Session ZC46: Particle-Laden Flows: Clustering II

Investigation of particle clustering in turbulent channel flow using Direct Numerical Simulations (DNS)

Particle-laden turbulent flows are prevalent in natural and industrial processes such as sedimentation in rivers, chemical reactors, pneumatic conveying of solids and gas scrubbers. Coupling between the particle and fluid phases as well as particle collisions can lead to flow modification. Hence, local particle concentration plays a vital role in the study of multiphase flow. Phenomenon like turbophoresis and particle clustering leads to formation of zones of high particle concentration. Particle response to fluid flow leads to the non-uniform spatial distribution of particles and depends on particle inertia, the ratio of particle size to the underlying fluid scales, etc. Many studies have been carried out to find the relevance of Stokes number on particle clustering. The present study is focused on the dependency of particle clustering on the Stokes number as well as the Reynolds number and mass loading, which are yet to be explored in detail. Direct Numerical Simulations (DNS) are carried out for vertical channel flow at different Reynolds numbers, Stokes numbers, and particle volume fractions. Particle clusters in the flow are identified by using the Voronoi tessellation method at different wall-normal locations. It is observed that clusters with larger areas are found at the channel center. Higher local particle concentration within the cluster is observed at high particle loading for both near-wall and channel center planes. PDFs of non-dimensionalized cluster area and particle concentration are used to reach a better understanding of cluster formation in the flow.   

Role of shear-induced lift force in the spatial distribution of resuspended particles

The Eulerian-Lagrangian point-particle model is coupled with direct numerical simulation of a wall-bounded turbulent flow to study the spatial distribution of particles resuspended from a fractal-like multiscale rough surface. A dynamical stochastic resuspension model is employed to model the process of particle resuspension on the surface. Particular attention is paid to the effect of shear-induced Saffman lift force. The computation results demonstrate that the shear-induced lift force can play a significant role in spatial particle distribution and particle statistics near the wall, e.g., the preferential accumulation, as well as local streaky clustering of particles near the wall, is remarkably weakened for all particles by including the shear-induced lift force. By analyzing the correlation between particle motion and flow structures, it is found that the centrifuging and turbophoresis effects are degraded by the lift force. A formal relation for particle number density distribution from the kinetic equation of the probability density function of particle position and velocity is extended to quantitatively elucidate the mechanism that leads to the different distributions of particles in the wall turbulent flow, especially the spanwise inhomogeneity of particle distribution.   

Clustering and chaotic motion of inertial particles in an isolated vortex

Inertial particles sample a flow field preferentially, getting centrifuged away from vortical regions and accumulating in strain-dominated regions. The dynamics of heavy particles in an axisymmetric vortex monopole are along expected lines - particles spirally migrate to infinity. We show that a deviation from axisymmetry for the vorticity profile can lead to intriguing clustering dynamics for inertial particles. We consider the Kirchhoff vortex, an elliptical patch of uniform vorticity that rotates with a constant angular velocity, and show that four fixed points exist for heavy particles in the irrotational exterior. They appear as saddles and stable spirals, and we investigate their stability as a function of the Stokes number. A background shear often strains elliptical vortices - the Kida vortex is an example. Beyond a critical shear rate, the Kida vortex is known to exhibit Lagrangian chaos; the tracer pathlines are chaotic. We study the dynamics of heavy inertial particles in a Kida vortex, investigating how particle inertia can compete with background shear to suppress the occurrence of chaotic trajectories.   

From hydrodynamics to dipolar colloids: modeling complex interactions and self-organization with generalized potentials

When spherical particles are submerged in a viscous fluid and subjected to oscillations, they align themselves in one-particle-thick chains or multiple-particle-wide bands. Both are oriented perpendicular to the oscillation direction with a regular spacing between them, which depends on the oscillatory forcing.

 

This self-organization is a nonlinear effect, driven by vortices in the period-averaged flow, or steady streaming flow. These vortices vary in size, position, and magnitude with flow conditions, resulting in complex particle-fluid interactions. Overall, the hydrodynamic interactions between two neighboring chains can be divided into short-range attraction, mid-range repulsion, and long-range attraction.

 

To capture the essential aspects of the self-organization, we introduce simplified model potentials that incorporate the aforementioned interactions. Using Monte Carlo simulations, we explore the parameter space and successfully replicate the patterns observed in the hydrodynamic system.

 

Furthermore, we apply our models to electrorheological fluids, consisting of colloidal particles with parallel dipole moments. We highlight the similarities between the systems, effectively bridging interdisciplinary gaps and enhancing the understanding of self-organization processes.   

Heavy inertial particles near two co-rotating vortices: Chaos, Entrapment and Collisions

Chaotic motion, collisions, clustering, mixing and entrainment of inertial particles is important for various natural and technological processes. To understand the origin of these, we study inertial particles with densities slightly higher than the background fluid near two co-rotating vortices. We find that heavy inertial particles can get entrapped indefinitely near fixed points, limit cycles or chaotic attractors, depending on the density ratio and Stokes number (St). As St is monotinically increased from zero, limit cycles can undergo period doubling bifurcations up to chaos, as well as period-doubling and then period-halving bifurcations back to a fixed point. The basin-of-attraction is generally large, and can persist even for St~O(1) for certain density ratios. Importantly, these behaviours cannot be predicted using a perturbative field description of particle velocity.   

Periodic orbits of particles settling under gravity in a viscous fluid

To understand basic features of the dynamics of particle systems settling under gravity in a very viscous fluid, it is useful to study simple models. A class of periodic orbits of three rigid spheres in a vertical plane is found numerically for certain intial configurations. The multipole expansion corrected for lubrication based on the Stokes equations is used. Basic features of the periodic solutions, including their sensitivity to small perturbations, are analyzed. It is shown that the same type of the periodic motion was observed elsewhere for a more complex system.   

Caustics caused by vortices on active and inactive particles

Small and heavy particles or droplets in vortical flows are centrifuged out of regions of high vorticity and form caustics, at intermediate Stokes number [Ravichandran and Govindarajan, Physics of Fluids 27, 033305 (2015)]. For a dilute suspension of non-interacting particles, if the particle velocity field can indeed be written down, caustics mark the divergence in the gradient of this field. Here we observe singular features in particle number-density. These singularities represent interparticle collisions which are consequential in coalescence and aggregation processes [Wilkinson et al. Phys. Rev. Lett. 97, 048501 (2006)]. 

In the limit of vanishing Stokes number, we find that the flow regions promoting caustics of finitely dense particles have significantly different characteristics from those of infinitely dense particles. This is exemplified in 2D where there is an upper limit on the background strain only for finitely dense particles. We study the motion of inertialess motile particles in ambient flows and show that these dynamics can be mapped to that of inertial non-motile particles. Using a singular perturbation analysis we show that self propelled particles display “active” caustics in the inner region of the vortex flow, and we numerically study the dynamic identification of caustics regions in turbulent flows based on the Okubo Weiss parameter and finite time Lyapunov exponents. Finally, we discuss how caustics limit the applicability of a continuum description of particles.   

The deformation of particle aggregates due to hydrodynamic shear and its role in disaggregation

Much of the particulate matter in natural aquatic environments exists in a state of aggregated clumps. This clumping influences the suspended particle buoyancy and drag, which in turn greatly alters its transport characteristics. Disaggregation, where particle aggregates break apart into smaller sub-aggregates, is a complex process that depends heavily on the aggregate morphology, interparticle bonds, and microscale hydrodynamic forces. This process is further complicated by the fact that much of the particulate matter in natural aquatic environments is biological (e.g. phytoplankton). To clarify the disaggregation process of marine phytoplankton aggregates, we conducted disaggregation experiments with two types of phytoplankton species; Odontella aurita and Skeletonema grethae. We compare their disaggregation characteristics to those of abiotic particles (sulfate polystyrene and polyethylene microspheres) with distinct interparticle bond forces, which we quantified using the extended DLVO theory. Experiments were conducted by using Lagrangian particle tracking in a custom-built, laminar-flow disaggregation tank. Here, we present a force balance analysis using the Maxey-Riley equation to determine the coupling force relevant to aggregate fragmentation. We found that the breakup strength of an aggregate can be derived from the inter-particle bonding force and its porous structure. Moreover, this study also revealed that individual aggregates display a shear-thickening behavior when subjected to tensile stress.   

Microfluidic manipulation of extracellular vesicles for mechanical property estimation

Recent discoveries have shown that dilute suspensions of colloidal particles with diameters ranging from 100 nm – 1 µm can be manipulated within microchannels (100 – 300 µm wide x 25-50 µm deep x 2-4 cm long) for a variety of applications. Our group has reported on migration and assembly of polystryrene colloidal particles previously.

Recently, extending our expertise in microfluidics and colloidal particle manipulation, we have evaluated the flow of extracellular vesicles (EVs) from cancer patients and associated tumor cell lines. We have shown that these vesicles can be separated and captured for further analysis from a complex, multi-component fluid. The separation and capture method was implemented on the same hybrid micro-nanofluidic device. The separation occurs through a nanochannel network, often implemented as a membrane bridging two microchannels. Similar to other results, the separation is a mechanical filtration process. As the extracellular vesicles are soft, lipid-covered structures that protect valuable cargo, the mechanical deformation analysis of these vesicles subject to a flow-based filtration was found to be deficient.

In this work we report on a methodology that uses flow through nanochannel membrane networks (diameter of filtration pores is ~ 200 nm) for EVs, classified to two size regimes as small EVs (< 150 nm diameter) and large EVs (> 150 nm) and combines the flow data with high resolution transmission electron microscopy. This combination approach allows quantification of mechanical deformation without damaging EVs or the EV-cargo for estimation of EV mechanical properties. We find that the EV properties estimated with a whole-EV deformation analysis yields results with the estimated modulus of elasticity being < 1 MPa for the specific Sarcoma-relevant EVs evaluated as a model system.