Experiments were performed to further investigate a quadratic interaction between stationary and travelling cross-flow modes that was revealed in the previous experiment by Corke et al. (J. Fluid Mech., vol. 856, 2018, pp. 822–849) in the boundary layer on a sharp right-circular cone at an angle of attack at Mach 6.0. As with the previous experiment, passive discrete roughness was applied near the cone tip, just upstream of Branch I of the linear stability neutral curve for stationary cross-flow modes. The passive roughness consisted of indentations (dimples) that were evenly spaced azimuthally to excite a specific azimuthal wavenumber. A plasma actuator was located just downstream of the discrete roughness array. This was designed to produce an azimuthally uniform unsteady disturbance with a frequency that was at the centre of the band of most amplified travelling cross-flow modes. Measurements consisted of off-wall azimuthal profiles of mean and fluctuating total pressure at different axial locations. Spectra of total-pressure fluctuations verified the receptivity of the boundary layer to the unsteady excitation. This affected the azimuthal and streamwise development of the stationary cross-flow modes, with a general effect to move the transition location upstream by approximately 16 %. The quadratic interaction between the stationary and travelling cross-flow modes was further enhanced by the excitation of the travelling cross-flow mode. This was particularly evident by an enlarged band of azimuthal wavenumbers over which a significant triple phase locking existed. The significantly enlarged range of wavenumber sum and difference interactions offered a mechanism for rapid spectral broadening that could account for the hastened transition by the addition of unsteady disturbances.

‘Freeze-out’ of amplitude growth, i.e. the amplitude growth stagnation of a shocked helium–air interface, is realized through a reflected shock, which produces baroclinic vorticity of the opposite sign to that deposited by the first shock. Theoretically, a model is constructed to calculate the relations among the initial parameters for achieving freeze-out. In particular, if the amplitude growth is within the linear regime at the arrival of the reflected shock, the time interval between the impacts of two shock waves is linearly related to the initial perturbation wavelength, and is independent of the initial perturbation amplitude. Experimentally, an air–SF$_6$ (or air–argon) plane interface is adopted to produce a weak reflected shock. Seven experimental runs with specific initial conditions are examined. For all cases, freeze-out is achieved after the reflected shock impact under the designed conditions.

Air exchange between people has emerged in the COVID-19 pandemic as the important vector for transmission of the SARS-CoV-2 virus. We study the airflow and exchange between two unmasked individuals conversing face-to-face at short range, which can potentially transfer a high dose of a pathogen, because the dilution is small when compared to long-range airborne transmission. We conduct flow visualization experiments and direct numerical simulations of colliding respiratory jets mimicking the initial phase of a conversation. The evolution and dynamics of the jets are affected by the vertical offset between the mouths of the speakers. At low offsets the head-on collision of jets results in a `blocking effect', temporarily shielding the susceptible speaker from the pathogen carrying jet, although, the lateral spread of the jets is enhanced. Sufficiently large offsets prevent the interaction of the jets. At intermediate offsets (8-10 cm for 1 m separation), jet entrainment and the inhaled breath assist the transport of the pathogen-loaded saliva droplets towards the susceptible speaker's mouth. Air exchange is expected, in spite of the blocking effect arising from the interaction of the respiratory jets from the two speakers.

We present a detailed comparison of the rheological behaviour of sheared sediment beds in a pressure-driven, straight channel configuration based on data that were generated by means of fully coupled, grain-resolved direct numerical simulations and experimental measurements previously published by Aussillous et al. (J. Fluid Mech., vol. 736, 2013, pp. 594–615). The highly resolved simulation data allow us to compute the stress balance of the suspension in the streamwise and vertical directions and the stress exchange between the fluid and particle phases, which is information needed to infer the rheology, but has so far been unreachable in experiments. Applying this knowledge to the experimental and numerical data, we obtain the statistically stationary, depth-resolved profiles of the relevant rheological quantities. The scaling behaviour of rheological quantities such as the shear and normal viscosities and the effective friction coefficient are examined and compared to data coming from rheometry experiments and from widely used rheological correlations. We show that rheological properties that have previously been inferred for annular Couette-type shear flows with neutrally buoyant particles still hold for our set-up of sediment transport in a Poiseuille flow and in the dense regime we found good agreement with empirical relationships derived therefrom. Subdividing the total stress into parts from particle contact and hydrodynamics suggests a critical particle volume fraction of 0.3 to separate the dense from the dilute regime. In the dilute regime, i.e. the sediment transport layer, long-range hydrodynamic interactions are screened by the porous medium and the effective viscosity obeys the Einstein relation.

By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor–Couette turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviours, i.e. the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction for O/W or for W/O. However, for W/O it is about $50\,\%$ larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviours are expected to be caused by the presence of surface-active contaminants from the walls of the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry and reach conclusions on emulsions where interfaces are fully covered by the surfactant. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a $-6/5$ scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich (Physicochemical Hydrodynamics, Prentice-Hall, 1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov (Dokl. Akad. Nauk. SSSR, vol. 66, 1949, pp. 825–828). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviours in dynamic emulsification, and connects them.

Studies on the evaporation of multicomponent droplets have revealed complex and important physical mechanisms, induced by preferential phase change or mediated by external vapour sources, e.g. occurrence of density-driven flows, phase separation, transient Marangoni flow and solutal effects, etc. With the addition of hygroscopic salts, the adhesive property of the droplet can be tuned, and the direction of water vapour mass flux reversed. This paper focuses on the dynamics of hygroscopic aqueous solution droplets, and analyses the interplay between different physical processes. Specifically, a lubrication-type model is established with the assumption of a precursor film in front of the three-phase contact line, which indicates qualitative agreement with our experimental results, quantitatively with respect to the initial spreading rates and qualitatively with respect to the overall behaviour. We derive the expression of absorptive mass flux combining the balance of chemical potential across the solution–air interface and the Hertz–Knudsen equation. Depending on the droplet state and the ambient condition, evaporation or vapour absorption occurs. The evaporative/absorptive mass flux varies both spatially and temporally as the droplet approaches equilibrium. It is demonstrated that the dominating mechanisms, i.e. capillary, thermal Marangoni and solutal Marangoni, compete with each other, and lead to diverse droplet dynamics at different stages of evaporation or vapour absorption. The findings shed light on the physical processes within droplets with both positive and negative interfacial mass fluxes, and provide rational explanations for the experimental observations.

Direct numerical simulations are carried out to study the effect of finite Weissenberg number up to $Wi=16$ on laminar and turbulent channel flows of an elastoviscoplastic (EVP) fluid, at a fixed bulk Reynolds number of $2800$. The incompressible flow equations are coupled with the evolution equation for the EVP stress tensor by a modified Saramito model that extends both the Bingham viscoplastic and the finite extensible nonlinear elastic-Peterlin (FENE-P) viscoelastic models. In turbulent flow, we find that drag decreases with both the Bingham and Weissenberg numbers, until the flow laminarises at high enough elastic and yield stresses. Hence, a higher drag reduction is achieved than in the viscoelastic flow at the same Weissenberg number. The drag reduction persists at Bingham numbers up to 20, in contrast to viscoplastic flow, where the drag increases in the laminar regime compared with a Newtonian flow. Moreover, elasticity affects the laminarisation of an EVP flow in a non-monotonic fashion, delaying it at lower and promoting it at higher Weissenberg numbers. A hibernation phenomenon is observed in the EVP flow, leading to large changes in the unyielded regions. Finally, plasticity is observed to affect both low- and high-speed streaks equally, attenuating the turbulent dissipation and the fragmentation of turbulent structures.

Entropy perturbations generate sound when accelerated/decelerated by a non-uniform flow. Current analytical models provide a good prediction of this entropy noise when the flow cross-sectional area changes are gradual, as is the case for nozzle flows. However, they typically rely on quasi-1-D and isentropic assumptions, and their predictions differ significantly from experimental measurements when sudden area increases are involved. This work uses a theoretical approach to quantitatively identify the main mechanisms responsible for the mismatch. A new form of the acoustic analogy is derived in which the entropy-related source terms are systematically identified for the first time. The theory includes three-dimensional and non-isentropic effects. The approach is applied to the flow through a sudden area expansion, for which the large-scale flow separation creates a recirculation zone. The derived acoustic analogy is simplified for low Mach numbers and frequencies, and solved using a Green's function method. The results provide the first quantitative evidence that the presence and spatial extent of the recirculation zone, rather than the flow non-isentropicity, is the dominant factor causing deviation from predictions from quasi-1-D, isentropic theory.

The supersonic wake of a circular cylinder in Mach 3 flow was studied through high-speed, focussing schlieren photography. The mean and unsteady behaviour of the separated shear layers, the reattachment process, the recompression wave and the early wake are analysed, and discussed in detail. The fluctuations in the wake are stronger and more coherent than those within the approaching shear layers and the recirculation region. The recompression of the shear layers energises the finer scales in the flow which leads to a departure from a $-$1 spectral roll-off observed in the schlieren spectra further upstream. The recompression wave exhibits low-frequency unsteadiness and a ripple-type motion which occurs as it is perturbed by shocklets radiating from the coherent structures in the wake. The wake consists of coherent disturbances with the same characteristic frequency as that for an incompressible flow over a cylinder; however, this instability is suppressed as the wake accelerates, presumably due to increasing compressibility. The primary instability of the wake flow has a characteristic frequency nearly twice that of its incompressible counterpart and it is shown to be driven by the presence of aeroacoustic resonance in the wake. It is also shown that the resonance, which leads to the formation of broadband standing waves in the wake, is the result of an interaction between the wake instabilities and upstream propagating acoustic waves in the wake. The acoustic waves originate upstream of the reattachment region and are believed to be generated by the unsteady separation on the cylinder surface.

Plane Poiseuille flow of a Bingham fluid in a channel armed with a superhydrophobic (SH) lower wall is analysed via a semi-analytical model, accompanied by complementary direct numerical simulations (DNS). The SH surface represents a groovy structure with air trapped inside its cavities. Therefore, the fluid adjacent to the wall undergoes stick–slip conditions. The model is developed based on introducing infinitesimal wall-induced perturbations into the motion equations, followed by Fourier series expansions, and solving the resulting equations as a boundary value problem. The Navier slip law accounts for the slip at the liquid/air interface (assuming the Cassie state). The presented analysis is fairly comprehensive, covering the creeping and inertial regimes for thick channels (via the semi-analytical and DNS solutions). The main dimensionless numbers are the Reynolds ($Re$), Bingham ($Bi$) and slip ($b$) numbers, as well as the groove periodicity length ($\ell$) and the slip area fraction ($\varphi$). By increasing $Bi$, the perturbation and slip velocity fields grow. As $Re$ increases, the perturbation and slip velocity fields become asymmetric. For certain flow parameters, an unyielded plug zone may appear on the SH wall liquid/air interface, while its formation is accelerated by inertial effects. The results classify the regimes of creeping and inertial flows via predicting the onset of the unyielded plug zone formation at the SH wall.