Fragmentation of a fluid body into droplets underlies many contamination and disease transmission processes where pathogens are transported in a liquid phase. An important class of such processes involves formation of a fluid ligament and its destabilization into droplets. Inertial detachment (Gilet & Bourouiba, J. R. Soc. Interface, vol. 12, 2015, 20141092) is one of these modes: upon impact on a sufficiently compliant substrate, the substrate's motion can transfer its impulse to a contaminated sessile drop residing on it. The fragmentation of the sessile drop is efficient at producing contaminated ejected droplets with little dilution. Inertial detachment, particularly from substrates of intermediate wetting, is also interesting as a fundamental fragmentation process on its own merit, involving the asymmetric stretching of the sessile drop under impulsive axial forcing with one-sided pinning due to the substrate's intermediate wetting. Our experiments show that the radius, $R_{tip}$, of the tip drop ejected become insensitive to the Bond number value for $Bo>1$. Here, $Bo$ quantifies the inertial effects via the relative axial impulsive acceleration compared with capillarity. The time, $t_{tip}$, of tip-drop breakup is also insensitive to $Bo$. Combining experiments, theory and validated numerics, we decipher the selection of $R_{tip}$ and its sensitivity to the surface-wetting and substrate foot dynamics. Using asymptotic theory in the large $Bo$ limit for which the thin-film/slender-jet approximations hold, we derive a reduced physical model that predicts $R_{tip}$ consistent with our experiments. Finally, we discuss how pathogen physical properties (e.g. wetting and buoyancy) within the sessile drop determine their distribution in the tip and secondary fragmentation droplets.

An asymptotic matching modal model is established based on the singular perturbation method for predicting mode evolution in single- and dual-mode interfaces accelerated by a shock wave. The startup process is incorporated into the model to provide a complete description of the mode evolution after the shock impact. Through considering the feedback from high-order harmonic to the third-order harmonic, the model accuracy is improved and the model divergence is prevented. In addition, the model can evaluate the mutual-coupling effect on the amplitude variations of high-order harmonics besides the ‘beat modes’. To validate the model, experiments on both light–heavy and heavy–light interfaces subject to a shock wave are conducted, and both single- and dual-mode interfaces formed by the soap-film technique are involved. The interface profiles extracted from mode decomposition and predicted by the model show high consistency with the experimental counterparts. Good agreement of the mode amplitude growths between the experiments and theoretical predictions shows the superiority of the model, especially for the heavy–light interface.

In this paper, we simulate the process of two-dimensional axisymmetric fluid–structure coupling of a droplet impacting on a flexible disk. The effects of dimensionless disk stiffness (K = 0.1–1000), Weber number (We = 1–500) and contact angle (θ = 130° and 60°) on the dynamics of the droplet impacting on the flexible disk are analysed. The results indicate that there are five typical impact modes for a hydrophobic surface (θ = 130°) and four typical impact modes for a hydrophilic surface (θ = 60°) within the range of considered parameters. The analysis of spreading factor reveals that a part of the energy is transferred to the substrate, which is manifested as a weakening of the droplet spreading, when the substrate deforms downwards due to the droplet impact; the squeezing of the droplet causes a tendency to flow from the centre of the droplet to the edge, which is manifested as an enhancement of the droplet spreading, when the substrate recovers from the downward deformation. The effect of the substrate flexibility on the maximum spreading factor depends on the competition of the two mechanisms above. Based on this, a modified scaling law of βmax has been proposed by introducing the effective Weber number (Wem). The analysis of impact force demonstrates that the peak of the impact force is related to the deflection of the flexible substrate which is different from that of a rigid wall; and three typical processes of impact force variation have been summarised. In addition, unlike the rigid substrate scenario, there is an energy interaction between the droplet and the flexible substrate after impact occurs, which is classified as three typical energy transformation processes.

We study experimentally the onset of Faraday waves near the end walls of a rectangular vessel containing two stably stratified fluid layers, subject to horizontal oscillations. These subharmonic waves (SWs) are excited, because the horizontal inertial forcing drives a harmonic propagating wave which displaces the interface in the vertical direction at the end walls. We find that the onset of SWs is regulated by a balance between capillary and viscous forces, where the rate of damping is set by the Stokes layer thickness at the wall rather than the wavelength of the SWs. We model the onset of SWs with a weakly damped Mathieu equation and find that the dimensional critical acceleration scales as $\nu _m^{1/2} \omega ^{3/2}$, where $\nu _m$ is the mean viscosity and $\omega$ is the frequency of forcing, in excellent agreement with the experiment over a wide range of parameters.

We explore the interaction of natural convection and mechanical ventilation in a room where fresh air is supplied at low level and stale air is extracted at high level. Turbulent buoyant plumes rising from heat sources interact with this upward airflow and establish a steady-state stratification with a warm upper layer above a layer of the cold supply air. Adapting the volume balance model used in natural ventilation (Linden et al., J. Fluid Mech., vol. 212, 1990, pp. 309–335) leads to the prediction that the upper layer will vent from the room when the ventilation volume flux exceeds the volume flux in the plumes at the ceiling. However, our new laboratory experiments establish that there is still a stable two-layer stratification beyond this point of critical ventilation. Motivated by our observations, we propose that the kinetic energy flux supplied by the plume leads to turbulent mixing in the upper layer. We propose a new model of this mixing which is consistent with our experiments in both the over- and under-ventilated regimes. This has important implications for air recirculation in buildings with large ventilation flows, particularly hospital operating theatres and clean rooms.

Liquid flowing down a fibre readily destabilises into a train of beads, commonly called a bead-on-fibre pattern. Bead formation results from capillary-driven instability and gives rise to patterns with constant velocity and time-invariant bead frequency $f$ whenever the instability is absolute. In this study, we develop a scaling law for $f$ that relates the Strouhal number $St$ and capillary number $Ca$ for Ostwaldian power-law liquids with Newtonian liquids recovered as a limiting case. We validate our proposed scaling law by comparing it with prior experimental data and new experimental data using xanthan gum solutions to produce a low capillary number $Ca \leq 10^{-2}$ regime. The experimental data encompasses both Ostwaldian and Newtonian flow, as well as symmetric and asymmetric patterns, and we find the data collapses along the predicted trend across seven orders of magnitude in $Ca$. Our proposed scaling law is a powerful tool for studying and applying bead-on-fibre flows where $f$ is critical, such as heat and mass transfer systems.

The eddy-viscosity model, as initially used to model the mean Reynolds stress, has been widely used in the linear analysis of turbulence recently by direct extension. In this study, the mechanism of the eddy viscosity in improving the prediction of fluctuation structures with linear analysis is clarified by investigating the statistical properties of forcing, eddy-viscosity term and their correlations. From the direct numerical simulation (DNS) results of turbulent channel flows with $Re_{\tau }=186$–$2003$, the spatial correlation of forcing is partially cancelled due to its interaction with eddy-viscosity terms. The stochastic forcing after excluding the eddy-viscosity term is nearly uncorrelated spatially, which better matches the condition where the resolvent modes are consistent with the spectral proper orthogonal decomposition (SPOD) modes from DNS. With the above findings, an optimisation framework is developed by minimising the spatial correlations of the stochastic forcing. The optimised eddy-viscosity profiles nearly overlap with the mean-quantity-based model in the near-wall region, but have different maximum values. Compared with the mean-quantity-based model, the optimised results enhance the consistency between the resolvent and DNS results significantly. Based on the optimised results, a new modelling framework is further abstracted, leaving only one to-be-modelled parameter of the maximum value of the eddy-viscosity profile. This parameter follows distinctive rules with spanwise flow scales, based on which a simplified predictive model is constructed. The resolvent modes predicted by the new model exhibit high consistency with SPOD modes, which are essentially comparable to the optimised results for wide ranges of streamwise and spanwise scales.

The presence of dispersed-phase droplets can result in a notable increase in a system's drag. However, our understanding of the mechanism underlying this phenomenon remains limited. In this study, we use three-dimensional direct numerical simulations with a modified multi-marker volume-of-fluid method to investigate liquid–liquid two-phase turbulence in a Taylor–Couette geometry. The dispersed phase has the same density and viscosity as the continuous phase. The Reynolds number $Re\equiv r_i\omega _i d/\nu$ is fixed at 5200, the volume fraction of the dispersed phase is up to $40\,\%$, and the Weber number $We\equiv \rho u^2_\tau d/\sigma$ is approximately 8. It is found that the increase in the system's drag originates from the contribution of interfacial tension. Specifically, droplets experience significant deformation and stretching in the streamwise direction due to shear near the inner cylinder. Consequently, the rear end of the droplets lags behind the fore head. This causes opposing interfacial tension effects on the fore head and rear end of the droplets. For the fore head of the droplets, the effect of interfacial tension appears to act against the flow direction. For the rear end, the effect appears to act in the flow direction. The increase in the system's drag is attributed primarily to the effect of interfacial tension on the fore head of the droplets which leads to the hindering effect of the droplets on the surrounding continuous phase. This hindering effect disrupts the formation of high-speed streaks, favouring the formation of low-speed ones, which are generally associated with higher viscous stress and drag of the system. This study provides new insights into the mechanism of drag enhancement reported in our previous experiments.

In this paper, aerobreakup in the stagnation region of high-Mach-number flow over a bluff body is studied with experiments and computations. Water drops of diameter 0.51–2.30 mm were acoustically levitated at sea level along the flight path of a rectangular $100\ {\rm mm} \times 150\ {\rm mm}$ rail-gun launched projectile. This enabled the study of aerobreakup at high Mach (3.03–5.12), post-shock Mach (1.5–1.9), Weber $(5 \times 10^4\unicode{x2013}4 \times 10^5)$ and Reynolds $(6 \times 10^4\unicode{x2013}3 \times 10^5)$ numbers. High-speed backlit shadowgraphy is used to record the flow structure. Computations are made for two cases, and it was found that the drop behaviour is not dominated by viscous or surface-tension effects and can be adequately captured by treating the gas as calorically perfect with the ratio of specific heats set to 1.3 to account for thermochemical effects. To assess drop surface stability at early breakup times, results from Newton's inclination method are used to determine the flow along the drop surface and input to a linear-stability analysis; from this, it was found that viscosity and surface tension can be neglected. Moreover, the acceleration term dominates the shear term at the stagnation point, a point accentuated as a drop flattens; this relation inverts closer to the drop equator. Linear-stability analysis was insufficient for modelling late-stage aerobreakup because the predicted wavelengths were too small and the expected aerobreakup times were non-physically short. To address this discrepancy, a nonlinear instability model with constant-rate growth is used that treats the accelerated drop surface as analogous to bubbles rising through a liquid; agreement with computations is good.

Turbulent mixing is a pivotal phenomenon in fusion research with profound implications for energy gain. A Reynolds-averaged Navier–Stokes model capable of predicting realistic mixing transition processes is of significant importance for fusion applications, yet such a model remains elusive. This work addresses the limitations of prevalent global transition criteria, proposing a new idea to quantify local transition characteristics based on the mixing state, recognizing its direct relevance to fusion reaction rates. We delve into the description and analysis of the spatiotemporal evolution of the mixing state and its interplay with the transition process. Then, a local transition indicator is developed and compared with conventional global criteria using the large-eddy simulation (LES) of Rayleigh–Taylor turbulent mixing. Building upon this foundation, we introduce a novel eddy viscosity model based on the local transition indicator. A posterior assessment using LES data validates that it significantly outperforms standard gradient transport models during the transition stage. Consequently, we integrate this new eddy viscosity model with the Besnard–Harlow–Rauenzahn model to construct a comprehensive transition model, which demonstrates reasonably good performance in comparison with LES results. This work paves the way for future research in developing advanced modelling strategies that can effectively address the complexities of transitional flows in fusion engineering applications.

Developing large-eddy simulation (LES) wall models for separated flows is challenging. We propose to leverage the significance of separated flow data, for which existing theories are not applicable, and the existing knowledge of wall-bounded flows (such as the law of the wall) along with embedded learning to address this issue. The proposed so-called features-embedded-learning (FEL) wall model comprises two submodels: one for predicting the wall shear stress and another for calculating the eddy viscosity at the first off-wall grid nodes. We train the former using the wall-resolved LES (WRLES) data of the periodic hill flow and the law of the wall. For the latter, we propose a modified mixing length model, with the model coefficient trained using the ensemble Kalman method. The proposed FEL model is assessed using the separated flows with different flow configurations, grid resolutions and Reynolds numbers. Overall good a posteriori performance is observed for predicting the statistics of the recirculation bubble, wall stresses and turbulence characteristics. The statistics of the modelled subgrid-scale (SGS) stresses at the first off-wall grids are compared with those calculated using the WRLES data. The comparison shows that the amplitude and distribution of the SGS stresses and energy transfer obtained using the proposed model agree better with the reference data when compared with the conventional SGS model.

Convective flows near a cylindrical solid inclusion in a fluid-saturated porous medium heated from above are studied using the Darcy–Boussinesq equations. The impermeability condition is imposed on the inclusion surface. Two-dimensional convective flows uniform in the direction of the cylinder axis are considered. An Oseen-like approximation is implemented, however, different from the conventional Oseen approximation, quasilinearization is applied to the nonlinear terms in the energy equation and not in the momentum equation. It is shown that, when the thermal conductivity of the inclusion is higher than that of the fluid, the convective flow at a distance from the inclusion larger than the inclusion size takes the form of horizontal vortices directed away from the inclusion. In the case of low thermal conductivity of the inclusion, the direction of convective circulation is opposite: in the horizontal plane passing through the cylinder axis, the fluid is leaking to the inclusion.