Session P27: Particle-laden Flows: General & Suspensions: Instability and Confined Flows

Mechanisms affecting ring-shaped particle deposition patterns in an inertial impactor

Experiments and simulations are presented showing the particle deposition patterns obtained from inertial impactors, particle sizing devices that are commonly used in field and laboratory applications.  This work focuses on low S/W impactors (S/W ~ O(0.01)), where W is the nozzle diameter and S is the distance of the nozzle to the impactor plate.  This low S/W condition results in ring-shaped particle deposition patterns where the ring diameter D is inversely proportional to the particle diameter d.  This behavior may enable development of single-stage impactors capable of obtaining particle size distributions over a range of diameters, something not possible in current multi-stage impactor implementations where S/W~1 and the deposition pattern is a disk and whose geometry is not sensitive to d.  The goal of the research presented here was to determine how S/W affects the relationship between D and d.  A subsequent goal was to then use simulations to determine the physical mechanisms that control the deposition patterns that are experimentally observed, thereby facilitating designs that maximize the sensitivity of D to d.  The experimental results show that while ring patterns require a small S/W, the sensitivity of D to d increases with S/W indicating that there is an optimal value of S/W.  Simulations reveal that the formation of rings and their diameter is determined by deviations of particles from their streamlines in a region very close to the impactor surface.  A discussion is presented of possible practical implementations of this small S/W approach for obtaining particle size distributions.    

Effect of relative humidity on particle bounce in inertial impactors

The role of relative humidity on particle bounce in an inertial impactor was investigated. Inertial impactors are devices used to obtain particle size distributions by passing particle-laden air through a nozzle and collecting particles on a flat surface placed directly below the nozzle. In this research monodisperse hygroscopic particles were impacted on a flat surface of a single stage inertial impactor while varying the relative humidity of the flow. The results show that a clear ring pattern occurs when the relative humidity is high. When the relative humidity is low secondary deposits beyond the ring occur. It was hypothesized that this behavior is due to the complex interactions between (i) the increase in repulsion between the hygroscopic particles and the hydrophobic surface with relative humidity, (ii) multiple bounces along the particle trajectory, and (iii) kinetic energy loss at each particle bounce. Particle trajectory simulations were performed where the effect of particle/surface interactions was quantified via the Hamaker constant (A) and the loss of kinetic energy via the coefficient of restitution (e). Values of (A, e) were found that forced the simulations to agree with the experimental results to a reasonable degree. The possible role of other effects is discussed including the Magnus effect and Saffman lift forces.   

Going with the Flow: Colloidal Dynamics at Moving Immiscible Fluid Interfaces

A wide array of processes, from membrane defouling to contaminant transport and groundwater remediation, involve interactions between deposited colloidal particles and an immiscible fluid interface. Previous works studying the interactions between individual particles and a moving interface have shown that the interplay between colloidal interactions, hydrodynamics, and capillarity plays a critical role in determining the transport of both colloids and fluid. However, in many cases, particle deposits form dense aggregates, giving rise to new complexities that cannot be described by single-particle models. To address this fundamental gap in knowledge, we directly visualize the interactions between multilayer colloidal particle deposits and moving immiscible fluid droplets in microchannels.

As the immiscible fluid interface passes over particles, we observe that they strongly adsorb to it, despite their lack of surface activity under quiescent conditions. We show that this surprising behavior arises due to the influence of capillary forces exerted by the fluid interface as it impinges on the particles, forcing them to overcome the electrostatic energy barrier to adsorption. Thus, the surface coverage of the interface by particles increases with time as the fluid droplet traverses the channel. Eventually, the interface becomes saturated with adsorbed particles—triggering an abrupt fluid-solid transition in its rheology that alters subsequent flow. As a consequence, the interface has a finite “carrying capacity”, continually sloughing off particles when it is sufficiently jammed. While injection of immiscible fluid interfaces has been explored for its potential to remove deposited particles from solid surfaces, our study reveals the limitation that fluid interfaces can rapidly become saturated by particles. Our results show that this limitation can be overcome by increasing fluid interfacial area, suggesting a new approach to anti-fouling using dispersed droplets.   

Characterization of the instability of a Rankine vortex in semi-dilute dusty flows using Linear stability analysis and Eulerian-Lagrangian simulations

This study investigates the effect of inertial particles on the stability of a two-dimensional Rankine vortex in semi-dilute dusty flows. Unlike the particle-free case where the vortex is stable to infinitesimal disturbances, we show that the feedback force from the suspended inertial particles triggers a novel instability specific to two phase flows. For weakly inertial particles with a typical Stokes number smaller than 0.01, we perform a linear stability analysis using continuum conservation equations, namely, the Two-Fluid model. These equations are coupled with the asymptotic particle velocity field for low Stokes particles whose velocity deviates from that of the suspending fluid by an inertial correction. The growth of the instability is characterized in terms of the disturbance azimuthal mode, the particle Stokes number, particle volume fraction, and mass loading. We show that the instability persists even for tracer particles (St = 0), provided that the mass loading exceeds a certain threshold. Comparison with Eulerian-Lagrangian simulations show that the linear stability analysis is able to predict the instability properties for small Stokes number. Additional Eulerian-Lagrangian simulations are presented for moderate and high Stokes number particles (St~1), where the effects of preferential concentration, and discrete nature of the particle phase are shown to control the dynamics of the particle-laden vortex.   

Uncertainty quantification analysis of point-particle Eulerian-Lagrangian systems with stochastic forcing

Particle-laden and droplet-laden flows are present in many anthropogenic and natural environments and have been a recurrent interest in the scientific community. Essentially two modeling frameworks can be considered to describe these environments including the Eulerian-Eulerian (EE) frame, which assumes  both phases as a continuum and the Eulerian-Lagrangian (EL) where the particle or dispersed phase is traced along its Lagrangian path and the carrier gas or liquid is modeled in the Eulerian frame. A key element in both modeling frames is the forcing between the phases. Particularly, in reduced models such as the point-particle model, this forcing is not known analytically in general for a wide range of particle conditions and can only be determined empirically or in a data-driven manner within certain confidence bounds. To alleviate this modeling inaccuracy, one must understand the propagation of the uncertainty of the forcing to the solution of the particle-laden flow problem. This can then be applied to multiscale and data-driven models in which uncertainty quantification plays a central role. In this talk, we will discuss a comprehensive analysis of the propagation of a quantified uncertainty in a random particle forcing into an Eulerian-Lagrangian system by developing and comparing the Monte Carlo method, the method of moments and the method of distributions. The Monte Carlo method and the probability density function model that follows from the method of distributions are closed. The method of moments is not and we close it a priori with the Monte Carlo results. The three methods are compared for multiple random forcing distributions and for two one-way coupled canonical problems with carrier flows that include a uniform flow and the stagnation flow.   

Effect of Urban Landscapes on the Transport and Spotting Risk of Firebrands

Firebrand spotting is a major mechanism associated with the propagation of wildfires, and it is caused by the transport and eventual settling of flying burning materials (known as firebrands or flying embers). Upon landing, firebrands can ignite local fuel, causing secondary fires, which can rapidly spread to unburned areas far from the main fire. This makes fire spreading behavior more erratic and difficult to predict, therefore reducing the effectiveness of fire mitigation methods. It is known that firebrand transport depends heavily on the characteristics of the ambient flow. Therefore, a better understanding of firebrand transport in turbulent flows over urban landscapes will allow to better guide fire mitigation methods and reduce fire losses associated with wildland-urban interface (WUI) fires.

In this study, the effect of topography-induced turbulence on the transport, smoldering lifetime and spotting risk of spherical firebrands is investigated. Large Eddy Simulation is used to simulate the turbulent flow over an idealized urban region. Smoldering particles of different sizes are released within the boundary layer and the evolution of their trajectories, dispersion, and combustion state are obtained using a Lagrangian transport model. When comparing these results with a case without obstacles, it is observed that firebrand dispersion and spotting potential are significantly enhanced under the presence of the complex turbulent flow induced by the non-flat topography.   

N2-instability in suspensions undergoing Couette flow

In this study, we consider the possibility of N₂-instability in suspensions, as proposed by Carpen and Brady [J. NonNewt. Fluid Mech. 102(2), 2002]. This transverse instability arises due to the jump in the second normal stress difference between two fluids. We perform a linear stability analysis in a two-layer Couette flow using a classical Morris-Boulay constitutive law for the suspension. Interestingly, this leads to an exact closed-form theoretical solution. Our results are slightly different from Carpen and Brady, suggesting that this instability depends much on the exact constitutive law for the suspension. We have also performed 3D numerical simulations of this instability in the linear regime and were able to validate our theoretical expressions. Although this two-layer Couette flow is appealing due to its simplicity, it is likely to show shear-induced resuspension and migration with time scales similar to the N₂-instability. This could possibly explain why it has not been definitely attested in experiments so far. We discuss configurations in which this instability could prevail over migration.   

Instabilities in two-dimensional suspension flows

We study the emergence of miscible fingering in quasi-two-dimensional suspension flows, by combining experiments and theory. We experimentally inject silicone oil into the mixture of the same oil and non-colloidal particles inside a highly confined channel. The gap thickness is comparable to the particle diameter, so that suspended particles form a monolayer inside the cell. Our experiments reveal that miscible fingering is observed at all concentrations, distinct from the continuum limit. In addition, the emergent fingers exhibit concentration-dependent wavelengths as well as continuous particle fluctuations, reminiscent of 2D droplet ensembles. To rationalize our observations, we develop a kinetic theory that implements long-range hydrodynamic interactions between highly confined particles.   

Extrusion of flexible microfiber suspensions

The flow of fiber suspensions occurs in industrial processes such as paper making and filtration. Recently, flexible (high aspect ratio) polymeric microfiber suspensions have been demonstrated to form gel-like materials under shear stress or during extrusion. Using microscopic imaging, we systematically studied the extrusion process in three dimensions. We found that during extrusion and dependent of the extrusion flow rate the extrudate volume fraction varies relative to the initial suspension volume fraction. At a small flow rate, the channel is clogged and the extrudate is purely the solvent. At a higher flow rate, the microfibers are extruded but at a higher volume fraction than their pre-extrusion state. The extrudate volume fraction reaches a plateau when the pre-extrusion volume fraction exceeds a critical value. Using rheometric measurements, we observed that the critical volume fraction is related to the emergence of yield stress in the suspension. A model to rationalize the experimentally generated extrusion phase diagram will be presented.   

Shear-induced migration of confined flexible fibers

In this experimental study, we report the shear-induced migration of flexible fibers in suspensions confined between two parallel plates.

Non-Brownian fiber suspensions are placed and imaged in a rheo-microscopic set-up, where the top and the bottom plates counter-rotate and create a Couette flow.

Initially, the fibers are near the bottom plate due to sedimentation.

Under shear, the fibers move with the flow and migrate towards the center between the two walls.

Statistical properties of the fibers, such as the mean values of the positions, orientations, and end-to-end lengths of the fibers, are used to characterize the behaviors of the fibers.

The observation shows that more flexible fibers exhibit faster migration.

Different behaviors of the fibers are quantified with different flexibilities of the fibers, and the structures and the dynamics of the fibers are correlated with the migration.   

Not Participating

We employed suspension balance model (SBM) and rheological constitutive laws to numerically examine the Taylor-Couette flow of concentrated, neutrally buoyant, and non-colloidal suspensions when the inner cylinder is rotating and the outer one is stationary. We varied the bulk particle volume fraction ϕ_b = 0.1 ~ 0.3, while the radius ratio of cylinders is η = 0.877 and the particle size ratio is ϵ (= d/a) = 60, d is the gap width of cylinders and a is the radius of particles. By varying the Reynolds number of suspensions based on the rotating angular velocity and the effective viscosity of suspensions, we also analyzed the imapct of suspended particles on flow transition. Although in the model the inertial migration of particles is neglected, similar to the reported experiments we observed the circular Couette flow (CCF) transitions via ribbons (RIB), spiral vortex flow (SVF), and wavy spiral vortex flow (WSVF) to wavy vortex flow (WVF). We also found a hysteresis during the transitions where the transitons to higher modes occur early at more dense suspensions. Moreover, friction and torque coefficients of the suspension flow are computed and compared.   

Not Participating

We study the role of shear induced migration and particle induced normal stresses on the boundary layer formation and stability of a particle-laden, gravity-driven shallow flow. Looking at the boundary layer formation at the 'shallow' limit, we find that increasing bulk particle volume fractions lead to a reduction in the entrance length. In the absence of particles, gravity-driven shallow flows are known to exhibit a long-wavelength instability, as first identified by Yih (1963), and a short wave instability, as identified by Kelley (1989). We perform a linear stability analysis and find that the shear-induced migration of particles leads to an enhancement of both modes of instability. We also find that this prediction of an enhanced instability is independent of the choice constitutive model used to describe the particle phase as long as the chosen model has elements of shear induced migration.