We study the settling of a heavy particle-laden phase layered above an unladen fluid. When the suspension has finite dilution, the dynamic of this set-up has remained largely unexplored. This system, which is fundamentally analogous to that found when studying the Rayleigh–Taylor instability, generates a mixing front whose width grows at an anomalous rate. In the present work, we explore the fluid and particle dynamics underpinning the mixing layer expansion. We perform particle-resolved direct numerical simulations to investigate the set-up: we use particle-to-fluid density ratios $\gamma =\{2,4,6,8\}$ and particle-laden phase volume fractions $\phi _{b}\approx 0.1$. The results show the emergence of flow structures analogous to Rayleigh–Taylor plumes. Downward-directed structures are preferentially sampled by the particles, and within their cores, particles are able to accelerate past their terminal velocity in still fluid, resulting in strongly enhanced settling rates. We quantify the intensity of turbulence in the mixing layer, showing possible evidence of an incipient energy cascade.

Most granular suspensions in nature and industrial applications comprise multimodal particles in a broad size range. Despite numerous studies attempting to establish a unified viscosity model for polydisperse suspensions with different particle size distributions (PSDs), the microstructure exhibits a strong PSD dependence, such as the peculiar shear-induced particle ordering in bidisperse suspensions. However, understanding of the stability of such ordered structures remains limited. In this study, we aim to reveal the role of microstructural transformation in the flow of shear thickening bidisperse suspensions with large particle size ratio. Discrete-particle simulations accounting for short-range hydrodynamic and contact forces were performed to simulate the simple shear flow of granular suspensions, with three PSDs at the small particle fraction: $\zeta _1=0.10, 0.26, 0.50$. We found that an order-to-disorder transition that occurs in the suspension with the theoretical optimal PSD ($\zeta _1=0.26$) causes unusual discontinuous shear thickening in inertial flows. The contact force network, accompanied by particle rearrangement, switches from sparse to nearly percolated, with decreased stress anisotropy. Compared with monodisperse and bidisperse suspensions that do not exhibit significant structural transformation during thickening, the layered structure in the $\zeta _1=0.26$ suspension reduces the effective friction of the system. These findings demonstrate the possibility of achieving stronger shear thickening of inertial flows by adopting an optimised PSD, which can help to achieve active rheology control by compositional tuning.

A neutrally buoyant rigid spheroid suspended in a wall-bounded plane Poiseuille flow undergoes cross-stream migration, driven by inertia. We examine theoretically the migration of a spheroid of aspect ratio $\kappa$ in the limit of small but finite particle Reynolds number (${\textit{Re}}_{\!p}$), and for small confinement ratios ($\lambda$), with the channel Reynolds number, ${\textit{Re}}_c = {\textit{Re}}_{\!p}/\lambda ^2$, assumed arbitrary; here, $\lambda =L/H$ with $L$ being the semimajor axis of the spheroid and $H$ denoting the separation between channel walls. For small $\lambda$, the asymptotic separation between the rotation-cum-orbital-drift and migration time scales implies that, to begin with, inertia rapidly drives the spheroid towards the tumbling orbit (orbit constant, $C=\infty$) with negligible migration; migration is subsequently driven by a time-averaged lift velocity, the average being over the orientations sampled in the inertially stabilized tumbling orbit. While spheroids with $\kappa \sim O(1)$ rotate with the Jeffery angular velocity to a very good approximation, deviations from Jeffery rotation, for both large and small $\kappa$, lead to a time-averaged inertial lift profile with equilibrium locations (zero crossings) that differ from the classical Segre–Silberberg predictions for a sphere. Beyond a threshold ${\textit{Re}}_c$, both slender spheroids and thin disks attain a steady orientation in the neighbourhood of the walls, and with increasing ${\textit{Re}}_c$, these rotation-arrested regions grow in extent, moving in towards the channel centreline. In contrast to spheres, but consistent with experiments, onset of rotation arrest causes the aforementioned equilibrium positions to move towards the centreline; further, for thin disks alone, the equilibrium positions themselves become rotation-arrested beyond a threshold ${\textit{Re}}_c$. The $\kappa$-dependence of the equilibrium positions can be leveraged towards developing passive shape-sorting protocols on microfluidic platforms.

When a non-spherical particle sediments, its velocity generally changes in time as the particle orientation changes in time. This gives extra dispersion of the particle position in addition to the thermal Brownian motion. Brenner (J. Colloid Interf. Sci., vol. 71, 1979, pp. 189–208) studied this effect and formulated how to calculate the gravity-induced dispersion (called Taylor dispersion in sedimentation). However, he conducted the explicit calculation only for torque-free particles which keep an isotropic orientational distribution in the steady-state. In this paper, we study the effect of the gravitational torque on the Taylor dispersion. We limit the analysis to particles having uniaxial symmetry. In this case, the gravitational torque is caused by the offset $l_{{c}}$, the distance between the hydrodynamic centre and the gravitational force centre. The effect of the gravitational torque is represented by a dimensionless parameter $\alpha$ (called the Langevin parameter by Brenner) which is proportional to $l_{{c}}$. We obtain analytical expressions for the Taylor diffusivity for the two limits $\alpha \ll 1$ and $\alpha \gg 1$. We show that the offset gives a significant effect on the diffusivity and changes the classical scaling of the Taylor dispersion at a large Péclet number. We also analyse the transient regime of the mean square displacement and show how the crossing time from the ballistic regime to the diffusive regime depends on the gravitational torque.

We study experimentally the detachment of a large pendant drop of non-Brownian monodisperse solid spheres in a Newtonian liquid, for high solid volume fractions ($0.55\leq \phi \leq 0.605$) compared with the critical volume fraction $\phi _{{c}}$ of the suspension. This set-up allows us to monitor both the bulk-effective deformation rate and the mean stress at the neck of the drop throughout detachment. The neck effective viscosity is found to decrease close to exponentially with the current neck radius, from a large initial value, $\eta _{{i}}$, down to the suspending liquid one. Experiments with different drop-to-particle size ratios indicate that, above $\phi _{{c}}$, the initial value $\eta _{{i}}$ is set by the viscosity-limited dilation of the particle phase. Observations on a transparent, doubly index-matched system reveal increasing deviation from axial symmetry and the collapse of capillary menisci at the drop interface during the exponential decay. A simplified model, based on the observed rheological evolution and the close-to-conical neck shape, captures the steeply accelerated detachment dynamics and shows how $\eta _{{i}}$ sets the breakup duration.

This work investigates, based on laboratory experiments, the influence of particles on the drainage of a bottle filled with an isodense suspension. Similarly to the drainage of a pure liquid, the flow rate remains constant during the whole emptying process and is primarily controlled by the size of the exit hole. Despite a hole-to-particle size ratio that would normally promote clogging, no such events are observed due to the periodic entrainment of air bubbles. The presence of particles causes a slight decrease in flow rate when increasing the particle initial packing fraction. Even for initial packing fractions of up to 60 %, it only decreases by at most 20 %. Revisiting the model of Clanet & Searby (2004) J. Fluid Mech. 510, 145–168, the flow rate is found to be linked to the rise velocity of the bubbles, which is surprisingly nearly independent of the packing fraction, even for values as high as 60 %. This counterintuitive result suggests that the suspension becomes heterogeneous, with a particle-depleted region in the pathway of the bubbles. Moreover, during drainage, the suspension exiting the bottle has a smaller packing fraction than the initial suspension, leading to an accumulation of particles inside the bottle and therefore an increase in the global packing fraction inside the vessel. When this latter reaches a critical value close to random loose packing, particles start to emerge above the liquid free surface. Based on accurate measurements that enable the computation of the mean packing fraction at all times, a model is proposed to describe this transition.

The shear rheology of suspensions is important in material manufacturing, biophysics and environmental processes. Particle geometry impacts rheology in a manner that depends on the particles’ individual rotational dynamics and interparticle interactions. In this work, we investigate the rheology of a suspension of self-aligning particles (SAPs), a class of rigid particles that, in a low Reynolds number simple shear flow, remain permanently aligned near the fluid lamellae without application of external torques. We focus on ring-shaped SAPs, which are robust against secondary effects such as perturbations to the shear flow, interparticle interactions and weak Brownian motion (Borker et al. 2024 Phys. Rev. Fluids 9, 043301). Using dynamic simulations under a slender-body theory framework, we demonstrate that SAP suspensions generate specific viscosities an order of magnitude smaller than those generated by tumbling particles of the same aspect ratio. As a result, SAP suspensions make only modest alterations to the suspension viscosity even at $O(1)$ values of the number density $\bar {n}$ non-dimensionalized by the in-plane radial extent of the ring. This reduction in the shear stress arises from persistent alignment, which suppresses the short tumbling events that dominate the rheology of conventional high-aspect ratio particles. Our results indicate a distinct hydrodynamic mechanism governing shear stresses in SAPs, including a regime near a critical aspect ratio that is dominated by dipoles per unit circumference and has no analogue in tumbling-particle suspensions. As a consequence, ring-shaped SAPs with different cross-sectional shapes impart shear stress of comparable magnitude at a given aspect ratio. In contrast to their weak contribution to shear stresses, SAP suspensions generate comparatively large normal stress differences due to the intrinsic asymmetry of their equilibrium orientation. This fundamentally differs from tumbling-particle suspensions which need collisions to generate normal stresses. Therefore, normal stresses in SAP suspensions scale linearly with $\bar {n}$ and are significantly larger than the $O(\bar {n}^2)$ normal stresses observed in tumbling-particle suspensions. Consequently, SAP suspensions exhibit non-Newtonian behaviour at lower volume fractions and may exhibit the Weissenberg effect at moderate number densities. Our findings highlight that SAPs offer access to rheological properties that are challenging to replicate in suspensions of conventional rigid particles. Overall, these findings offer new insight into tuning the bulk rheology of particle suspensions by controlling the orientational dynamics of individual particles.

We perform direct numerical simulations of elastoviscoplastic (EVP) duct flows at particle volume fractions up to $\phi = 15\,\%$. Unlike Newtonian suspensions, which exhibit pronounced drag increase with particle loading, EVP suspensions show only modest drag growth in dilute and semi-dilute conditions and achieve significant drag reduction relative to their Newtonian counterparts beyond a threshold $\phi$ that increases with the Bingham number. This behaviour results from two coupled mechanisms: viscoelasticity drives particles away from the walls towards the duct core, and the unyielded plug traps them with negligible slip, thereby minimising their stress contribution. As a consequence, the mean velocity profile remains largely independent of solid volume fraction, with viscous and elastic stresses nearly unchanged. In addition, we observe pronounced shear thinning in viscoelastic and EVP suspensions, in contrast to earlier predictions. These findings demonstrate that accurate drag prediction requires explicit modelling of the local solid fraction in EVP particle-laden flows.

The orientation dynamics of a spheroidal magnetic particle in a viscous fluid subject to a rotating magnetic field is analysed for realistic two-parameter models for the magnetic moment. It is shown that the equations can be mapped onto those for a spherical magnetic particle in a steady magnetic field subject to shear flow. Time evolution equations for the azimuthal and meridional angles of the orientation vector are derived from the condition that the sum of the hydrodynamic and magnetic torques is zero in the viscous limit. One parameter is $\omega ^{\dagger}$, the ratio of the magnetic field frequency and the particle viscous relaxation rate. For the non-hysteretic Langevin model, the second parameter is the ratio of the saturation moment $m_s$ and the susceptibility $\chi$ times the magnetic field $H,\!(m_s/\chi\! H)$. There is parallel corotation of the particle with the field for $\omega ^{\dagger} \lt \omega _b^{\dagger}$, and parallel slip relative to the magnetic field for high $\omega ^{\dagger} \gt \omega _b^{\dagger}$, where $\omega _b^{\dagger}$ is the breakdown frequency. For the hysteretic Stoner–Wohlfarth model, the second parameter is $h$, the ratio of the Zeeman energy and the anisotropy energy due to the misalignment between the moment and the particle axis. There are three states, parallel corotation for low $\omega ^{\dagger}$, precessed corotation for high $\omega ^{\dagger}$ and low $h$, where the orientation precesses relative to the axis of rotation of the magnetic field, and parallel slip at high $\omega ^{\dagger}$ and high $h$.

The settling dynamics of fractal aggregates in constant-density environments and through miscible density interfaces are investigated via particle-resolved direct numerical simulations, which provide the settling velocity as a function of the fractal dimension, Galileo number, and particle and fluid densities. In a fluid of uniform density the settling velocity increases with the fractal dimension and the Galileo number. This behaviour is captured by an empirical relationship that holds over a broad range of parameter values. In the presence of a miscible density interface, consistent with earlier observations we observe that lighter fluid is carried into the denser layer by the aggregate’s pore spaces, which we quantify based on the concept of $\alpha$-shapes. This causes the aggregate to slow down, until the lighter pore fluid is replaced by the denser fluid via a combination of diffusion and convection. The degree of the aggregate’s slowdown depends on the ratio of the density differences between the aggregate and the two fluids, and it can again be captured by an empirical relationship. The duration of the slowdown is determined by the pore fluid replacement time, which in turn depends on the relative importance of convection and diffusion, and hence on the aggregate’s geometry. A relationship is derived that captures the dependence of this replacement time on the shape of the aggregate, the ratio of the density differences, and the Galileo number.

Entropically driven fluid–solid transitions in monodisperse, purely repulsive hard spheres (MPRHS) are well established in theory, simulation and experiment for atomic and colloidal systems. For MPRHS, however, coexistence is usually located via bulk free-energy calculations; the underlying microscopic balance between configurational and vibrational entropy is left implicit. Frenkel clarified this mechanism explicitly as an exchange of long-range configurational entropy for short-range vibrational entropy, but in the pristine MPRHS limit the nucleation barrier near coexistence is so high that phase separation is predicted only on astronomical time scales. Consistent with this, even unbiased simulations do not show spontaneous, equilibrium fluid–crystal coexistence; transient mixtures are mostly overtaken by a single phase; observed coexistence is still algorithmically driven. Nearly hard-sphere colloid experiments do observe fluid–crystal coexistence, but always in the presence of unavoidable triggers such as gravity and walls. We treat the hard-sphere phase diagram as settled and ask how the entropic exchange mechanism can be revealed in nearly hard-sphere colloidal simulations. We probe the mechanism on finite time scales by introducing minimal perturbations that trigger phase separation: small reductions in hardness that increase locally accessible free volume (and thus gently increase vibrational entropy), and 2 %–4 % distributed crystal seeds. These perturbations produce coexisting fluid and crystal domains with crystal fraction, phase envelope and osmotic pressure that, with systematically increasing particle hardness, approach the hard-sphere limit. These results demonstrate that slight enhancements to vibrational entropy provide a dynamically accessible route to realising the long-range/short-range entropy exchange required for phase separation.

The mechanical properties of confining boundaries can fundamentally alter the flow behaviour of shear-thickening suspensions. We study a dense cornstarch suspension sheared beneath a viscous silicone oil layer, using the oil viscosity to tune boundary compliance. Flow visualisation and rheometry reveal two distinct regimes. With compliant boundaries, long-lived heterogeneities emerge via density waves or persistent clusters, maintained by a balance between interface deformation and particle rearrangement. With more resistant confinement, we observe transient jamming events, marked by abrupt spanning of load-bearing structures across the suspension thickness and the emergence of secondary stress waves. The onset stress of these events remains constant at the discontinuous shear thickening (DST) threshold, independent of bounding viscosity. Our results reveal that boundary compliance selects the lifetime and morphology of heterogeneous structures, offering a means to amplify otherwise short-lived microscopic processes and providing new insight into the interplay between shear thickening, shear jamming and confinement mechanics.

Controlling multiphase flow in disordered media is central to diverse practical contexts. Although nanoparticles have been widely utilised to modify surface wettability, factors governing their effects on dynamic displacement patterns remain unclear. Here, we identify the criterion for nanoparticle-induced wettability alteration during displacement by combining interfacial-scale wetting models, pore-scale microfluidic experiments and simulations. Motivated by striking contrasts in static wettability, we find that nanoparticle adsorption on solid surfaces affects displacement interfaces only when spreading of wetting films is pre-established, corresponding to corner-flow conditions. Displacement experiments under varying intrinsic wettability show that wetting-film development and non-aqueous droplet detachment are strengthened exclusively on moderately water-wet surfaces satisfying the corner-flow criterion. Investigations across designed porous structures with varying degrees of structural hierarchy validate the generality of the wettability criterion, while improvement in displacement efficiency diminishes with reduced hierarchy. The structural effect arises from variations in flow heterogeneity, with stronger heterogeneity simultaneously promoting film flow and ganglion mobilisation. The coupled impacts of wettability and structural conditions are summarised in an illustrative phase diagram delineating nanoparticle-tuned multiphase displacement. Our findings offer mechanistic insights into complex fluid flow in porous media and suggest optimised strategies for displacement control via nanoparticle suspensions.

Microswimmers in suspension exhibit collective swimming behaviour, forming various self-organised structures including ordered, aggregated and turbulent-like structures. When mixed with passive particles phase-separation is known to occur, but due to the difficulty of accurately handling many-body hydrodynamic interactions, the formation of self-organised structures in mixed suspensions has remained unexplored so far. In this study, we investigate the dynamics of mixed dense suspensions of spherical bottom-heavy squirmers and obstacle spheres using Stokesian dynamics in three dimensions, taking hydrodynamic interactions into account. The results show that without an external orienting mechanism the formation of orientational order is in general disturbed by the presence of passive spheres. An initially phase-separated state is metastable for neutral or puller squirmers at high packing densities. When the squirmers are bottom-heavy, phase-separation can occur dynamically in some cases, notably as a fibrillar kind of separation for neutral squirmers and pullers at medium densities. We also observed a novel form of lamellar phase-separation for pullers at high densities with strong bottom-heaviness, with a sandwich-like structure consisting of a layer of passive particles pushed by a layer of swimmers, followed by a gap. These results indicate that microstructure and particle transport undergo significant changes depending on the type of swimmer, highlighting the importance of hydrodynamic interactions. These insights allow for a deeper understanding of the behaviour of active particles in complex fluids and to control them using external torques.

The effects of confinement and polydispersity on the shear-induced diffusivity of non-Brownian, neutrally buoyant spheres suspended in a Newtonian fluid are investigated using simulations that incorporate short-range lubrication forces, surface roughness and frictional contacts. Simulations were performed at a fixed volume fraction of 0.45 for multiple values of particle roughness and friction coefficient. Confinement by bounding walls promoted layered structures that suppressed particle mobility and reduced diffusivity, while also diminishing the influence of friction and roughness. In contrast, high polydispersity disrupted layering and enhanced diffusivity, even in confined systems. Polydispersity also led to size-dependent demixing, with smaller particles preferentially migrating towards the walls and exhibiting higher mobility. These results have implications for modelling and controlling transport in suspensions, where confinement and polydispersity alter the effects of friction and roughness on shear-induced diffusion.

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.

We analyse the dynamics of a weakly elastic spherical particle translating parallel to a rigid wall in a quiescent Newtonian fluid in the Stokes limit. The particle motion is constrained parallel to the wall by applying a point force and a point torque at the centre of its undeformed shape. The particle is modelled using the Navier elasticity equations. The series solutions to the Navier and the Stokes equations are used to obtain the displacement and velocity fields in the solid and fluid, respectively. The point force and the point torque are calculated as series in small parameters $\alpha$ and $1/H$, using the domain perturbation method and the method of reflections. Here, $\alpha$ is the measure of elastic strain induced in the particle resulting from the fluid’s viscous stress and $H$ is the non-dimensional gap width, defined as the ratio of the distance of the particle centre from the wall to its radius. The results are presented up to $\textit {O}(1/H^3)$ and $\textit {O}(1/H^2)$, assuming $\alpha \sim 1/H$, for cases where gravity is aligned and non-aligned with the particle velocity, respectively. The deformed shape of the particle is determined by the force distribution acting on it. The hydrodynamic lift due to elastic effects (acting away from the wall) appears at $\textit {O}(\alpha /H^2)$ in the former case. In an unbounded domain, the elastic effects in the latter case generate a hydrodynamic torque at O($\alpha$) and a drag at O($\alpha ^2$). Conversely, in the former case, the torque is zero, while the drag still appears at O($\alpha ^2$).