confinement. Second, we analyse the EOF of PE solutions in nanochannels with various wall effects, such as surface charge density, slip length and adsorption length. When the surface charge is absent, the adsorption length significantly influences the direction and magnitude of the EOF, whereas the slip length has no effect. When the wall becomes increasingly charged, the influence of adsorption length on EOF gradually diminishes, while the importance of the slip length progressively intensifies and the EOF is highly influenced by the co-action of various wall effects in a complicated manner. When the surface wall is oppositely charged to polymer monomers, the EOF mobility varies nonlinearly with the surface charge density, while a zero net flow of EOF followed by a direction reversal is discovered when the wall is likely charged to polymer monomers.

The settling of highly elastic non-Brownian closed fibres (called loops) under gravity in a viscous fluid is investigated numerically. The loops are represented using a bead–spring model with harmonic bending potential and finitely extensible nonlinear elastic stretching potential. Numerical solutions to the Stokes equations are obtained with the use of HYDROMULTIPOLE numerical codes, which are based on the multipole method corrected for lubrication to calculate hydrodynamic interactions between spherical particles with high precision. Depending on the elasto-gravitation number $B$, a ratio of gravitation to bending forces, the loop approaches different attracting dynamical modes, as described by Gruziel-Słomka et al. (2019 Soft Matt. 15, 7262–7274) with the use of the Rotne–Prager mobility of the elastic loop made of beads. Here, using a more precise method, we find and characterise a new mode, analyse typical time scales, velocities and orientations of all the modes, compare them and investigate their coexistence. We analyse numerically the transitions (bifurcations) to a different mode at certain critical values of the elasto-gravitation number.

The settling dynamics of finite size, slightly heavier-than-fluid Kolmogorov-scale particles in homogeneous, isotropic turbulence at moderate volume loadings is investigated. A thoroughly validated two-way-coupled, point-particle model based on the complete Maxey–Riley–Gatignol equation of motion is used with closure models for all forces, including the history force, together with corrections for the self-disturbance field created by the particle using a novel zonal-advection-diffusion-reaction method. Settling dynamics is investigated by varying turbulence intensities relative to the particle settling speed in quiescent flow for multiple Stokes numbers. The length scales associated with the turbulence structures that strongly interact with and influence the settling dynamics are investigated using multiscale statistical analysis of the fluid velocity and second invariant of the velocity gradient tensors sampled by the particles. The time scales are investigated using trajectory curvature angle statistics of inertial and fluid particles. Low-to-moderate Stokes number particles tend to sample strain-rate dominated regions of the flow, tend to follow the curvature of the flow paths and show enhanced settling at higher turbulence intensities due to fast tracking and preferential sampling. Higher Stokes number particles, on the other hand, have a tendency to travel in straight lines relative to the flow and result in reduced settling speeds due to loitering. For the low mass loadings considered in this work, there is minimal global effect on the turbulent flow characteristics; however, it is found that the Kolmogorov-scale particles interact with and locally modify flow structures approximately twice their size, whereas they sample flow velocities from scales up to ten times the particle size, influencing preferential sampling and settling characteristics.

Capsules are widely used in bioengineering, chemical engineering and industry. The development of drug delivery systems using deformable capsules is progressing, yet the regulation of drug release within a capsule remains a challenge. Meanwhile, a microswimmer enclosed in a capsule can generate a large lubrication force on the capsule membrane, which could result in deformation and mechanical damage to the membrane. In this study, we numerically investigate how a capsule can be damaged by an enclosed microswimmer. The capsule membrane is modelled as a two-dimensional neo-Hookean material, with its deformability parametrised by capillary number. An isotropic brittle damage model is applied to express membrane rupture, with the Lighthill–Blake squirmer serving as the microswimmer model. In a sufficiently small capillary number regime, pusher-type squirmers exhibit stable swimming along the capsule membrane, while neutral-type and puller-type squirmers exhibit swimming towards the membrane and remain stationary. As capillary number increases, the damage to the membrane increases and rupture occurs in all swimming modes. For pusher-type squirmers, the critical capillary number leading to rupture is dependent on the initial incidence angle, whereas neutral-type and puller-type squirmers are independent of the initial value. Furthermore, we present methods for controlling membrane damage by magnetically orienting the microswimmer. The findings reveal that a static magnetic field can orient the microswimmer, leading to membrane damage and rupture even for a capsule that cannot be damaged by free swimming, while controlling the swimming path with a rotating magnetic field enables soft membranes to maintain deformation without rupture.

The flow-induced oscillations of a clamped flexible ring in a uniform flow were explored using the penalty immersed boundary method. Both inverted and conventional ring configurations were examined, with systematic analysis focused on the effects of bending rigidity and eccentricity. Four distinct oscillation modes were identified across parameter variations: flapping (F), deflected oscillation (DO), transverse oscillation (TO) and equilibrium (E) modes. Each mode exhibited a 2S wake pattern. The inverted ring sustained the DO mode under low bending rigidity with a deflected shape, transitioning to the TO mode at higher bending rigidity. In the TO mode, a lock-in phenomenon emerged, enabling the inverted ring to achieve a high power coefficient due to a simultaneous rise in both oscillation amplitude and frequency. By contrast, the conventional ring exhibited the F mode at low bending rigidity and transitioned to the E mode as rigidity increased, although its power coefficient remained lower because of reduced critical bending rigidity. For the inverted ring, low eccentricity enhanced oscillation intensity but limited the operational range of the TO mode. In contrast, for the conventional ring, reducing eccentricity led to an increase in oscillation amplitude. Among the investigated configurations, the inverted-clamped ring achieved the highest energy-harvesting efficiency, surpassing those of the conventional clamped ring and a buckled filament.

The work investigates the response dynamics of non-premixed jet flames to blast waves that are incident along the jet axis. In the present study, blast waves, generated using the wire-explosion technique, are forced to sweep across a non-premixed jet flame that is stabilised over a nozzle rim positioned at a distance of 264 mm from the source of the blast waves. The work spans a wide range of fuel-jet Reynolds numbers ($Re$; ranging from 267 to 800) and incident blast-wave Mach numbers ($M_{s,r}$; ranging from 1.025 to 1.075). The interaction imposes a characteristic flow field over the jet flame marked by a sharp discontinuity followed by a decaying profile and a delayed second spike. The second spike in the flow field profile corresponds to the induced flow that follows the blast front. While the response of the flame to the blast front was minimal, it was found to detach from the nozzle rim and lift off following the interaction with the induced flow. Subsequently, the lifted flame was found to reattach back at the nozzle or extinguish, contingent on the operating $Re$ and $M_{s,r}$. Alongside flame lift-off, flame-tip flickering was aggravated under the influence of the induced flow. A simplified theoretical model extending the vorticity transport equation was developed to estimate the change in flickering time scales and length scales owing to the interaction with the induced flow. The observed experimental trends were further compared against theoretical predictions from the model.

The nonlinear disturbance caused by either a localised pressure distribution moving at constant speed on the free surface of a liquid of finite depth or a flow over a topographic obstacle, is investigated using (i) the weakly nonlinear forced Kadomtsev–Petviashvili equation which is valid for depth-based Froude numbers near unity and (ii) the fully nonlinear free-surface Euler system. The presence of a steady v-shaped Kelvin wave pattern downstream of the forcing is established for this model equation, and the wedge angle is characterised as a function of the depth-based Froude number. Inspired by this analysis, it is shown that the wake can be eliminated via a careful choice of the forcing distribution and that, significantly, the corresponding nonlinear wave-free solution is stable so that it could potentially be seen in a physical experiment. The stability is demonstrated via the numerical solution of an initial value problem for both the model equation and the fully nonlinear Euler system in which the steady wave-free state is attained in the long-time limit.

The interaction between elastic structures and fluid interfaces, known as ‘hydroelastic’ problems, presents unique challenges to classical frameworks established for rigid spheres and liquid droplets. In this work, we experimentally demonstrate an intriguing phenomenon where ultrasoft hydrogel spheres rebound from a water surface at high impact speeds, even when their density exceeds that of water. We further propose a theoretical force-balance model, incorporating energy redistribution and potential flow theory, to predict the critical impact speed for the transition from sinking to rebounding, as well as the temporal evolution of both spreading diameter and cavity expansion. Our findings extend the classical Weber- and Bond-number-dominated paradigms for rigid spheres and liquid droplets, demonstrating that hydrogel dynamics is controlled by a modified elastocapillary Mach number, with rebound achievable even for hydrophilic spheres. These findings improve the understanding of soft-impact hydrodynamics and offer design principles for applications in biomimetic robotics and energy-absorbing materials.

We investigate the dynamics of a pair of rigid rotating helices in a viscous fluid, as a model for bacterial flagellar bundle and a prototype of microfluidic pumps. Combining experiments with hydrodynamic modelling, we examine how spacing and phase difference between the two helices affect their torque, flow field and fluid transport capacity at low Reynolds numbers. Hydrodynamic coupling reduces the torque when the helices rotate in phase at constant angular speed, but increases the torque when they rotate out of phase. We identify a critical phase difference, at which the hydrodynamic coupling vanishes despite the close spacing between the helices. A simple model, based on the flow characteristics and positioning of a single helix, is constructed, which quantitatively predicts the torque of the helical pair in both unbounded and confined systems. Finally, we show the influence of spacing and phase difference on the axial flux and the pump efficiency of the helices. Our findings shed light on the function of bacterial flagella and provide design principles for efficient low-Reynolds-number pumps.