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.