We revisit the interaction of an initially uniform near-inertial wave (NIW) field with a steady background flow, with the goal of predicting the subsequent organisation of the wave field. To wit, we introduce an exact analogy between the Young–Ben Jelloul (YBJ) equation and the quantum dynamics of a charged particle in a steady electromagnetic field, whose potentials are expressed in terms of the background flow. We derive the time-averaged spatial distributions of wave kinetic energy, potential energy and Stokes drift in two asymptotic limits. In the ‘strongly quantum’ limit, where the background flow is weak compared with wave dispersion, we compute the wave statistics by extending a strong-dispersion expansion initially introduced by YBJ. In the ‘quasi-classical’ limit, where the background flow is strong compared with wave dispersion, we compute the wave statistics by leveraging the equilibrium statistical mechanics of classical systems. We compare our predictions with numerical simulations of the YBJ equation, using an instantaneous snapshot from a two-dimensional turbulent flow as the steady background flow. The agreement is very good in both limits. In particular, we quantitatively describe the preferential concentration of NIW energy in anticyclones. We predict weak NIW concentration in both asymptotic limits of weak and strong background flow, and maximal anticyclonic concentration for background flows of intermediate strength, providing theoretical underpinning to observations reported by Danioux, Vanneste and Bühler (2015 J. Fluid Mech., vol. 773, R1).

This study investigates the aerobreakup mechanisms of a liquid droplet initially at a temperature below its critical point impacted by a shockwave in a supercritical environment, i.e. transcritical conditions, occurring in high-pressure/speed liquid-fuelled propulsion systems. Aerobreakup droplet breakup mechanisms have been extensively studied at atmospheric conditions, not considering the significant changes in fluid properties past the critical point that occur within very short breakup time scales in shock-dominated flows. Furthermore, the effects of decreased surface tension forces due to the weakening of intermolecular forces at supercritical conditions on the droplet breakup behaviour have not been resolved to date. This study aims to address these major gaps by developing a direct numerical simulation method to investigate the governing mechanism of droplet aerobreakup at transcritical conditions considering the changes in surface tension. A diffuse interface method coupled with a real-gas equation of state is developed to capture the fluid behaviour beyond the critical point. The results show that simultaneous changes in surface tension and density ratio unique to transcritical flows dictate the droplet aerobreakup mechanisms and the resultant breakup modes. This study presents the first transcritical droplet breakup regime map as a function of Weber number and density ratio compared with the classical breakup criteria commonly accepted for subcritical conditions, proving that the breakup is facilitated at supercritical conditions. The findings are expected to significantly contribute to the development of transcritical droplet aerobreakup models to enable the simulation of spray-shock interaction needed for designing new high-speed/pressure liquid fuel injection systems.

Despite its significance in biology and materials science, the dynamics of multicomponent vesicles under shear flow remains poorly understood because of its nonlinear and strongly coupled nature, especially regarding the role of membrane heterogeneity in driving non-equilibrium behaviour. Here we present a thermodynamically consistent phase-field model, which is validated against experiments, for the quantitative investigation of the dynamics. While prior research has primarily focused on viscosity or bending rigidity contrasts, we demonstrate that surface tension heterogeneity can also trigger swinging and tumbling in vesicles under shear. Additionally, our systematic phase diagram reveals three previously unreported dynamical regimes arising from the interplay between bending rigidity heterogeneity and shear flow. Overall, our model provides a robust framework for understanding multicomponent vesicle dynamics, with findings offering new physical insights and design principles for tuneable vesicle-based carriers.

A unified lattice Boltzmann method is employed to investigate Rayleigh–Bénard convection (RBC) subjected to sidewall heating and unipolar charge injection from the bottom wall. The study focuses on how the complex and nonlinear coupling between the buoyancy and Coulomb effects modify the heat transfer, flow structure and the transition between buoyancy- and Coulomb-dominated regimes. The results show that a side-heated wall, in the absence of charge injection, enhances the heat transfer rate and changes the scaling law between the Nusselt number $\textit{Nu}$ and Rayleigh number $Ra$ from $\textit{Nu} = 0.22Ra^{0.29}$ (classical RBC) to $\textit{Nu} = 0.56 Ra^{0.22}$ due to an additional buoyancy effect from the sidewall. When the electric charge is injected from the bottom wall, it is shown that the thermal boundary layer thickness decreases, leading to a further enhancement of heat transfer. Furthermore, systematic simulations over a broad range of $Ra$ and electric Rayleigh numbers $T$ reveal that, at given $T$, $\textit{Nu}$ remains constant when $Ra$ is low, indicating a Coulomb-dominated regime. Beyond a critical value of $Ra$, a power-law relationship between $\textit{Nu}$ and $Ra$ emerges, signifying a transition to the buoyancy-dominated regime. This transition can be well predicted by a dimensionless parameter, which is developed considering buoyancy to Coulomb forces. In addition, by analysing the flow structure using the Fourier mode decomposition, a phase diagram describing the dominant flow modes is proposed. The results demonstrate that the proposed dimensionless parameter not only delineates the transition between the two heat transfer regimes but also accurately captures the flow mode shift. Our findings offer new insights into the complex interaction between buoyancy and Coulomb effects and their influence on heat transfer and flow structure, with potential implications for the design of heat exchangers aimed at actively and efficiently controlling heat transfer.

Rate-dependent viscosity in power-law fluids significantly affects contact line stress singularities and moving contact line behaviour. Contact line forces show more severe divergence for shear-thickening fluids ($n\gt 1$) or remain finite for shear-thinning fluids ($n\lt 1$). Complementing earlier self-similar derivations of spreading laws by Starov et al. (J. Colloid Interface Sci. vol. 257, 2003, pp. 284–290) for shear-thinning drops, we extend the classical Cox-Voinov theory to power-law fluids and obtain explicit dynamic contact angle relationships – results that are more fundamental than previously reported spreading laws. This development provides a unified yet fundamentally distinct description of advancing contact line behaviour across the full range of shear-thinning and shear-thickening rheologies. We show that the apparent dynamic contact angle $\theta _{d}$ depends critically on the characteristic dissipation length $h^{*}\propto U^{n/(n-1)}$, fundamentally altering its dependence on contact line speed $U$. For shear-thinning fluids (n < 1) with less diverging contact line stresses, this length scale yields $\theta _{d}\sim C{a_{\textit{local}}}^{1/3}$ in the familiar Cox–Voinov form in terms of the local capillary number $ \textit{Ca}_{\textit{local}} = (h/h^{*})^{1-n}$, with the contact line motion dissipated within $h^{*}$ extending beyond local wedge height $h$, thereby eliminating the need for a microscopic cutoff. This feature also renders $\theta _{d}$ size dependent and varying with the spreading radius $R$, recovering $R\propto t^{n/(3n+7)}$and $\theta _{d}\propto U^{3n/(2n+7)}$ as previously derived by Starov et al. (2003). For shear-thickening fluids (n > 1) that exhibit more strongly diverging contact line stresses, by contrast, the contact line motion is dissipated within a much narrow region $h^{*}$ that is much smaller than the required microscopic cutoff hm. A complete precursor theory is also developed, showing $ h_{m} \propto U^{-n/(4-n)}$. This leads to $\theta_{d} \propto U^{n/(4-n)}$, making the global spreading behaviour highly sensitive to the contact line microstructure. Importantly, regardless of the microscopic mechanisms, the apparent dynamic contact angle relationship can always be expressed in the analogous Cox–Voinov form $\theta _{d}\sim {\textit{Ca}_{\textit{eff}}}^{1/3}$ in terms of the effective capillary number $\textit{Ca}_{\textit{eff}}=\eta_{\kern-1.5pt f}U/\gamma=(h^*/h_m)^{n-1}$ (with the surface tension γ) based on the microscopic viscosity $\eta_{\kern-1.5pt f}\propto (U/h_{m})^{n-1}$ associated with the local shear rate $ U/h_{m}$ across the cutoff $ h_{m}$. The present Cox-Voinov generalisation can be applied to more realistic rheological laws such as the Carreau model, where self-similar solutions may no longer exist, thereby enabling a direct mapping of non-Newtonian spreading dynamics onto equivalent Newtonian behaviour and offering a more robust framework for the design and control of droplet dynamics in practical applications.

Wave–sea-ice interactions shape the transition zone between open ocean and pack ice in the polar regions. Most theoretical paradigms, implemented in coupled wave–sea-ice models, predict exponential decay of the wave energy but some recent observations deviate from this behaviour. Expanding on a framework based on wave energy dissipation due to ice–water drag, we account for drifting sea ice to derive an improved model for wave energy attenuation. Analytical solutions replicate the observed non-exponential wave energy decay and the spatial evolution of the effective attenuation rate in Antarctic sea ice.

This work presents an efficient statistical model to simulate expected scalar transport in fractured porous media below the representative elementary volume scale. We focus on embedded, highly conductive, isolated fractures. The statistical integro-differential fracture model (Sid-FM) solves for ensemble-averaged solutions directly, avoiding computationally expensive Monte Carlo simulation. The expected fluid exchange between isolated fractures and the porous matrix is modelled via a non-local kernel function, leading to a set of integro-differential equations. The model is validated against reference data from Monte Carlo simulations for statistically one-dimensional test cases and shows good agreement.

The collisions between elongated particles in turbulence play an important role in various natural and industrial processes. In this study, we establish a theoretical model to estimate the collision kernels of monodisperse elongated passive particles in homogeneous isotropic turbulence. The model is composed of two terms: the collision kernel with fixed relative angles and the angular-volumetric number density of neighbouring pairs, where we first derive under the Gaussian hypothesis of the fluid velocity gradients and then incorporate a non-Gaussianity factor into the formulations. The collision kernels obtained by the present model are in a good agreement with that of direct numerical simulations. Moreover, our model provides insights into the mechanism of the relative alignment between nearby particle pairs and the chain formation in turbulence, from the perspective of particle collisions.

The study investigates the influence of temperature-dependent viscosity on the stability of buoyancy-driven flow in a vertical porous slab bounded by impermeable walls and subject to Robin thermal boundary conditions. Three viscosity–temperature relationships are considered – linear, quadratic and exponential. A normal-mode linear stability analysis is carried out for two porous flow models: Model I, representing Darcy flow with the transient velocity term neglected, and Model II, its counterpart that retains it. The resulting stability eigenvalue problem is solved numerically to obtain neutral stability curves and the critical parameters, with emphasis on the roles of the Prandtl–Darcy number, Biot number and viscosity parameters. The similarities and differences between the two models, as well as those among the viscosity–temperature laws, are examined in detail. For linear and quadratic viscosity variations, Model I predicts unconditional stability irrespective of boundary heat exchange, whereas Model II admits instability when the boundaries are thermally imperfect. In contrast, exponential viscosity variation promotes instability in both models. In Model I, instability is confined to a restricted range of Biot numbers, which depends sensitively on the exponential viscosity parameter, while the flow remains stable for all thermal boundary conditions when this parameter is less than 8.2070. Model II, however, displays qualitatively distinct behaviour characterised by mode transitions and the emergence of two instability regimes of Biot number separated by a stability window.

Lime carbonation direct air capture (DAC) systems remove atmospheric carbon dioxide (CO2) by carbonating calcium hydroxide (Ca(OH)2) to produce calcium carbonate (CaCO3), which can release CO2 for durable storage. Accurate and precise measurement of generated CaCO3 is essential in quantifying CO2 removed from the atmosphere, and for optimizing the carbonation process. Methods for measurement of carbonate content are well established, but have yet to be applied to materials produced by this system (i.e., almost solely Ca(OH)2 and CaCO3). Five carbonate content analysis techniques (loss on ignition, LOI; thermogravimetric analysis, TGA; combustion analysis of carbon via infrared absorption, CAC-IR; volumetric calcimetry; and quantitative Fourier transform infrared spectroscopy, FTIR) were investigated for their measurement accuracy and precision over a range of carbonate contents. Sample throughput and levelized cost of analysis were considered in addition to accuracy and precision. LOI and CAC-IR proved favorable against equal consideration of the four factors. Weighting for accuracy and precision, LOI was favorable. Standard operating procedures, including established accuracy and precision levels, for viable carbonate content quantification techniques should be developed, tested, and presented to assure carbon credit buyers, the scientific community, and the public on the validity of carbon credits generated by lime carbonation DAC.

We investigate the interfacial fluid dynamics and heat transfer at nanoscales using an improved diffuse interface approach for liquid–vapour interfaces in non-equilibrium. Conventional Navier–Stokes–Korteweg (NSK) formulations often fail to accurately capture transport phenomena across extremely thin interfaces due to underestimation of interface resistances. In this work, we improve the NSK model by adding a production term in the momentum equation based on higher-order corrections. To enhance interface resistances, viscosity and thermal conductivity are made dependent on the density gradient, increasing resistance only within the interface region. The gradient-based coefficients are determined by fitting to solutions of the Enskog–Vlasov equation for Couette flow of Struchtrup & Frezzotti (2022 J. Fluid Mech., vol. 940, p. A40). Applying these fitted equations to pure heat conduction and planar evaporation problems shows that the model accurately captures interfacial transport, making it a useful tool for studying nanoscale evaporation, thermal management and the droplet dynamics on solid surfaces.

Flexible substrates are effective in suppressing splashing, but they simultaneously lead to inhibition of spreading (Howland et al. 2016 Phys. Rev. Lett. vol. 117, 184502; Vasileiou et al. 2016 Proc. Natl Acad. Sci. USA vol. 113, pp. 13307−13312). In addition, there has been limited investigation and no established scaling law for the splashing threshold in the case of flexible substrates. To address these points, this paper proposes a lotus-leaf-like disk that can effectively suppress droplet splashing without inhibiting the maximum spreading of droplets. This situation is numerically studied in this paper. Five dynamic modes of the impacting droplet are identified with various Weber numbers (defined as the inertia force relative to the surface tension force) and different disk’s stiffnesses. The threshold Weber number of splashing is developed by considering the flexibility of substrates. Finally, the results demonstrate that the proposed method not only suppresses the splashing but also maintains the maximum spreading.

This study investigates the low-frequency dynamics of a turbulent separation bubble (TSB) forming over a backward-facing ramp, with a focus on large-scale coherent structures associated with the so-called `breathing motion’. Using time-resolved particle image velocimetry (PIV) in both streamwise and spanwise planes, we examine the role of sidewall confinement, an aspect largely overlooked in previous research. Spectral proper orthogonal decomposition (SPOD) of the streamwise velocity field reveals a dominant low-rank mode at low Strouhal numbers ($St \lt 0.05$), consistent with prior observations of TSB breathing. Strikingly, the spanwise-oriented PIV data uncover a previously unreported standing-wave pattern, characterised by discrete spanwise wavenumbers and nodal/antinodal structures, suggesting the presence of spanwise resonance. To explain these observations, we construct a resolvent-based model that imposes free-slip conditions at the sidewall locations by superposing left- and right-travelling three-dimensional modes. The model accurately reproduces the spanwise structure and frequency content of the measured SPOD modes, demonstrating that sidewall reflections lead to the formation of standing-wave-like patterns. Global stability analysis reveals a zero-frequency eigenmode originating from a centrifugal instability, giving rise to the observed low-frequency breathing. Downstream, the associated coherent structures are further amplified through non-modal lift-up mechanisms. Our findings highlight the critical influence of spanwise boundary conditions on the selection and structure of low-frequency modes in TSBs. This has direct implications for both experimental and numerical studies relying on spanwise-periodic boundary conditions and offers a low-order framework for predicting sidewall-induced modal dynamics in separated flows.

A computational fluid dynamics simulation of subcooled flow boiling of water at 10.5 ${\rm bar}$, with an applied heat flux of $1\,{\rm MW}\,{\rm m}^{-2}$ and subcooling of 10 ${\rm K}$, was performed using an interface tracking method. The simulation replicated the conditions of an experiment conducted at MIT. The objectives are to elucidate heat-transfer mechanisms in moderate-pressure subcooled boiling and to validate the simulation method, with a focus on quantities that are difficult to measure experimentally, such as the distributions of velocity, temperature, bubble number density and heat-flux partitioning. Due to the small bubble size under high pressure, fine grids are required. Simulated bubble shapes, wall temperatures and vapour area fractions show good agreement with the experimental results. The simulations reveal that a very thin liquid layer (${\lt}4\,\unicode{x03BC}{\rm m}$) surrounding the bubbles is highly effective at removing heat from the surface. The local wall heat fluxes beneath medium and large bubbles, excluding the heat flux associated with seed-bubble generation, are approximately 0.9 and 0.4 ${\rm MW}\,{\rm m}^{-2}$, respectively; the latter is smaller because of the presence of thicker liquid films (14–70 $\unicode{x03BC}{\rm m}$) that thermally insulate the wall. In the single-phase liquid region, the heat transfer coefficient reaches $42\,{\rm kW}\,{\rm m}^{-2}\,{\rm K}^{-1}$ as a result of strong turbulent heat flux in the wall-normal direction; this turbulent heat flux is approximately eight times larger than in the equivalent single-phase liquid flow.

Thin liquid films play an instrumental role in the coating industry. In many cases, these films consist of multiple components and are applied in multiple layers. However, multilayer multicomponent coatings can readily develop thickness non-uniformities due to Marangoni flows driven by solute concentration gradients. Previous flow visualisation experiments have demonstrated that the addition of surfactant can suppress such non-uniformities, but the physical mechanisms underlying this suppression have not yet been definitively established. We investigate the growth of film-height non-uniformities in a two-layer multicomponent coating consisting of a solute-rich bottom layer, a solute-depleted top layer and surfactant. A lubrication-theory-based model that accounts for vertical and lateral gradients in solute and surfactant concentrations is developed. The resulting coupled nonlinear partial differential equations describing the film height, solute concentration and surfactant concentration are solved with a pseudospectral method. Our findings reveal that surfactant-induced Marangoni flows can significantly decrease film-height non-uniformities by competing with Marangoni flows due to solute concentration gradients. Several simplifications of the governing equations are explored to determine how well predictions from these simplified models compare with the full lubrication-theory-based model, thereby providing insight into dominant physical mechanisms in different parameter regimes. The role of surfactant solubility and sorption kinetics in controlling perturbation growth is also examined.