The influence of miscibility and liquid wettability during droplet impact onto thin wall films is investigated experimentally. Despite similar liquid properties and impact conditions, differences in the splashing limit, in the crown extension and in the duration of the ascending phase are observed. These differences are related to the interfacial tension of the droplet/wall-film liquid pairs, which is linked to their miscibility and wettability. More precisely, by calculating the crown surface energy, we show that the energy stored in the interface between droplet and wall film (if any) is not negligible and leads to smaller crown extensions and tendentially the need for more kinetic energy to initiate splashing. Similarly, by calculating a modified capillary time taking into account all surface and interfacial tensions, we show that the interfacial tension acts as a non-negligible recoiling force, which reduces the duration of the ascending phase. The dynamics of this ascending phase is well captured for different wall-film thicknesses if accounting for the variations of the liquid masses in movement. Overall, droplet/wall-film interactions can be seen as inertio-capillary systems where the interfacial tension between droplet and wall film plays a significant role in the storage of energy and in the crown kinetics during the impact process. In addition, this analysis highlights that viscous losses have already a significant effect during the crown extension phase, by dissipating almost half of the initial energies for droplet impact onto thin wall films, and most likely by influencing the capillary time scale through damping.

Tiny drops of millimetre size are known to bounce on a solid surface if the surface is superhydrophobic. Recent experiments show that bouncing can occur even on hydrophilic surfaces under conditions where the drop is supported on a thin cushion of gas preventing it from making contact with the surface. We present a detailed insight into this observation by simulating bouncing dynamics of a drop on a flat solid surface using axisymmetric direct numerical simulations. The dynamics of drop motion is governed by three important dimensionless parameters, namely, Reynolds number, $Re$, Weber number, $We$, and capillary number, $Ca_g$. We generate a phase diagram in the $We\text {--}Re$ plane separating the wettability-independent (non-contact bouncing) and wettability-dependent (contact bouncing) regions. We show that $We=2.14$ is the optimum value of Weber number which can support a gas cushion for the widest range of Reynolds numbers. The phase diagram is further divided into five sub-regions based on the shape of the drop and the gas film beneath it. The simulations can reproduce experimentally reported gas films of ${\sim }1\ \mathrm {\mu }\textrm {m}$ with excellent agreement spatially and temporally. Simulations also reproduce well-known scaling laws for a variety of parameters characterising the gas film. New scaling laws for the radial extent of the gas film as well as time taken for impact are derived. For higher Weber and Reynolds numbers, a bouncing drop captures a gas bubble inside it consistent with simple experiments carried out for water drops bouncing on superhydrophobic surfaces.

Surfactants at fluid interfaces not only lower and cause gradients in surface tension but can induce additional surface rheological effects in response to dilatational and shear deformations. Surface tension and surface viscosities are both functions of surfactant concentration. Measurement of surface tension and determination of its effects on interfacial flows are now well established. Measurement of surface viscosities, however, is notoriously difficult. Consequently, quantitative characterization of their effects in interfacial flows has proven challenging. One reason behind this difficulty is that, with most existing methods of measurement, it is often impossible to isolate the effects of surface viscous stresses from those due to Marangoni stresses. Here, a combined asymptotic and numerical analysis is presented of the pinch-off of a surfactant-covered Newtonian liquid jet. Similarity solutions obtained from slender-jet theory and numerical solutions are presented for jets with and without surface rheological effects. Near pinch-off, it is demonstrated that Marangoni stresses become negligible compared to other forces. The rate of jet thinning is shown to be significantly lowered by surface viscous effects. From analysis of the dynamics near the pinch-off singularity, a simple analytical formula is derived for inferring surface viscosities. Three-dimensional, axisymmetric simulations confirm the validity of the asymptotic analyses but also demonstrate that a thinning jet traverses a number of intermediate regimes before eventually entering the final asymptotic regime.

We study the dynamics of dilute, slightly negatively buoyant, millimetre-size spherical particles fully suspended in a smooth-wall open channel flow. The Reynolds number is $Re_{\tau } = 570$ and the particle Stokes number is ${{\textit {St}}}^{+} = 15$. Particle image velocimetry and tracking are used to obtain simultaneous, time-resolved flow fields and particle trajectories. Particles travel at a lower mean velocity than the fluid: in the log layer this is due to the oversampling of slow fluid regions, but closer to the wall the cause is instantaneous slip between particles and fluid. The particle Reynolds stresses exceed those of the fluid. Near the wall, the particle streamwise diffusivity is larger than the momentum diffusivity, while the opposite is true for the wall-normal component. The particle transport is strongly linked to ejections, while the role of sweeps is marginal, and there is no evidence of turbophoresis. The concentration profile follows a power law with a shallower slope than predicted by equilibrium theories that neglect particle inertia. Upward-/downward-moving particles display positive/negative mean streamwise acceleration due to the particle–fluid slip. The particles that contact the wall are faster than the local fluid both before reaching the wall and after leaving it. Therefore, they are decelerated by drag and pushed downward by shear-induced lift. The durations of wall contact follow exponential distributions with characteristic time scale close to the particle response time. Lift-offs coincide with particles meeting a fluid ejection. These observations emphasize the competing effects of inertia and gravity.

Direct numerical simulation of flow in a turbulent channel with a random rough bottom wall is performed at friction Reynolds number $Re_{\tau }=400$ and $600$. The rough surface corresponds to the experiments of Flack et al. (Flow Turbul. Combust., vol. 104, 2020, pp. 317–329). The computed skin-friction coefficients and the roughness functions show good agreement with experimental results. The double-averaging methodology is used to investigate mean velocity, Reynolds stresses, dispersive flux and mean momentum balance. The roll-up of the shear layer on the roughness crests is identified as a primary contributor to the wall-normal momentum transfer. The mean-square pressure fluctuations increase in the roughness layer and collapse onto their smooth-wall levels away from the wall. The dominant source terms in the pressure Poisson equation are examined. The rapid term shows that high pressure fluctuations observed in front of and above the roughness elements are mainly due to the attached shear layer formed upstream of the protrusions. The contribution of the slow term is smaller. The slow term is primarily increased in the troughs and in front of the roughness elements, corresponding to the occurrence of quasi-streamwise vortices and secondary vortical structures. The mean wall shear on the rough surface is highly correlated with the roughness height, and depends on the local roughness topography. The probability distribution function of wall shear stress fluctuations is consistent with higher velocities at roughness crests and reverse flow in the valley regions. Extreme events are more probable due to the roughness. Events with comparable magnitudes of the streamwise and spanwise wall shear stress occur more frequently, corresponding to a more isotropic vorticity field in the roughness layer.

While the dynamics of Newtonian fluid drops on an inclined non-wettable surface has been widely reported, that of viscoplastic drops is less well known. Combining experimental and theoretical analysis, we reveal unique behaviours of viscoplastic drops on an inclined superhydrophobic surface: (i) decoupled rolling, sliding and sticking motions and (ii) two distinct rolling modes, i.e. viscous rolling and rigid-body rolling. First, determined by the relative magnitudes of gravitational, yield and adhesive stresses, a viscoplastic drop rolls, slides or sticks on a superhydrophobic surface. To the best of our knowledge, this is the first distinct differentiation of viscoplastic drop motions on a superhydrophobic surface, which is a clear departure from the previous observations of Newtonian drops on superhydrophobic surfaces and viscoplastic drops on hydrophilic/hydrophobic surfaces. We subcategorized two types of rolling as liquid-like viscous rolling and solid-like rigid-body rolling. With a low Deborah number (i.e. dimensionless viscoplastic relaxation time), the viscoplastic drop shows a viscous rolling as a Newtonian drop does on an inclined surface. With a high Deborah number, however, the viscoplastic drop does not have enough time to be ‘fluid’. Consequently, the ellipsoidal drop deforms to be more spherical as it goes down the inclined surface, and tumbles, as if a solid body initiates its rolling by ‘tipping’.

Shock oscillations within a model two-dimensional axisymmetric inlet with a constant area isolator are investigated under the condition of maintaining an unseparated boundary layer throughout the inlet/isolator section. Power spectral densities of the wall-pressure fluctuations beneath each shock leg intersecting the isolator surface exhibited a very low frequency broadband oscillation in the 10–100 Hz range as well as a very high frequency broadband oscillations above 10 kHz. Whereas the high frequency oscillations are attributed to the incoming boundary layer fluctuations, detailed investigations into the pressure fluctuation communication pathways within the isolator and their length scale of communication are made to elucidate the origin of the low frequency fluctuations. It was found that the downstream propagation of pressure fluctuations is primarily by the convection of the boundary layer structures and this communication occurred over several boundary layer thicknesses. The upstream propagation occurs through acoustic waves that extend over a distance of one local boundary layer thickness. Based on this understanding, a physical model is constructed, which makes an accurate prediction of pressure power spectrum of the low frequency shock wave oscillations; the model predictions also favourably compare with the shock oscillations in external shock boundary layer interactions without shock-induced flow separation.

Several studies concerning the turbulent pipe flow of generalized Newtonian (GN) fluids may be found in the literature, but not for channel flow, although that has been extensively studied for other types of non-Newtonian fluids, such as those with viscoelastic effects. Direct numerical simulations corresponding to statistically converged turbulent channel flow of GN fluids at a low frictional Reynolds number have been performed. The shear-dependent viscosity is introduced through the Carreau fluid model, and results corresponding to the Newtonian fluid case are compared to those of moderate shear-thickening and shear-thinning fluid behaviour. The different statistics studied reveal that shear-dependent fluid rheology appears mainly to affect the flow within the inner layer region and with shear-thinning behaviour; suppressing near-wall structures such as quasi-streamwise vortices and low-speed streaks, inhibiting turbulence generating events and leading to different drag reduction features. These include: enhancement of streamwise turbulence intensity and suppression of the other cross-sectional intensities, decrease of the Reynolds shear stress (leading to a lessening in turbulent production), decrease in energy redistribution between individual components of the Reynolds stress tensor through the velocity–pressure gradient term and overall increase in turbulence anisotropy at both small and large scales. In particular, it is noted that at the channel centre ‘rod-like’ turbulence states, a known low-Reynolds-number behaviour, are more clearly seen with shear-thinning fluid rheology.

Saturated film boiling over an elliptical heater is investigated in the mixed regime considering both aiding and orthogonal liquid flow configurations relative to gravity. A computational framework developed for phase change problems on unstructured grids based on a coupled level set and volume of fluid interface capturing method is used to characterize interface evolution and vapour wake dynamics alongside quantifying heat transfer at low values of the Froude number (Fr). The influence of hydrodynamic and thermal conditions along with cross-flow direction for a fixed heater geometry manifests in the form of varied wake profiles with the quasi-steady nature of film boiling lost as Fr increases. Additionally, while the heater aspect ratio affects the rate of vapour infusion into the wake, the heater orientation significantly affects the film boiling behaviour. With horizontal cross-flow, higher angles of incidence entail a lower influence of flow inertia while augmenting buoyancy-driven vapour removal leading to enhanced heat transfer compared to aiding flow under certain cases, and adding a further dimension to the interplay between buoyancy and inertia. Similarly an anomalous impairment of heat transfer with an increase in cross-flow velocity arises from a competing influence of buoyancy and drag as an artefact of heater and cross-flow configurations. The mutual coupling of liquid and vapour wakes is also discussed in detail under such conditions. Finally, a shape factor $(\psi )$ is proposed to comprehensively predict the heat transfer in conjunction with correlations for a circular heater, and determined based on the effect of the elliptical geometry in the mixed regime.

We study the longitudinal dispersion of a passive tracer by a two-dimensional pressure-driven flow through a layer of heterogeneous porous rock which is bounded above and below by impermeable seal rock. We assume there are localised regions of different permeability at random vertical positions within an otherwise uniform layer. This leads to a Fickian-type dispersion (Eames & Bush, Proc. R. Soc. Lond. A, vol. 455, issue 1990, 1999, pp. 3665–3686) and a shear near the boundaries (Rabinovich et al., Phys. Rev. E, vol. 86, issue 4, 2012, 046601). We illustrate this effect in a long two-dimensional layer, consisting of $(a)$ long and thin lenses and $(b)$ elliptical lenses, using expressions for depth-dependent mean speed and dispersivity to derive a depth-averaged transport equation for the flow. We derive asymptotic solutions for the layer-averaged dispersal of tracer, showing that at long times the spreading of the tracer is controlled by the shear. We discuss the importance of our results for the interpretation of tracer dispersal tests in layered permeable rocks.

The mechanism underpinning the generation of screech tones has remained an open question for many years. In this paper, direct experimental observations of the shock-leakage mechanism first proposed by Manning & Lele (AIAA Paper 1998, p. 282) are presented. Ultra-high-speed schlieren images are filtered to preserve only upstream-propagating components, with the upstream motion of the shock tip and subsequent emission of an acoustic wave visible for a number of operating conditions. The flow visualizations are supported by the ray-tracing model for shock leakage of Shariff & Manning (Phys. Fluids., vol. 25, issue 7, 2013, 076103), applied to velocity fields corresponding to a reconstructed screech cycle. The predictions of the model, when applied to real data, are in close agreement with the phenomena observed in the flow visualizations. It is demonstrated that shock leakage does not necessarily occur either at the point of maximum wave amplitude or maximum vorticity fluctuation. While the first point of shock leakage is shown to vary between cases, sound emission from multiple sources is observed for most cases considered. Finally, it is shown that variations in vortex strength captured in the velocity data are sufficient to explain variation in shock-leakage location observed in the flow visualization data.