We use particle-based simulation to study the rheology of dense suspensions comprising mixtures of small colloids and larger grains subject to contact, lubrication and Brownian forces. These suspensions exhibit shear thinning at low shear rates and shear thickening at high shear rates. By systematically varying the volume fraction of the two species, we demonstrate a monotonic increase in viscosity when grains are added to colloids, but, conversely, a non-monotonic response in both the viscosity and shear-thickening onset when colloids are added to grains. Both effects are most prominent at intermediate shear rates where diffusion and convection play similar roles in the dynamics. We rationalise these results by measuring the maximum flowable volume fraction as functions of the Péclet number and composition, showing that in extreme cases increasing the solids content can disrupt grain contacts and thus allow a jammed suspension to flow. These results establish a constitutive description for the rheology of bidisperse suspensions across the colloidal-to-granular transition, with implications for flow prediction and control in multicomponent particulate systems.

We investigate the inertial migration of slender, axisymmetric, neutrally buoyant filaments in planar Poiseuille flow over a wide range of channel Reynolds numbers (${\textit{Re}}_c \in [0.5, 2000]$). Filaments exhibit complex oscillatory trajectories during tumbling, with the lateral migration velocity strongly coupled to their orientation. Using a singular perturbation approach, we derive a quasi-analytical expression for the migration velocity that captures both instantaneous and period-averaged behaviour. Finite-size effects are incorporated through solid-phase inertia and the influence of fluid inertia on the orientation dynamics. To validate the theory, we develop a fully resolved numerical framework based on the lattice Boltzmann and immersed boundary methods. The theoretical predictions show good agreement with simulation results over a wide range of Reynolds numbers and confinement ratios. Our model outperforms previous theories by providing improved agreement in predicting equilibrium positions across the investigated range of ${\textit{Re}}_c$, particularly at high values. Notably, it captures the inward migration trend toward the channel centreline at high ${\textit{Re}}_c$ and reveals a new dynamics, including the cessation and resumption of tumbling under strong inertial effects. These findings provide a robust foundation for understanding filament migration and guiding inertial microfluidic design.

Double-diffusive linear instability of a power-law fluid flow through porous media with various heat source functions is studied with two permeable infinite parallel walls. The energy balance equation accounts for viscous dissipation, and the temperature and concentration on the boundaries are assumed to be isothermal and isosolutal, respectively. After non-dimensionalisation with appropriate scales, the governing equations are subjected to infinitesimal disturbances on the base flow, and are used to study the stability theory. The results obtained revealed that for large and small values of the Péclet number ($\textit{Pe}$), an increasing source function ($Q_{\textit{Is}}$) delays the onset of convective motion by diminishing the vertical temperature gradient and hence suppressing buoyancy, resulting in a higher critical Rayleigh number (${\textit{Ra}}_c$). In contrast, the non-uniform source ($Q_{\textit{Ns}}$) can destabilise the system due to localised heating, which increases buoyancy and favours the growth of perturbations. Generally, increasing Lewis number (${\textit{Le}}$) tends to suppress the instability under opposing buoyancy conditions, whereas in the case of aiding buoyancy, a sufficiently large throughflow can counteract this stabilising effect. Under the influence of viscous dissipation and source parameters, a pseudo-plastic fluid is more stable compared to a dilatant fluid. In convective rolls, when thermal and solutal diffusivities are equal, dilatant fluids exhibit multicellular convection. Under aiding buoyancy, streamlines develop three counter-rotating vortices, whereas under opposing buoyancy, the pattern attains a symmetric structure.

Wall pressure fluctuations (WPFs) over aerodynamic surfaces contribute to the physical origin of noise generation and vibrational loading. Understanding the generation mechanism of WPFs, especially those exhibiting extremely high amplitudes, is important for advancing design and control in practical applications. In this work, we systematically investigate extreme events of WPFs in turbulent boundary layers and the compressibility effects thereon. The compressibility effects, encompassing extrinsic and intrinsic ones, ranging from weak to strong, are achieved by varying Mach numbers and wall temperatures. A series of datasets at moderate Reynolds numbers obtained from direct numerical simulation are analysed. It is found that the intermittency of WPFs depends weakly on extrinsic compressibility effects, whereas intrinsic compressibility effects significantly enhance intermittency at small scales. Coherent structures related to extreme events are identified using volumetric conditional average. Under extrinsic compressibility effects, extreme events are associated with the weak dilatation structures induced by interactions of high- and low-speed motions. When intrinsic compressibility effects dominate, these events are associated with the strong alternating positive and negative dilatation structures embedded in low-speed streaks. Furthermore, Poisson-equation-based pressure decomposition is performed to partition pressure fluctuations into components governed by distinct physical mechanisms. By analysing the proportion of each pressure component in extreme events, it is found that the contributions of the slow pressure and viscous pressure exhibit weak dependence on the compressibility effects, especially the extrinsic ones, and the varying trend of contributions of the rapid pressure with compressibility effects is opposite to that of the compressible pressure component.

Aerothermal issues in hypersonic transitional swept shock wave/boundary-layer interactions (SBLIs) are critical for the structural safety of high-speed vehicles but remain poorly understood. In this work, previously scarce, high-resolution heat transfer distributions of the hypersonic transitional swept SBLIs, are obtained from fast-responding temperature-sensitive paint (fast TSP) measurements. A series of $34^\circ$ compression ramps with sweep angles ranging from $0^\circ$ to $45^\circ$ are tested in a Mach 12.1 shock tunnel, with a unit Reynolds number of 3.0 $\times$ 10$^{6}$ m$^{-1}$. The fast TSP provides a global view of the three-dimensional aerothermal effects on the ramps, allowing in-depth analysis on the sweep effects and the symmetry of heat transfer. The time-averaged results reveal that the heat flux peak near reattachment shifts upstream with decreasing amplitude as the sweep angle increases, and a second peak emerges in the $45^\circ$ swept ramp due to a type V shock–shock interaction. Downstream of reattachment, the heat flux streaks induced by Görtler-like vortices weaken with increasing sweep angle, whereas their dominant projected wavelengths show little dependence on sweep angle or spanwise location. Away from the ramp’s leading side, the transition onset of the reattached boundary layer gradually approaches the reattachment point. Finally, a general quasi-conical aerothermal symmetry is identified upstream of reattachment, although spanwise variations in transition onset, shock–shock interaction and heat flux streaks are found to disrupt this symmetry downstream of reattachment with varying degrees.

The modulation of drag through dispersed phases in wall turbulence has been a longstanding focus. This study examines the effects of particle Stokes number ($\textit{St}$) and Froude number ($\textit{Fr}$) on drag modulation in turbulent Taylor–Couette (TC) flow, using a two-way coupled Eulerian–Lagrangian approach with Reynolds number ${\textit{Re}}_i = r_i \omega _i d/\nu$ fixed at 3500. Here, $\textit{St}$ characterises particle inertia relative to the flow time scale, while $\textit{Fr}$ describes the balance between gravitational settling and inertial forces in the flow. For light particles (small $\textit{St}$), drag reduction is observed in the TC system, exhibiting a non-monotonic dependence on $\textit{Fr}$. Specifically, drag reduction initially increases and then decreases with stronger influence of gravitational settling (characterised by inverse of $\textit{Fr}$), indicating the presence of an optimal $\textit{Fr}$ for maximum drag reduction. For heavy particles, a similar non-monotonic trend can also be observed, but significant drag enhancement results at large $\textit{Fr}^{-1}$. We further elucidate the role of settling particles in modulating the flow structure in TC flow by decomposing the advective flux into contributions from coherent Taylor vortices and background turbulent fluctuations. At moderate effects of particle inertia and gravitational settling, particles suppress the coherence of Taylor vortices which markedly reduces angular velocity transport and thus leads to drag reduction. However, with increasing influence of particle inertia and gravitational settling, the flow undergoes abrupt change. Rapidly settling particles disrupt the Taylor vortices, shifting the bulk flow from a vortex-dominated regime to one characterised by particle-induced turbulence. With the dominance of particle-induced turbulence, velocity plumes – initially transported by small-scale Görtler vortices near the cylinder wall and large-scale Taylor vortices in the bulk region – are instead carried into the bulk by turbulent fluctuations driven by the settling particles. As a result, angular velocity transport is enhanced, leading to enhanced drag. These findings offer new insights for tailoring drag in industrial applications involving dispersed phases in wall-bounded turbulent flows.

Based on the generalised Saint-Venant equations for granular flow on an inclined chute, we show how to generate solitary waves from localised perturbations at the inlet. Such perturbations usually give rise to a group of roll waves, but by choosing the system parameters appropriately, the formation of all but the first wave can be suppressed, thus turning this first one into a solitary wave. This calls for a highly diffusive flow, which is realised for inclination angles close to the minimal angle required to keep the granular material flowing.