We derive a self-consistent hydrodynamic theory of coupled binary fluid–surfactant systems from the underlying microscopic physics using Rayleigh’s variational principle. At the microscopic level, surfactant molecules are modelled as dumbbells that exert forces and torques on the fluid and interface while undergoing Brownian motion. We obtain the overdamped stochastic dynamics of these particles from a Rayleighian dissipation functional, which we then coarse-grain to derive a set of continuum equations governing the surfactant concentration, orientation, fluid density and velocity. This approach introduces a polarisation field $\boldsymbol{p}(\boldsymbol{r},t)$, representing the average orientation of surfactants, which plays a central role in suppressing droplet coalescence. The remaining hydrodynamic equations are consistently obtained from a mesoscopic free energy functional. The resulting model accurately captures key surfactant phenomena, including surface tension reduction and droplet stabilisation, as confirmed by both perturbation theory and numerical simulations, and is thermodynamically consistent with both the Gibbs adsorption isotherm and Henry’s law for adsorbed surfactant concentration.

A coupled computational-fluid-dynamics/finite-element methodology is implemented to investigate the free aerodynamic separation of clusters of equally sized spheres arranged in regular configurations in Mach-20 flow, representing an idealized meteoroid-fragmentation scenario. The regular nature of the initial agglomeration geometries – touching sphere pairs, tetrahedral four-sphere arrangements and face-centred-cubic 13-sphere configurations – allows a systematic exploration of both individual sphere motions and bulk cluster dynamics as the initial orientation is varied. For sphere pairs, a stable lifting configuration arises when the spheres are in contact in a skewed configuration, a phenomenon that can also emerge in the more populous clusters. In the tetrahedral survey, comprising 38 initial orientations, shock surfing of downstream bodies is found to play a significant role in driving the separation dynamics. Despite substantial variations in detailed sphere motions with initial orientation, the trajectory type and final lateral velocity collapse reasonably well with the initial polar angle of the sphere within the cluster. Indices describing the bluntness and asymmetry of the initial configuration are introduced and correlate well with the collective cluster dynamics, though not always in an intuitive way. For the 13-sphere clusters, the dependency of individual sphere lateral velocities follows a similar trend with initial polar angle to the four-sphere case, suggesting that a simplified separation model may be possible for such configurations. The influence of the initial cluster bluntness on the bulk dynamics is somewhat reduced, however, indicating a tendency towards more homogeneous separation as the cluster population is increased.

We present a combined theoretical and numerical investigation of the inertial exit dynamics of a long horizontal circular cylinder vertically lifted out of a finite-size liquid bath at constant velocity. The various steps of the exit dynamics are studied in detail: from the formation of a bulge on the surface ahead of the cylinder to the coating of the cylinder by a liquid film while crossing the interface. We focus on inertial dynamics, a regime characteristic of large exit velocities, i.e. large Reynolds numbers ($500 \lt \textit{Re} \lt 10\,000$) and negligible interfacial effects. The dynamics is investigated through two-dimensional computations of the Navier–Stokes equations using a finite element method with moving boundaries. We describe in detail the exit dynamics while emphasising the effect of various parameters on surface deformation and resistive force. We identify subtle effects and interplay, such as initial free-surface response after impulsive start-up, the important role of the lateral bounding of the reservoir, and the close relationship between wake size and surge amplitudes as revealed by comparing with free-slip cylinder simulations. All these aspects are shown to be crucial to accurately predict the coated film thickness and the exit force.

This study presents a novel extension of the Onsager variational principle to incorporate inertial and thermal effects in fluid dynamics, thereby establishing a unified variational framework for modelling non-isothermal two-phase flows with liquid–vapour phase transitions and wetting effects on solid substrates. From this framework, we naturally derive a thermodynamically consistent model for the fluid system, comprising two-phase Navier–Stokes equations, an equation for the total energy, and dynamic boundary conditions that account for thermal and wetting effects. The derivation is independent of the equation of state, and generalises the dynamic van der Waals theory. To address the computational complexity of the resulting dynamic system, we propose a lattice Boltzmann method based on double distribution functions, which enables accurate and robust simulations of coupled fluid and thermal transport. Numerical experiments – including droplet evaporation, bubble nucleation and departure, and Leidenfrost droplet impact – demonstrate good agreement with theoretical predictions and experimental data, indicating that the proposed numerical method can effectively capture complex thermohydrodynamic phenomena.

Wavy topography can exert a significant influence on gravity-driven flows in porous media. Building on the low-dimensional theoretical framework for a wavy topography of height $f(x) = A[1 - \cos (\lambda x)]$, where $A$ is the amplitude and $\lambda$ is the wavenumber of the topography, under small-slope conditions ($A\lambda \ll 1$) Di et al. (2025 J. Fluid Mech., vol. 1016, A16), we extend the framework to constant-flux injection while incorporating uniform drainage and localised leakage through low-permeability substrates. A key dimensionless topographic intensity, emerges as the ratio of the pressure gradient required to overcome topographic slopes to the characteristic viscous gradient driving the flow, thereby quantifying topographic resistance. Our results show that a larger topographic intensity retards current advancement, while drainage, governed by the drainage intensity, imposes an upper bound on propagation distance. Leakage proves highly sensitive to the along-slope position of fissured zones. Comparisons with a macroscopic sharp-interface flow model indicate that the low-dimensional model simplifies the two-phase dynamics in substrates via a Darcy’s sink term, yielding underestimates of propagation during drainage and leakage. Applied to the field of carbon dioxide sequestration, our low-dimensional model reveals how injection flux modulates the early-stage flow dynamics over wavy cap rocks, offering theoretical insights into sequestration performance.

In this work, we will present evidence for the incompatibility of smoothed particle hydrodynamics (SPH) methods and eddy viscosity models. Taking a coarse-graining perspective, we physically argue that SPH methods operate intrinsically as Lagrangian large eddy simulations for turbulent flows with strongly overlapping discretisation elements. However, these overlapping elements in combination with numerical errors cause a significant amount of implicit subfilter stresses (SFS). Considering a Taylor–Green flow at $Re=10^4$, the SFS will be shown to be relevant where turbulent fluctuations are created, explaining why turbulent flows are challenging even for current SPH methods. Although one might hope to mitigate the implicit SFS using eddy viscosity models, we show a degradation of the turbulent transition process, which is rooted in the non-locality of these methods.

Flame–wall interaction (FWI) of lean premixed hydrogen/air flames is critical in wall-bounded combustors, where thermodiffusive instabilities strongly influence quenching. To capture these effects efficiently in realistic configurations, reduced-order combustion models such as flamelet tabulation are desirable, as they lower resolution requirements and computational cost. In this study, advanced flamelet manifolds incorporating a mixture-averaged species diffusion model and thermal diffusion are developed to represent the FWI of thermodiffusively unstable lean hydrogen/air flames. A central challenge is the simultaneous capture of intrinsic instabilities and heat losses, each complex in itself. Separate manifolds addressing these effects are first introduced, providing the foundation for joint manifolds that capture both simultaneously. In this context, the choice of flamelet databases is examined by comparing freely propagating flames with exhaust gas recirculation, commonly used in flamelet modelling to represent enthalpy variations, with one-dimensional head-on quenching (HOQ) flames, which are essential for accurate prediction of wall heat flux and pollutant formation in hydrocarbon flames. The models are evaluated through both a-priori and a-posteriori analyses across increasingly complex configurations, culminating in the HOQ of a thermodiffusively unstable flame, where both instability and quenching must be captured simultaneously. Results show excellent agreement with reference simulations using detailed chemistry, accurately reproducing key features of the flame front, thermochemical state and global flame properties such as consumption speed and quenching wall heat flux. This marks a key advance in modelling hydrogen combustion and provides a robust foundation for studying safety-critical phenomena such as flame flashback linked to near-wall flame propagation.

Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow–wall coupling challenge deterministic estimation strategies. To address this, we introduce a novel generative modelling framework based on conditional flow matching for synthesising instantaneous velocity fluctuation fields from wall observations, with explicit quantification of predictive uncertainty. Our method integrates continuous-time flow matching with a probabilistic forward operator trained using stochastic weight-averaging Gaussian, enabling zero-shot conditional generation without model re-training. We demonstrate that the proposed approach not only recovers physically realistic, statistically consistent turbulence structures across the near-wall region but also effectively adapts to various sensor configurations, including sparse, incomplete and low-resolution wall measurements. The model achieves robust uncertainty-aware reconstruction, preserving flow intermittency and structure even under significantly degraded observability. Compared with classical linear stochastic estimation and deterministic convolutional neural network methods, our stochastic generative learning framework exhibits superior generalisation for unseen realisations under same flow conditions and resilience under measurement sparsity with quantified uncertainty. This work establishes a robust semi-supervised generative modelling paradigm for data-consistent flow reconstruction and lays the foundation for uncertainty-aware, sensor-driven modelling of wall-bounded turbulence.