Discontinuous shear-thickening (DST) fluids exhibit unique instability properties in a wide range of flow conditions. We present numerical simulations of a scalar model for DST fluids in a planar simple shear using the smoothed particle hydrodynamics approach. The model reproduces the spatially homogeneous instability mechanism based on the competition between the inertial and microstructural time scales, with good congruence to the theoretical predictions. Spatial inhomogeneities arising from a stress-splitting instability are rationalised within the context of local components of the microstructure evolution. Using this effect, the addition of non-locality in the model is found to produce an alternative mechanism of temporal instabilities, driven by the inhomogeneous pattern formation. The reported arrangement of the microstructure is generally in agreement with the experimental data on gradient pattern formation in DST. Simulations in a parameter space representative of realistic DST materials resulted in aperiodic oscillations in measured shear rate and stress, driven by formation of gap-spanning frictional structures.

Underwater capillary tubes fill rapidly with the surrounding liquid. Capillary and hydrostatic pressures push the liquid into the tube, causing the air to exit as bubbles at the other end. We study the natural filling process of a vertical capillary tube immersed in water during several bubble formation events. A theoretical model is proposed that captures the dynamics of the meniscus inside the capillary tube as it fills with water. We find good agreement with the experimental data that describe this special case of spontaneous flow using a dynamic contact angle model based on molecular kinetic theory.

We investigate the influence of the Reynolds number on the spatial development of an incompressible planar jet. The study relies on direct numerical simulations (DNS) at inlet Reynolds numbers between $500 \leqslant Re \leqslant 13\,500$, being the widest range and the largest values considered so far in DNS. At the lowest $Re$, the flow is transitional and characterised by large quasi-two-dimensional vortices; at the largest $Re$, the flow reaches a fully turbulent regime with a well-developed self-similar region. We provide a complete description of the flow, from the instabilities in the laminar near-inlet region, to the self-similar regime in the turbulent far field. At the inlet, the leading destabilisation mode is sinusoidal/asymmetric at low Reynolds number and varicose/symmetric at large Reynolds number, with both modes coexisting at intermediate $Re$. In the far field, the mean and fluctuating statistics converge to self-similar profiles only for $Re\geqslant 4500$; the flow anisotropy, the budget of the Reynolds stresses and the energy spectra are addressed. The spreading of the jet is quantified via the turbulent–non-turbulent interface (TNTI). We find that the thickness of the turbulent region, and the shape and fractal dimension of the TNTI become $Re$-independent for $Re \geqslant 4500$. Comparisons with previous numerical and experimental works are provided whenever available.

A liquid film flowing down a fibre becomes unstable, leading to the formation of droplets that travel downstream. The droplet spacing and speed depend on the flow rate for a given nozzle and fibre radii. We show that fibre morphology further modifies the droplet spacing. In particular, we study the effect of the size of the beads in a granular chain on the evolution of the film thickness. We show that, when the size of the bead exceeds a critical value, the selection mechanism for instability modes is modified from regularly spaced droplets to coarsening by droplet merging. Droplet formation for flow over a single bead on the fibre is modified successively over subsequent beads in the downstream. Further, we show that if the perturbation in the flow produced by the bead is introduced as a velocity perturbation at the nozzle inlet, the formation of droplets on the fibre is qualitatively similar to that for the bead.

This study explores the Faraday instability as a mechanism to enhance heat transfer in two-phase systems by exciting interfacial waves through resonance. The approach is particularly applicable to reduced-gravity environments where buoyancy-driven convection is ineffective. A reduced-order model, based on a weighted residual integral boundary layer method, is used to predict interfacial dynamics and heat flux under vertical oscillations with a stabilising thermal gradient. The model employs long-wave and one-way coupling approximations to simplify the governing equations. Linear stability theory informs the oscillation parameters for subsequent nonlinear simulations, which are then qualitatively compared against experiments conducted under Earth’s gravity. Experimental results show up to a 4.5-fold enhancement in heat transfer over pure conduction. Key findings include: (i) reduced gravity lowers interfacial stability, promoting mixing and heat transfer; and (ii) oscillation-induced instability significantly improves heat transport under Earth’s gravity. Theoretical predictions qualitatively validate experimental trends in wavelength-dependent enhancement of heat transfer. Quantitative discrepancies between model and experiment are rationalised by model assumptions, such as neglecting higher-order inertial terms, idealised boundary conditions, and simplified interface dynamics. These limitations lead to underprediction of interface deflection and heat flux. Nevertheless, the study underscores the value of Faraday instability as a means to boost heat transfer in reduced gravity, with implications for thermal management in space applications.

We consider laminar forced convection in a shrouded longitudinal-fin heat sink (LFHS) with tip clearance, as described by the pioneering study of (Sparrow, Baliga & Patankar 1978 J. Heat Trans. 100). The base of the LFHS is isothermal but the fins, while thin, are not isothermal, i.e. the conjugate heat transfer problem is of interest. Whereas Sparrow et al. numerically solved the fully developed flow and thermal problems for a range of geometries and fin conductivities, we consider the physically realistic asymptotic limit where the fins are closely spaced, i.e. the spacing is small relative to their height and the clearance above them. The flow problem in this limit was considered by (Miyoshi et al. 2024, J. Fluid Mech. 991, A2), and we consider the corresponding thermal problem. Using matched asymptotic expansions, we find explicit solutions for the temperature field (in both the fluid and fins) and conjugate Nusselt numbers (local and average). The structure of the asymptotic solutions provides further insight into the results of Sparrow et al.: the flow is highest in the gap above the fins, hence heat transfer predominantly occurs close to the fin tips. The new formulas are compared with numerical solutions and are found to be accurate for practical LFHSs. Significantly, existing analytical results for ducts are for boundaries that are either wholly isothermal, wholly isoflux or with one of these conditions on each wall. Consequently, this study provides the first analytical results for conjugate Nusselt numbers for flow through ducts.

The constant temperature and constant heat flux thermal boundary conditions, both developing distinct flow patterns, represent limiting cases of ideally conducting and insulating plates in Rayleigh–Bénard convection flows, respectively. This study bridges the gap in between, using a conjugate heat transfer (CHT) set-up and studying finite thermal diffusivity ratios $\kappa _s \! / \! \kappa _f$ to better represent real-life conditions in experiments. A three-dimensional Rayleigh–Bénard convection configuration including two fluid-confining plates is studied via direct numerical simulations given a Prandtl number ${Pr}=1$. The fluid layer of height $H$ and horizontal extension $L$ obeys no-slip boundary conditions at the two solid–fluid interfaces and an aspect ratio of ${\Gamma }=L/H=30$ while the relative thickness of each plate is ${\Gamma _s}=H_s/H=15$. The entire domain is laterally periodic. Here, different $\kappa _s \! / \! \kappa _f$ are investigated for moderate Rayleigh numbers $Ra=\left \{ 10^4, 10^5 \right \}$. We observe a gradual shift of the size of the characteristic flow patterns and their induced heat and mass transfer as $\kappa _s \! / \! \kappa _f$ is varied, suggesting a relation between the recently studied turbulent superstructures and supergranules for constant temperature and constant heat flux boundary conditions, respectively. Performing a linear stability analysis for this CHT configuration confirms these observations theoretically while extending previous studies by investigating the impact of a varying solid plate thickness $\Gamma _s$. Moreover, we study the impact of $\kappa _s \! / \! \kappa _f$ on both the thermal and viscous boundary layers. Given the prevalence of finite $\kappa _s \! / \! \kappa _f$ in nature, this work is a starting point to extend our understanding of pattern formation in geo- and astrophysical convection flows.

The ‘vorticity transport’ theory by G. I. Taylor states that, in two-dimensional (2-D) turbulent flows, it is not the momentum of the eddies which is conserved from one step of their random walk to the other (the so-called Reynolds–Prandtl analogy), but their vorticity, implying that the conservation laws for the time-averaged profiles for the velocity $u$ and concentration of a passive scalar $c$ must be different. This theory predicts that, across a 2-D wake or a jet, both fields (scaled by their maximal value) are exactly related to each other by $u=c^2.$ We reexamine critically this problem on hand of several experiments with plane and round turbulent jets seeded with high and low diffusing scalars, and conclude that the microscopic equations for $u$ and $c$ are identical, but that the differences between the $u$- and $c$-fields is a genuine mixing problem, sensitive to the dimensionality of the flow and to the intrinsic diffusivity of the scalar $D$, through the Schmidt number ($Sc=\nu /D$) dependence of the flow coarsening scale. We observe that $u=c^{\beta }$ with $\beta =2$ in plane jets irrespective of $Sc$, $\beta =3/2$ in round jets at $Sc=1$ and $\beta =1$ in round jets for $Sc\to \infty$. We explain why, because measurements dating back to the 1930s–40s were all made for heat transport in air ($Sc\approx 1$), agreement with Taylor‘s vision was only coincidental. The experiments and the new representation proposed here are strictly at odds with Reynolds’ analogy, although essentially an adaptation of it to eddies transporting momentum and mass, but liable to exchange mass with a smooth reservoir along their Brownian path.

Hydrodynamic density functional theory (DFT) is applied to analyse dynamic contact angles of droplets to assess its predictive capability regarding wetting phenomena at the microscopic scale and to evaluate its feasibility for multiscale modelling. Hydrodynamic DFT incorporates the influence of fluid–fluid and solid–fluid interfaces into a hydrodynamic theory by including a thermodynamic model based on classical DFT for the chemical potential of inhomogeneous fluids. It simplifies to the isothermal Navier–Stokes equations far away from interfaces, thus connecting microscopic molecular modelling and continuum fluid dynamics. In this work, we use a Helmholtz energy functional based on the perturbed-chain statistical associating fluid theory (PC-SAFT) and the viscosity is obtained from generalised entropy scaling, a one-parameter model which takes microscopic information of the fluid and solid phase into account. Deterministic (noise-free) density and velocity profiles reveal wetting phenomena including different advancing and receding contact angles, the transition from equilibrium to steady state and the rolling motion of droplets. Compared with a viscosity model based on bulk values, generalised entropy scaling provides more accurate results, which stresses the importance of including microscopic information in the local viscosity model. Hydrodynamic DFT is transferable as it captures the influence of different external forces, wetting strengths and (molecular) solid roughness. For all results, good quantitative agreement with non-equilibrium molecular dynamics simulations is found, which emphasises that hydrodynamic DFT is able to predict wetting phenomena at the microscopic scale.

Wall-resolved large-eddy simulations of flow over an axisymmetric body of revolution (DARPA SUBOFF bare model) at $ \it{Re}_L=1.1\times 10^6$ are performed to investigate wall pressure fluctuations under the combined effects of transverse curvature and varying pressure gradients. Due to the coexistence of convex and concave streamwise curvatures, the flow in the stern region features alternating zones of favourable and adverse pressure gradients (APGs). The simulation validates experimental findings by Balantrapu et al. (2023, J. Fluid Mech., vol. 960, A28), confirming that in APG-dominant axisymmetric boundary layers without streamwise curvatures, the root mean square wall pressure fluctuations ($p_{w,rms}$) decrease downstream alongside the wall shear stress ($\tau _w$), maintaining a constant ratio $p_{w,rms}/\tau _{w}$. This study further finds that when streamwise curvatures and strong streamwise pressure gradient variations present, this relationship breaks down, suggesting that $\tau _w$ is not the dominant contributor to wall pressure fluctuations. Instead, the local maximum Reynolds shear stress $-\rho \langle u_su_n\rangle _{max }$ emerges as a more robust pressure scaling parameter. Normalising the wall pressure spectra by $-\rho \langle u_su_n\rangle _{max }$ yields better collapse across the entire stern region compared to conventional inner or mixed scaling methods. The magnitude and location of $-\rho \langle u_su_n\rangle _{max }$ significantly influence the spectral levels of wall pressure fluctuations across different frequency bands. As the turbulence intensity and $-\rho \langle u_su_n\rangle _{max }$ shift away from the wall, outer-layer structures – with larger spatial and temporal scales – dominate the coherence of wall pressure fluctuations. This mechanism drives sustained attenuation of high-frequency pressure fluctuations and a simultaneous increase in both the streamwise and transverse correlation lengths of wall pressure fluctuations over the stern region.