Alan L. Graham

Bio: Alan L. Graham is an academic researcher from Los Alamos National Laboratory. The author has contributed to research in topics: Newtonian fluid & Shear flow. The author has an hindex of 21, co-authored 71 publications receiving 2662 citations. Previous affiliations of Alan L. Graham include University of Sydney & University of New Mexico.

A constitutive equation for concentrated suspensions that accounts for shear‐induced particle migration

Abstract: A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear‐induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start‐up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady‐state experiments as well as for different particle sizes.

Experimental observations of particle migration in concentrated suspensions: Couette flow

Abstract: Nuclear magnetic resonance (NMR) imaging was used to observe the evolution of radial concentration and velocity profiles of initially well‐mixed concentrated suspensions of spheres in viscous Newtonian liquids undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). In Couette flow, particles migrate from the high shear‐rate region near the inner rotating cylinder to the low shear‐rate region at the outer wall. The particle concentration near the outer wall approaches maximum packing for randomly distributed spheres at steady state, and velocity profiles reveal that the suspension is almost stagnant in these regions. For unimodal suspensions of spheres, the shear‐induced migration of large particles results in concentric two‐dimensional, circular sheets of particles arranged in hexagonal close‐packed arrangements extending inward from the outer wall. This paper examines the functional dependence of particle migration in concentrated suspensions undergoing shear flow in a wid...

Migration of particles undergoing pressure-driven flow in a circular conduit

Abstract: This study focuses on the demixing of neutrally buoyant suspensions of spheres during slow, pressure driven flows in circular conduits. Distributions of the solid fraction of particles, φ, and the suspension velocity, ν, are measured at different lengths from a static in-line mixer. Experiments were conducted over a range of volume average solids fractions, φbulk (0.10⩽φ⩽0.50), and at two different ratios of the particle radius, a, to the radius of the circular conduit, R (a/R=0.0256 and a/R=0.0625). At φbulk⩾0.20, the particles rapidly migrate to the low-shear-rate region in the center of the conduit. This migration results in a blunting of the ν profile, relative to the parabolic profile observed in homogeneous Newtonian fluids. For the flow geometry with the smaller ratio of a/R, the φ profile builds to a sharp maximum or cusp in the center. Particle structures are observed in the experiments with the higher a/R. The entrance lengths for the development of the φ and ν fields, Lφ and Lν, respectively, are strong functions of a/R and φbulk. Lφ and Lν rapidly decrease as φ and a/R increase. Over the range of our data, the ν profiles are observed to develop more rapidly than the φ profiles. The experimental results are compared with fully developed flow predictions from the shear-induced migration (SIM) model and the suspension balance (SB) model. At the smaller a/R, the SIM model more accurately predicts the experimental results. At larger a/R, some qualitative features of the experimental results are better predicted by the SB model, however, neither model provides good quantitative predictions, especially at low φbulk.

Note: NMR imaging of shear‐induced diffusion and structure in concentrated suspensions undergoing Couette flow

Abstract: This note describes nuclear magnetic resonance (NMR) imaging of two concentrated suspensions undergoing flow between rotating concentric cylinders (wide‐gap, annular Couette flow). Suspensions of both monodisperse (50% by volume) and bidisperse (60% by volume) spheres are studied. We find that particles migrate from the higher shear rate regions near the rotating inner cylinder to the lower shear rate regions near the stationary outer wall, establishing large concentration gradients after only a short time. In addition, the large particles in the bimodal suspension form concentric cylindrical sheets, parallel to the axis of the Couette device, which rotate relative to each other. In the Couette devices used in these studies, no significant axial migration of the particles is observed: the dispersion of particles is almost entirely in the radial direction. This particle migration and structure formation is believed responsible for torque reductions and other anomalous behavior witnessed during rheological ...

Particle migration in a Couette apparatus: Experiment and modeling

Abstract: 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...

Computational fluid dynamics of dispersed two-phase flows at high phase fractions

Abstract: This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.