This work investigates the long-time asymptotic behaviour of a diffusing passive scalar advected by fluid flow in a straight channel with a periodically varying cross-section. The goal is to derive an asymptotic expansion for the scalar field and estimate the time scale over which this expansion remains valid, thereby generalising Taylor dispersion theory to periodically modulated channels. By reformulating the eigenvalue problem for the advection–diffusion operator on a unit cell using a Floquet–Bloch-type eigenfunction expansion, we extend the classical Fourier integral of the flat channel problem to a periodic setting, yielding an integral representation of the scalar field. This representation reveals a slow manifold that governs the algebraically decaying dynamics, while the difference between the scalar field and the slow manifold decays exponentially in time. Building on this, we derive a long-time asymptotic expansion of the scalar field. We show that the validity time scale of the expansion is determined by the real part of the eigenvalues of a modified advection–diffusion operator, which depends solely on the flow and geometry within a single unit cell. This framework offers a rigorous and systematic method for estimating mixing time scales in channels with complex geometries. We show that non-flat channel boundaries tend to increase the time scale, while transverse velocity components tend to decrease it. The approach developed here is broadly applicable and can be extended to derive long-time asymptotics for other systems with periodic coefficients or periodic microstructures.

Elastoviscoplastic effects on liquid plug propagation and rupture occurring in airways are studied computationally using the Oldroyd-B and Saramito–Herschel–Bulkley models. The relevant parameters are selected from physiological values representative of the eighth-to-tenth generation branches of a typical adult lung. The respiration pushes the liquid plug, depositing a trailing film thicker than the leading film. As a result, the liquid plug gets drained and eventually ruptures. We model airway reopening considering a rigid axisymmetric tube whose inner surface is coated by a thin non-Newtonian liquid film. A critical elastic behaviour is revealed: for low Weissenberg number (subcritical), the viscoelastic stress is released in the liquid plug, while for high Weissenberg number (supercritical), the stretched polymeric chains release their stresses in the trailing film, giving rise to (i) hoop stress that increases the film thickness and (ii) axial stress that leads to a speed-up of the liquid plug. Under supercritical conditions, we also identify a resonance that amplifies the elastic stresses. A mechanical analogy is proposed to elucidate the resonance phenomenon. The occurrence of the resonance is robust upon a variation of Weissenberg number, Laplace number, reference solvent-to-total dynamic viscosity ratio, the surfactant elastoviscoplastic mucus. Our simulations confirm that a presence of surfactants do not significantly affect the results, except for the expected delay of airway reopening due to air–mucus surface contamination. Such a novel elastocapillary mechanism increases the risk of epithelial cell damage regardless of the occurrence of plug rupture.

An imposed constant magnetic field parallel to the interface in the Rayleigh–Taylor framework strongly modifies the dynamics of the flow. The growth rate of the turbulent mixing layer is almost doubled compared with the purely hydrodynamic case, mainly due to a strong reduction of small-scale mixing. Indeed, magnetic tension inhibits the small-scale perturbations from developing, which in turn creates a strong anisotropy with structures elongated in the field direction. Two theoretical predictions for the asymptotic state of the magnetic Rayleigh–Taylor instability (MRTI) are put forward. First, considering the large-scale dynamics, an upper bound for the mixing layer growth rate is obtained. Second, the phenomenology is embedded in a buoyancy–drag equation from which an analytical relation between the growth rate, mixing, anisotropy and induced magnetic fields is derived. Both predictions are successfully assessed with high resolution direct numerical simulations of the Boussinesq–Navier–Stokes equations under the magnetohydrodynamics approximation. These predictions characterize the quasi-self-similar state of the MRTI driven by strong magnetic fields.

Fluidic levitation of different types of objects is achieved using laboratory experiments and described using simple mathematical models. Air bubbles, liquid tetrabromoethane droplets and solid spherical polytetrafluoroethylene beads were levitated in flowing water inside vertically oriented cylindrical tubes having diameters of 5, 8 and 10 mm. The centre of mass of all levitated objects was observed to undergo horizontal oscillations once a stable levitation point had been established. A simple model that considers the balance of gravitational, buoyancy and drag forces (as well as wall effects) was used to successfully predict the flow rates that are required to obtain stable levitation of objects with a range of different sizes. Horizontal motion was shown to be driven by vortex shedding of the objects in the tubes, and the dependence of the frequency of oscillation on their size was predicted.

Swimming and flying animals demonstrate remarkable adaptations to diverse flow conditions in their environments. In this study, we aim to advance the fundamental understanding of the interaction between flexible bodies and heterogeneous flow conditions. We develop a linear inviscid model of an elastically mounted foil that passively pitches in response to a prescribed heaving motion and an incoming flow that consists of a travelling wave disturbance superposed on a uniform flow. In addition to the well-known resonant response, the wavy flow induces an antiresonant response for non-dimensional phase velocities near unity due to the emergence of non-circulatory forces that oppose circulatory forces. We also find that the wavy flow destructively interferes with itself, effectively rendering the foil a low-pass filter. The net result is that the waviness of the flow always improves thrust and efficiency when the wavy flow is of a different frequency than the prescribed heaving motion. Such a simple statement cannot be made when the wavy flow and heaving motion have the same frequency. Depending on the wavenumber and relative phase, the two may work in concert or in opposition, but they do open the possibility of simultaneous propulsion and net energy extraction from the flow, which, according to our model, is impossible in a uniform flow.

A backward swept shape is one of the common features of the wings and fins in animals, which is argued to contribute to leading-edge vortex (LEV) attachment. Early research on delta wings proved that swept edges could enhance the axial flow inside the vortex. However, adopting this explanation to bio-inspired flapping wings and fins yields controversial conclusions, in that whether and how enhanced spanwise flow intensifies the vorticity convection and vortex stretching is still unclear. Here, the flapping wings and fins are simplified into revolving plates with their outboard 50 $\%$ span swept backward in either linear or nonlinear profiles. The local spanwise flow is found to be enhanced by these swept designs and further leads to stronger vorticity convection and vortex stretching, thus contributing to local LEV attachment and postponing bursting. These results further prove that a spanwise gradient of incident velocity is sufficient to trigger a regulation of LEV intensity, and a concomitant gradient of incident angle is not necessary. Moreover, an attached trailing-edge vortex is generated on a swept wing and induces an additional low-pressure region on the dorsal surface. The lift generation of swept wings is inferior to that of the rectangular wing because the extended stable LEV along the span and the additional suction force near the trailing edge are not comparable to the lift loss due to the reduced LEV intensity. Our findings evidence that a swept wing can enhance the spanwise flow and vorticity transport, as well as limit excessive LEV growth.

Surface tension gradients of air–liquid–air films play a key role in governing the dynamics of systems such as bubble caps, foams, bubble coalescence and soap films. Furthermore, for common fluids such as water, the flow due to surface tension gradients, i.e. Marangoni flow, is often inertial, due to the low viscosity and high velocities. In this paper, we consider the localised deposition of insoluble surfactants onto a thin air–liquid–air film, where the resulting flow is inertial. As observed by Chomaz (2001 J. Fluid Mech. 442, 387–409), the resulting governing equations with only inertia and Marangoni stress are similar to the compressible gas equations. Thus, shocks are expected to form. We derive similarity solutions associated with the development of such shocks, where the mathematical structure is closely related to the Burgers equation. It is shown that the nonlinearity of the surface tension isotherm has an effect on the strength of the shock. When regularisation mechanisms are included, the shock front can propagate and late-time similarity solutions are derived. The late-time similarity solution due to regularisation by capillary pressure alone was found by Eshima et al. (2025 Phys. Rev. Lett. 134, 214002). Here, the regularisation mechanism is generalised to include viscous extensional stress.

The present study deals with the electrophoresis of a non-polarizable droplet with irreversibly adsorbed ionic surfactants suspended in monovalent or multivalent electrolyte solutions. The impact of the non-uniform surface charge density, governed by the interfacial surfactant concentration, along with Marangoni, hydrodynamic and Maxwell stresses on droplet electrophoresis is analysed. At a large ionic concentration, the hydrodynamic steric interactions and correlations among finite-sized ions manifest. In this case the viscosity of the medium rises as the local volume fraction of the finite-sized ions is increased. The governing equations, incorporating these short-range effects, are solved numerically based on the regular linear perturbation analysis under a weak applied electric field consideration. We find that the electrophoretic velocity consistently decreases with an increase in the droplet-to-electrolyte viscosity ratio due to the Marangoni stress caused by inhomogeneous surfactant distribution. This monotonic relationship with droplet viscosity is absent for the case of constant surface charge density, where a low-viscosity droplet may exhibit a lower mobility than a high-viscosity droplet. In the presence of ionic surfactant, a continuous variation of mobility with surfactant concentration is found. For a monovalent electrolyte, mobility decreases significantly at an elevated ionic concentration due to the short-range effects described above. Reversal in mobility is observed in multivalent electrolytes due to the correlations among finite-sized ions, attributed to overscreening of surface charge and formation of a coion-rich layer within the electric double layer. In this case a toroidal vortex develops adjacent to the droplet and the reversed mobility enhances as the Marangoni number is increased. This mobility reversal is delayed for low-viscosity droplets.

Most turbulent boundary-layer flows in engineering and natural sciences are out of equilibrium. While direct numerical simulation and wall-resolved large-eddy simulation can accurately account for turbulence response under such conditions, lower-cost approaches like wall-modelled large-eddy simulation often assume equilibrium and struggle to reproduce non-equilibrium effects. The recent ‘Lagrangian relaxation-towards-equilibrium’ (LaRTE) wall model (Fowler et al. 2022 J. Fluid Mech. vol. 934, 137), formulated for smooth walls, applies equilibrium modelling only to the slow dynamics that are more likely to conform to the assumed flow state. In this work, we extend the LaRTE model to account for wall roughness (LaRTE-RW) and apply the new model to turbulent flow over heterogeneous roughness and in accelerating and decelerating flows over rough surfaces. We compare predictions from the new LaRTE-RW model with those from the standard log-law equilibrium wall model (EQWM) and with experimental data to elucidate the turbulence response mechanisms to non-equilibrium conditions. The extended model transitions seamlessly across smooth-wall and fully rough regimes and improves prediction of the skin-friction coefficient, especially in recovering trends at roughness transitions and in early stages of pressure-gradient-driven flow acceleration or deceleration. Results show that LaRTE-RW introduces response delays that are beneficial when EQWMs react too quickly to disturbances, but it is less effective in flows requiring rapid response, such as boundary layers subjected to accelerating–decelerating–accelerating free stream conditions. These findings emphasize the need for further model refinements that incorporate fast turbulent dynamics not currently captured by LaRTE-RW.