Magnets have been utilised widely for their ability to induce rapid contact – such as snapping between magnets and ferromagnetic materials. Yet, how such interactions proceed under immersion in a viscous fluid remains poorly understood. Here, we study this problem using the classical configuration of a smooth solid sphere approaching a plane in a quiescent fluid. Induced magnetic attraction, a spatially varying force analogous to short-range dispersion forces, offers a plausible route to overcome the constraint of a diverging hydrodynamic drag, which is well understood using the framework of classical lubrication theory. Instinctively, one might expect it to enable finite-time contact. However, our experiments reveal a counterintuitive result: while magnetic forces accelerate the sphere towards the surface, reducing the approach time by two orders of magnitude compared with gravity, they ultimately fail to effectuate contact in finite time, as induced magnetic interactions are unable to mitigate lubrication drag, which is singular at the thin gap limit, and transitions to an exponential descent characteristic of constant forcing. We support these findings with a simple theoretical model that accurately predicts the magnetic force law from purely kinematic observations. Finally, we outline the conditions under which spatially varying forces can enable true finite-time contact and discuss future experimental directions.

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.

Plastic pollution in our aquatic systems is a pressing issue, and the spread of these particles is determined by several factors. In this study, the advection and dispersion of negatively buoyant finite-size particles of four different shapes (spheres, circular cylinders, square cylinders and flat cuboids) and two sizes (6 and 9 mm) are investigated in turbulent open-channel flow. The volume, mass and characteristic length are fixed for each size. Four different turbulent conditions are considered, varying the free stream velocity $U_{\infty }=$ 0.25 and 0.38 m s–1 and turbulence intensity ($(u'/U)_\infty =4$ % and 9 %). The particles are released individually from below the water surface. A catch-grid is placed along the bottom floor to mark the particle landing location. The average particle advection distance remains unchanged between the turbulence levels, suggesting that the mean settling velocity is independent of turbulence in this regime. Based on the root mean square of the landing locations, the particle dispersion varies with particle shape, size, settling velocity and turbulent flow conditions. For the square cylinders investigated in this work, the effect of particle shape on dispersion is difficult to predict at low flow velocities and turbulence intensities. As the turbulent fluctuations increase, the dispersion becomes more predictable for all shapes. An empirical expression is proposed to relate turbulent velocity fluctuations, integral length scales, particle settling velocity and particle size to streamwise dispersion. It is found that finite-size inertial particles do not disperse per simple turbulent diffusion, meaning that particle geometry has to be incorporated into dispersion models.

We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall – an outcome that is harmful in case of allergens and pathogens, but beneficial in case of aerosolised drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil (J. Fluid Mech. 762, 2015, 68–109, to describe the dynamics of the mucus–air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh–Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Our simulations are eased by the fact that the effects of cilia and air turn out to be rather simple: the long-term interface profile is slowly translated by cilia and is unaffected by the laminar airflow. The streamlines of the airflow, though, are strongly modified by the non-uniform mucus film, and this has important implications for aerosol entrapment. Particles spanning a range of sizes (0.1–50 microns) are modelled using the Maxey–Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces – particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted zones that enable diffusive particles to deposit on the wall.

Inertial sedimentation of a cloud of cylinders released within a confined fluid-filled cell is experimentally investigated. Various cylinder numbers, $N_c$, aspect ratios, $\xi$, solid-to-fluid density ratios, $\rho _c / \rho _{\!f}$, and settling velocities corresponding to moderate Reynolds numbers are examined. The parameters correspond to two distinct path regimes for isolated cylinders: oscillatory trajectories for higher-density cylinders and rectilinear sedimentation for lower-density cylinders. In both cases, we observe the formation of subgroups (termed objects of class $N$) composed of $N$ cylinders in contact, as well as their recombination due to splitting or merging. Depending on the parameters, specific distributions of class-$N$ objects are found. In addition, beyond the formation of individual objects, large-scale vertical columnar structures emerge, made of densely packed objects and alternating regions of ascending and descending fluid. These structures, driven by complex interactions between local clustering and global flow organisation, which persist throughout the sedimentation process, are highly sensitive to $\xi$. Despite its inner complex dynamics, the group is observed to sediment as a collective entity, with a constant velocity exceeding that of an isolated cylinder. This velocity may be predicted from multi-scale information. Fluctuating velocities of the objects are further analysed. Different mechanisms for horizontal and vertical components are identified. Horizontal fluctuations are related to intrinsic particle mobility, while vertical fluctuations are attributed to strong wakes and vertical streams. Both fluctuations are mainly influenced by the cylinders’ aspect ratio, which also affects the structural and spatial distribution of the objects.

Large-scale circulation (LSC) dynamics have been studied in thermal convection driven by heat-releasing particles via the four-way coupled Euler–Lagrange approach. We consider a wide range of Rayleigh–Robert number (${\textit{Rr}}=4.97\times 10^{5} - 4.97 \times 10^{8}$) and density ratio ($\hat {\rho }_r=1- 1000$) that characterize the thermal buoyancy and the particle inertia, respectively. An intriguing flow transition has been found as $\hat {\rho }_r$ continuously increases, involving in sequence three typical LSC regimes, i.e. the bulk-flow-up regime, the marginal regime and the bulk-flow-down (BFD) regime. The comprehensive influence of the LSC regime transition is demonstrated by examining the key flow statistics. As integral flow responses, the heat transfer efficiency and flow intensity change substantially when the LSC regime transition happens, and the thermal boundary layer thicknesses at the top and bottom walls exhibit similar alterations. Significant local accumulation of particles occurs as $\hat {\rho }_r$ increases to a sufficiently high value, resulting in a great modification in the flow dynamics. Specifically, particles aggregate near the sidewalls and heat the local surrounding fluid to generate rising warmer plumes that drive the LSC regime transition. Of interest, well-patterned cellular structures of particles take place near the top wall and obtain notable deviation from the thermal convection cells for the BFD regimes. A mechanical interpretation is proposed and substantiated based on a conceptual vortex–particle model, namely, the centrifugal motion of heat-releasing particles that is confirmed to play a driving role for the LSC regime transition.

A novel particle-resolved direct numerical simulations (PR-DNS) method for non-spherical particles is developed and validated in the open-source MFiX (Multi-phase Flow with Interphase eXchanges) code for simulating the suspension of non-spherical particles and fluidisation. The model is implemented by coupling superquadric Discrete Element Method-Computational Fluid Dynamics (DEM-CFD) with the immersed boundary method. The model was first validated by applying it to analyse fluid dynamic coefficients ($C_{\!D} , C_{\!L} , C_{\!T}$) of superellipsoids and cylinders at different Reynolds numbers, and the PR-DNS results closely matched those of previous methods, demonstrating the reliability of the current PR-DNS approach. Then, the model was applied to the simulation of the fluidisation of spheres and cylinders. The PR-DNS results were compared with both particle-unresolved superquadric DEM-CFD simulation and experimental data. The pressure drop, height distribution and orientation distribution of particles were analysed. The results show that the PR-DNS method provides a reliable method for reproducing fluidisation experimental results of non-spherical particles. In addition, the comparison of the drag correction coefficients predicted by existing models with that obtained from PR-DNS results indicates the need for a new drag model for particle-unresolved simulation of non-spherical particles.

The inertial migration of hydrogel particles suspended in a Newtonian fluid flowing through a square channel is studied both experimentally and numerically. Experimental results demonstrate significant differences in the focusing positions of the deformable and rigid particles, highlighting the role of particle deformability in inertial migration. At low Reynolds numbers (${Re}$), hydrogel particles migrate towards the centre of the channel cross-section, whereas the rigid spheres exhibit negligible lateral motion. At finite ${Re}$, they focus at four points along the diagonals in the downstream cross-section, in contrast to the rigid particles which focus near the centre of the channel face at similar ${Re}$. Numerical simulations using viscous hyperelastic particles as a model for hydrogel particles reproduced the experimental results for the particle distribution with an appropriate Young’s modulus of the hyperelastic particles. Further numerical simulations over a broader range of ${Re}$ and the capillary number ($Ca$) reveal various focusing patterns of the particles in the channel cross-section. The phase transitions between them are discussed in terms of the inertial lift and the lift due to particle deformation, which would act in the direction towards lower shear. The stability of the channel centre is analysed using an asymptotic expansion approach to the migration force at low ${Re}$ and $Ca$. The theoretical analysis predicts the critical condition for the transition, which is consistent with the direct numerical simulation. These experimental, numerical and theoretical results contribute to a deeper understanding of inertial migration of deformable particles.

We study the interaction between a pair of particles suspended in a uniform oscillatory flow. The time-averaged behaviour of particles under these conditions, which arises from an interplay of inertial and viscous forces, is explored through a theoretical framework relying on small oscillation amplitude. We approximate the oscillatory flow in terms of dual multipole expansions, with which we compute time-averaged interaction forces using the Lorentz reciprocal theorem. We then develop analytic approximations for the force in the limit where Stokes layers surrounding the particles do not overlap. Finally, we show how the same formalism can be generalised to the situation where the particles are free to oscillate and drift in response to the applied flow. The results are shown to be in agreement with existing numerical data for forces and particle velocities. The theory thus provides an efficient means to quantify nonlinear particle interactions in oscillatory flows.

We introduce a novel unsteady shear protocol, which we name rotary shear (RS), where the flow and vorticity directions are continuously rotated around the velocity-gradient direction by imposing two out-of-phase oscillatory shears (OSs) in orthogonal directions. We perform numerical simulations of dense suspensions of rigid non-Brownian spherical particles at volume fractions ($\phi$) between 0.40 and 0.55, subject to this new RS protocol, and compare with the classical OS protocol. We find that the suspension viscosity displays a similar non-monotonic response as the strain amplitude ($\gamma _0$) is increased: a minimum viscosity is found at an intermediate, volume-fraction-dependent strain amplitude. However, the suspension dynamics is different in the new protocol. Unlike the OS protocol, suspensions under RS do not show absorbing states at any $\gamma _0$ and do not undergo the reversible–irreversible transition: the stroboscopic particle dynamics is always diffusive, which we attribute to the fact that the RS protocol is inherently irreversible due to its design. To validate this hypothesis, we introduce a reversible-RS (RRS) protocol, a combination of RS and OS, where we rotate the shear direction (as in RS) until it is instantaneously reversed (as in OS), and find the resulting rheology and dynamics to be closer to OS. Detailed microstructure analysis shows that both the OS and RRS protocols result in a contact-free, isotropic to an in-contact, anisotropic microstructure at the dynamically reversible-to-irreversible transition. The RS protocol does not render such a transition, and the dynamics remains diffusive with an in-contact, anisotropic microstructure for all strain amplitudes.

Accurate prediction of the hydrodynamic forces on particles is central to the fidelity of Euler–Lagrange (EL) simulations of particle-laden flows. Traditional EL methods typically rely on determining the hydrodynamic forces at the positions of the individual particles from the interpolated fluid velocity field, and feed these hydrodynamic forces back to the location of the particles. This approach can introduce significant errors in two-way coupled simulations, especially when the particle diameter is not much smaller than the computational grid spacing. In this study, we propose a novel force correlation framework that circumvents the need for undisturbed velocity estimation by leveraging volume-filtered quantities available directly from EL simulations. Through a rigorous analytical derivation in the Stokes regime and extensive particle-resolved direct numerical simulations (PR-DNS) at finite Reynolds numbers, we formulate force correlations that depend solely on the volume-filtered fluid velocity and local volume fraction, parametrised by the filter width. These correlations are shown to recover known drag laws in the appropriate asymptotic limits and exhibit a good agreement with analytical and high-fidelity numerical benchmarks for single-particle cases, and, compared with existing correlations, an improved agreement for the drag force on particles in particle assemblies. The proposed framework significantly enhances the accuracy of hydrodynamic force predictions for both isolated particles and dense suspensions, without incurring the prohibitive computational costs associated with reconstructing undisturbed flow fields. This advancement lays the foundation for robust, scalable and high-fidelity EL simulations of complex particulate flows across a wide range of industrial and environmental applications.

We study aeolian saltation over an erodible bed at full transport capacity in a wind tunnel with a relatively thick boundary layer. Lagrangian tracking of size-selected spherical particles resolves their concentration, velocity and acceleration. The mean particle concentration follows an exponential profile, while the mean particle velocity exhibits a convex shape. In contrast to current assumptions, both quantities appear sensitive to the friction velocity. The distributions of horizontal accelerations are positively skewed, though they contain negative tails associated with particles travelling faster than the fluid. The mean wind velocity profiles, reconstructed down to millimetric distances from the bed using the particle equation of motion, have an approximately constant logarithmic slope and do not show a focal point. The aerodynamic drag force increases with distance from the wall and, for the upward moving particles, exceeds the gravity force already at a few particle diameters from the bed. The vertical drag component resists the motion of both upward and downward moving particles with a magnitude comparable to the lift force, which is much smaller than gravity but non-negligible. Coupling the assumption of ballistic vertical motion and the measured streamwise velocities, the mean trajectories are reconstructed and found to be strongly influenced by aerodynamic drag. This is also confirmed by the direct identification of trajectory apexes, and demonstrated over a wide range of friction velocities. Taken together, these results indicate that aerodynamic drag and lift may play a more significant role in the saltation process than presently recognized, being complementary rather than alternative to splash processes.

We experimentally investigate the rotational dynamics of neutrally buoyant flat bodies of revolution (spheroids, disks and rings with different cross-sectional shapes) in shear flows. In the Stokes regime, the axis of revolution of these rigid particles moves in one of a family of closed periodic Jeffery orbits. Inertia is able to lift the orbit degeneracy and induces drift among several rotations towards limiting stable orbits. Furthermore, permanent alignment can be achieved for disks and rings with triangular cross-sectional shapes, provided the inertia is sufficiently high. The bifurcations between the different dynamics are compared with those predicted by small-inertia asymptotic theories and numerical simulations.

Fingering instabilities readily occur if a less viscous fluid displaces a more viscous fluid in a narrow gap due to the action of destabilising viscous forces. If the fluids are miscible, the instability can be suppressed in the limit of large advection as complicated flow structures are formed across the gap. Using a fluid to displace a monolayer of non-colloidal particles suspended in the same fluid, Luo et al. (2025 J. Fluid Mech. vol. 1011, A48) suppress the formation of the cross-gap structures and identify a new fingering mechanism which instead relies on long-range dipolar disturbance flows generated by the particle confinement.

Dynamics of a spherical particle and the suspending low-Reynolds-number fluid confined between two concentric spherical walls were studied numerically. We calculated the particle’s hydrodynamic mobilities at various locations in the confined space. It was observed that the mobility is largest near the middle of confined space along the radial direction, and decays as the particle becomes closer to no-slip walls. At a certain confinement level, the maximal mobility occurs near the inner wall. We also calculated the drift velocity of the particle perpendicular to the external force. The magnitude of the drift velocity normalised by the velocity along the external force was found to depend on particle location and the confinement level; it is observed that the maximal drift velocity occurs near the wall. Fluid vortices in the confined space induced by particle motion were observed and analysed. In addition, we studied particle trajectories in the flow when the walls rotate at constant angular velocities. The externally applied force, rotation-induced flow and centrifugal/centripetal force, and particle–wall interaction lead to various modes of particle motion. This work lays the foundation to understand and manipulate particulate transport in microfluidic applications such as intracellular transport and encapsulation technologies.

This study employs a direct numerical simulation method to investigate the wake pattern evolutions of flows past an insulated spheroid and provides expressions of force and torque coefficients influenced by a streamwise magnetic field in an incompressible, conducting, viscous fluid. A total of 1150 cases are examined covering a parameter range of Reynolds number $50 \leqslant \textit{Re} \leqslant 250$, aspect ratio $1.5 \leqslant \beta \leqslant 6$, inclination angle $0^\circ \leqslant \theta \leqslant 90^\circ$, and interaction parameter $0 \leqslant N \leqslant 10$, where $\beta$ and $N$, respectively, reflect the anisotropy of the spheroid and the strength of magnetic field. Nine wake patterns are classified based on wake structure features and summarised in three maps of regimes according to the inclination angle. The transition mechanisms among these wake patterns are also investigated under the influence of a streamwise magnetic field. Furthermore, expressions for drag, lift and torque coefficients are derived with the help of three fundamental physical criteria. Results indicate that the force and torque expressions give a good prediction within the present parameter space $\{\textit{Re}, \beta , \theta , N\}$.

Particle suspensions in confined geometries can become clogged, which can have a catastrophic effect on function in biological and industrial systems. Here, we investigate the macroscopic dynamics of dense suspensions in constricted geometries. We develop a minimal continuum two-phase model that allows for variation in particle volume fraction. The model comprises a ‘wet solid’ phase with material properties dependent on the particle volume fraction, and a seepage Darcy flow of fluid through the particles. We find that spatially varying geometry (or material properties) can induce emergent heterogeneity in the particle fraction and trigger the abrupt transition to a high-particle-fraction ‘clogged’ state.

In this study, the statistical properties and formation mechanisms of particle clusters that consider the influence of particle–wall interactions in particle-laden wall turbulence are systematically investigated through wind tunnel experiments. In the experiments, two particle release modes, including particle top-releasing mode (Case 1) and particle locally laying mode (Case 2), were adopted to establish varying conditions with different particle–wall interaction strengths. The Voronoï diagram method was employed to identify the particle clusters, and the impact of particle–wall interactions on the characteristics of the clusters was analysed. The results indicate that particle–wall interaction is the predominant factor in the formation of particle clusters in the near-wall region. Under Case 1 and Case 2, the maximum concentration of particles in the clusters could reach nearly five times the average particle concentration; however, the clusters with large particle numbers ($N_C\gt 5$) in Case 1 tended to form near the wall and the vertical velocities of these clusters were greater than the average velocities of all particles. In contrast, under Case 2, clusters with large particle numbers exhibited a higher probability of occurrence further from the wall and the vertical velocities of these clusters were lower than the average velocity of all particles. Furthermore, this study found that the presence of particle clusters in these flows significantly alters the flow field properties surrounding them, implying that a region of high strain and low vorticity constitutes an essential but non-sufficient condition for the generation of particle clusters in wall turbulence.

Uniform arrays of particles tend to cluster as they sediment in viscous fluids. Shape anisotropy of the particles enriches this dynamics by modifying the mode structure and the resulting instabilities of the array. A one-dimensional lattice of sedimenting spheroids in the Stokesian regime displays either an exponential or an algebraic rate of clustering depending on the initial lattice spacing (Chajwa et al. 2020 Phys. Rev. X vol. 10, pp. 041016). This is caused by an interplay between the Crowley mechanism, which promotes clumping, and a shape-induced drift mechanism, which subdues it. We theoretically and experimentally investigate the sedimentation dynamics of one-dimensional lattices of oblate spheroids or discs and show a stark difference in clustering behaviour: the Crowley mechanism results in clumps comprising several spheroids, whereas the drift mechanism results in pairs of spheroids whose asymptotic behaviour is determined by pair–hydrodynamic interactions. We find that a Stokeslet, or point-particle, approximation is insufficient to accurately describe the instability and that the corrections provided by the first reflection are necessary for obtaining some crucial dynamical features. As opposed to a sharp boundary between exponential growth and neutral eigenvalues under the Stokeslet approximation, the first-reflection correction leads to exponential growth for all initial perturbations, but far more rapid algebraic growth than exponential growth at large dimensionless lattice spacing $\tilde {d}$. For discs with aspect ratio $0.125$, corresponding to the experimental value, the instability growth rate is found to decrease with increasing lattice spacing $\tilde {d}$, approximately as $\tilde {d}^{ -4.5}$, which is faster than the $\tilde {d}^{-2}$ for spheres (Crowley 1971 J. Fluid Mech. vol. 45, pp. 151–159). It is shown that the first-reflection correction has a stabilising effect for small lattice spacing and a destabilising effect for large lattice spacing. Sedimenting pairs predominantly come together to form an inverted ‘T’, or ‘$\perp$’, which our theory accounts for through an analysis that builds on Koch & Shaqfeh (1989 J. Fluid Mech. vol. 209, pp. 521–542). This structure remains stable for a significant amount of time.