Lisa Ann Mondy

Particle migration in a Couette apparatus: Experiment and modeling

Suspensions comprised of neutrally buoyant spheres in Newtonian fluids undergoing creeping flow in the annular region between two rotating, coaxial cylinders (a wide-gap Couette) display a bulk migration of particles towards regions of lower shear rate. A series of experiments are performed to characterize this particle migration, including the influence of particle size, surface roughness, and volume fraction. Little, if any, effect of particle surface roughness is observed. An existing continuum diffusive-flux model [Phillips et al. (1992)] for predicting particle concentration profiles in monomodal suspensions is evaluated using the current series of experimental data. This model predicts a dependence of the migration rate on the square of the suspended particles’ radius, a2; whereas the present experiments indicate that systems with average particle volume fractions of 50% display a rate that scales with a3. Previous use of the diffusive-flux model has assumed constant values for diffusion coefficient...

Flow-aligned tensor models for suspension flows

Abstract Models to describe the transport of particles in suspension flows have progressed considerably during the last decade. In one class of models, designated as suspension balance models, the stress in the particle phase is described by a constitutive equation, and particle transport is driven by gradients in this stress. In another class of models, designated as diffusive flux models, the motion of particles within the suspension is described through a diffusion equation based on shear rate and effective viscosity gradients. Original implementations of both classes of models lacked a complete description of the anisotropy of the particle interactions. Because of this, the prediction of particle concentration in torsional flows in parallel plate and cone-and-plate geometries did not match experimental data for either class of models. In this work, the normal stress differences for the suspension balance formulation are modeled using a frame-invariant flow-aligned tensor. By analogy, the diffusive flux model is reformulated using the same flow-aligned tensor, which allows separate scaling arguments for the magnitude of the diffusive flux to be implemented in the three principal directions of flow. Using these flow-aligned tensor formulations, the main shortcomings of the original models are eliminated in a unified manner. Steady-state and transient simulations are performed on various one-dimensional and two-dimensional flows for which experimental data are available, using finite-difference and finite-element schemes, respectively. The results obtained are in good agreement with experimental data for consistent sets of empirical constants, without the need for ad hoc additional terms.

Modelling of concentrated suspensions using a continuum constitutive equation

We simulate the behaviour of suspensions of large-particle, non-Brownian, neutrally-buoyant spheres in a Newtonian liquid with a Galerkin, finite element, Navier–Stokes solver into which is incorporated a continuum constitutive relationship described by Phillips et al . (1992). This constitutive description couples a Newtonian stress/shear-rate relationship (where the local viscosity of the suspension is dependent on the local volume fraction of solids) with a shear-induced migration model of the suspended particles. The two-dimensional and three-dimensional (axisymmetric) model is benchmarked with a variety of single-phase and two-phase analytic solutions and experimental results. We describe new experimental results using nuclear magnetic resonance imaging to determine non-invasively the evolution of the solids-concentration profiles of initially well-mixed suspensions as they separate when subjected to slow flow between counter-rotating eccentric cylinders and to piston-driven flow in a pipe. We show good qualitative and quantitative agreement of the numerical predictions and the experimental measurements. These flows result in complex final distributions of the solids, causing rheological behaviour that cannot be accurately described with typical single-phase constitutive equations.

The viscosity-volume fraction relation for suspensions of rod-like particles by falling-ball rheometry

The relative viscosities of suspensions of randomly oriented rods in a Newtonian fluid were measured using falling-ball rheometry. The rods were monodisperse and sufficiently large to render colloidal and Brownian forces negligible. Steel and brass ball bearings were dropped along the centreline of cylindrical columns containing the suspensions. The terminal velocities of the falling balls were measured and used to determine the average viscosities of the suspensions. The suspensions behaved as Newtonian fluids in that they were characterized by a constant viscosity. They exhibited a linear relative viscosity-volume fraction relationship for volume fractions less than 0.125, and, for volume fractions between 0.125 and 0.2315, the specific viscosity increased with the cube of the volume fraction. The relative viscosity was found to be independent of falling-ball size for a ratio of falling ball to fibre length greater than 0.3. It was found to be independent of the diameter of the containing cylindrical column for a ratio of column diameter to fibre length greater than 3.2. The value determined for the intrinsic viscosity is in good agreement with theoretical predictions for suspensions of randomly oriented rods.

Nuclear magnetic resonance imaging of particle migration in suspensions undergoing extrusion

Nuclear magnetic resonance imaging was used to measure fluid velocity and fluid fraction in suspensions flowing into an abrupt four-to-one contraction in pipe diameter, through a section of smaller diameter pipe, and out of an abrupt expansion back to the original pipe size. Suspensions of 50% by volume of particles in a Newtonian liquid were forced to flow by a plunger moving at a constant, slow velocity. Two sizes (100 and 675 μm diameter) of suspended spheres were studied. Conditions were such that buoyant, inertial, Brownian, and surface forces could be assumed to be negligibly small. Little change in particle concentration was seen in the region of the contraction until the plunger was within about one pipe diameter of the contraction. The particles in the small diameter section of pipe migrated toward the pipe axis, the region of lowest shear rate. Particle concentration varied downstream of the pipe expansion, especially in a suspension of the larger particles. Over time, particles were partially s...

Shear-induced particle migration in suspensions of rods

Shear‐induced migration of particles occurs in suspensions of neutrally buoyant spheres in Newtonian fluids undergoing shear in the annular space between two rotating, coaxial cylinders (a wide‐gap Couette), even when the suspension is in creeping flow. Previous studies have shown that the rate of migration of spherical particles from the high‐shear‐rate region near the inner (rotating) cylinder to the low‐shear‐rate region near the outer (stationary) cylinder increases rapidly with increasing sphere size. To determine the effect of particle shape, the migration of rods suspended in Newtonian fluids was recently measured. The behavior of several suspensions was studied. Each suspension contained well‐characterized, uniform rods with aspect ratios ranging from 2 to 18 at either 0.30 or 0.40 volume fraction. At the same volume fraction of solids, the steady‐state, radial concentration profiles for rods were independent of aspect ratio and were indistinguishable from those obtained from suspended spheres. On...

Direct measurements of shear-induced particle migration in suspensions of bimodal spheres

A variety of studies reported in the literature have established that initially well mixed suspensions subjected to non-homogeneous shear flows attain an anisotropic particulate structure. It has also been shown that non-homogeneous shearing causes suspensions of unimodal spheres to demix, i.e., gradients in solids concentration are formed. The objective of this study was to determine the effect of non-homogeneous shear flows on suspensions of bimodal particles, and specifically, to determine if the solids concentration gradients which develop are accompanied by size segregation of the coarse with respect to the fine fraction. We used the simplest and most direct methods to determine the relative solids concentrations: visual observation of tracer particles in transparent suspensions and physical separation of the coarse and fine solid fractions. Three different types of non-homogeneous shear flows were examined, and in each case the data support two main conclusions: 1) suspended particles migrate from regions of high shear rate to regions of low shear rate, and 2) the coarse fraction of particles migrates much faster than the fine fraction, leading to size segregation of initially well-mixed suspensions. While the former conclusion is consistent with other studies reported in the literature, to our knowledge this paper provides the first data supporting and, to a limited extent, quantifying the latter conclusion.

Stage Response Calibration of the Mark III and Marple Personal Cascade Impactors

Experimental and correlated stage responses (the fraction of particles entering an impactor that are collected on a stage) are presented for the Andersen Mark III and Marple personal cascade impactors. The impactors were operated upright and fully assembled so that interstage interference and wall losses could be properly studied. The observed stage responses showed maxima that fell significantly short of unity, meaning that a monodisperse aerosol is never collected exclusively on one stage, but is distributed among several stages and internal losses. Correlations for the stage responses are presented so that the experimental results can be used to determine size distributions with available data-inversion algorithms. Simulations with log-normal distributions show significant differences between dpa50 histograms and the more accurate distributions that result by taking the response functions into account.

NMR measurements and simulations of particle migration in non-newtonian fluids

Shear-induced migration of particles is studied during the slow flow of suspensions of neutrally buoyant spheres, at 50% particle volume fraction, in an inelastic but shear-thinning, suspending fluid. The suspension is flowing in between a rotating inner cylinder and a stationary outer cylinder. The conditions are such that nonhydrodynamic effects are negligible. Nuclear magnetic resonance (NMR) imaging demonstrates that the movement of particles away from the high shear rate region is more pronounced than for a Newtonian suspending liquid. We test a continuum constitutive model for the evolution of particle concentration in a flowing suspension proposed by Phillips et al., but extended to shear-thinning, suspending fluids. The fluid constitutive equation is Carreau-like in its shear-thinning behavior but also varies with the local particle concentration. The model captures many of the trends found in the experimental data, but does not yet agree quantitatively. In fact, quantitative agreement with a diffusive flux constitutive equation would be impossible without the addition of another fitting parameter that may depend on the shear-thinning nature of the suspending fluid. Because of this, we feel that the Phillips model may be fundamentally inadequate for simulating flows of particles in non-Newtonian suspending fluids without the introduction of a normal stress correction or other augmenting terms.

A numerical study of three‐dimensional Jeffery orbits in shear flow

We perform numerical simulations of rods and spheroids undergoing Jeffery orbits in a variety of shear flows. The numerical simulations are based on the boundary element method, which allows for the accurate modeling of the problem geometry. We compare the period of rotation for spheroids and rods, both far from walls and very close to walls. We find that the wall effects in three dimensions are minimal, even for flow in gaps not much larger than the longest dimension of the particle. We also show that two‐dimensional simulations grossly overpredict the wall effects seen in three dimensions. Results are similar for both linear and nonlinear shear flows. We also briefly look at the orbital motion of a particle in close proximity to another particle, and show that, again, there is very little effect on the period of rotation, although the resulting centroid trajectories are very different from that of an isolated particle.