Particles In non-Newtonian Fluids Research Articles

Lift of a Spherical Particle Subject to Vorticity and/or Spin

A LTHOUGH the drag and gravitational forces are typically the most important to particle motion, the lift force can often be significant and can even approach the magnitude of the other two forces in some circumstances for surface spin velocities on the order of the translational particle velocity. As such, there are a number of multiphase systems in which consideration of lift is vital. The lift has been noted to be important for lateral migration in tubes (Saffman [1]), effectiveness of microcentrifuges (Heron et al. [2]), and particle deposition in boundary layers (Young and Leeming [3]). Another flowfield for which particle lift effects are important is that of the rotating bioreactor, which allows animal tissue growth under idealized conditions, similar to that obtained in microgravity conditions [4]. In many of these conditions, the particle can be considered as spherical and solid and the surrounding fluid as incompressible and Newtonian, as will be the focus of this review. However, there have beenmany excellent reviews on particle lift that discuss other conditions. In particular, the review by Leal [5] discussed dynamics and theoretical results for nonspherical particles, deformable particles, and particles in non-Newtonian fluids. On the subject of clean bubbles, Drew [6], Magnaudet and Eames [7], and Tomiyama et al. [8] discussed theory and models for lift in shear, rotational, and straining flows. For noncontinuum conditions, Wang [9] investigated the effect of particle spin in free-molecular flow and obtained a lift force that acted in a direction opposite to that of drag in continuum creeping-flow conditions. Recently, Volkov [10] investigated the transition between the continuum and the freemolecular regimes for spinning particles to obtain the critical Knudsen number at which particle spin did not yield lift. To discuss solid particle lift for incompressible continuum Newtonian flow, it is helpful to first define the dimensionless parameters that influence lift, as well as the various forms of the lift coefficient. In general, the particle velocity v is defined as the translational velocity of the particle center of mass xp. The continuous-fluid velocity is generally defined in all areas of the domain unoccupied by particles. However, a hypothetical continuous-phase velocity can be extrapolated to the particle centroid and will be denoted as u and termed the “unhindered velocity.”The relative velocity of the particlesw is then based on the unhindered velocity (i.e., along a particle trajectory):

Bubbles, drops and particles in non‐newtonian fluids. R. P. Chhabra

The Canadian Journal of Chemical EngineeringVolume 85, Issue 2 p. 251-252 Book Review Bubbles, drops and particles in non-newtonian fluids. R. P. Chhabra Jalel Azaiez, Jalel Azaiez University of CalgarySearch for more papers by this author Jalel Azaiez, Jalel Azaiez University of CalgarySearch for more papers by this author First published: 19 May 2008 https://doi.org/10.1002/cjce.5450850216Citations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume85, Issue2April 2007Pages 251-252 RelatedInformation

A Study of Particle Settling in Non-Newtonian Fluids—Part I: A New Method for the Study of Particle Settling in Drilling and Fracturing Fluids

A drag force measurement method is presented which makes it possible to study the settling of particles in transparent and opaque fluids. A dimensionless treatment that takes into account the shear thinning effects of fluids was applied to normalize the measured drag force data. A wide range of particle Reynolds numbers can be covered by this method and a profile of friction factor versus Reynolds number can be established by the proposed dimensionless treatment. An algorithm for the prediction of settling of particles in non-Newtonian fluids was introduced. It can be executed by a computer program. With a good set of experimental data, the settling velocities predicted by the computer model are very close to the measured ones in the fluids tested. This method can be used to study the suspension properties of drilling and fracturing fluids, transparent or opaque. The wide coverage of Reynolds number range simplifies the experiment.

Bubbles, drops, and particles in non-Newtonian fluids

Preface Preface to the First Edition Acknowledgements About the Author INTRODUCTION, SCOPE, AND ORGANIZATION NON-NEWTONIAN FLUID BEHAVIOR Definition of a Newtonian Fluid Non-Newtonian Fluids: Definition, Examples of Different Types, Mathematical Models Dimensional Considerations in the Mechanics of Viscoelastic Fluids Experimental Techniques: Rheometry RIGID PARTICLES IN TIME-INDEPENDENT FLUIDS WITHOUT A YIELD STRESS Governing Equations for a Sphere Spherical Particles in Newtonian Fluids Spheres in Shear-thinning Fluids Spheres in Shear-thickening Fluids Light Spheres Rising in Pseudoplastic Media Pressure Drop due to a Settling Sphere Non-Spherical Particles RIGID PARTICLES IN VISCOPLASTIC FLUIDS Static Equilibrium of Particles Flow Field: Shape and size of flow zones Drag Force Role of Values of Yield stress used in correlations Time Effects RIGID PARTICLES IN VISCOELASTIC FLUIDS Flow over a sphere Flow over a cylinder Other Studies Involving Interactions Between Non-Newtonian Characteristics, Particle Shape, Flow Field, etc. FLUID PARTICLES IN NON-NEWTONIAN MEDIA Formation of Fluid Particles Shapes of Bubbles and Drops in Free Rise or Fall Terminal Velocity-Volume Behavior in Free Motion Drag Behavior of Single Particles Bubble and Drops Ensembles in Free Motion Coalescence of Bubbles and Drops Breakage of Drops Motion and Deformation of Bubbles and Drops in Confined Flows NON-NEWTONIAN FLUID FLOW IN POROUS MEDIA AND PACKED BEDS Porous Medium Definition, Examples and Characterization Flow of Newtonian Fluids Flow of Non-Newtonian Fluids Miscellaneous Effects Two Phase Gas/Liquid Flow FLUIDIZATION AND HINDERED SETTLING Two-Phase Fluidization Sedimentation or Hindered Settling Three Phase Fluidized Beds MOMENTUM, HEAT AND MASS TRANSFER IN BOUNDARY LAYER FLOWS Boundary Layer Flows Viscoelastic Effects in Boundary Layers Mass Transfer from Bubbles Mass Transfer from Drops Mass Transfer from Ensembles of Bubbles and Drops Heat and Mass Transfer in Fixed Beds Heat and Mass Transfer in Fluidized Beds Heat and Mass Transfer in Three Phase Fluidized Beds Heat Transfer from Tube Bundles WALL EFFECTS Definition For Rigid Spheres For Non-Spherical Particles For Drops and Bubbles FALLING OBJECT RHEOMETRY Falling Ball Method Rolling Ball Method Rotating Sphere Viscometer Falling Cylinder Viscometer *All Chapters contain Introduction, Summary and Nomenclature sections References Subject index Author index

An experimental study of the settling velocities of single particles in non-Newtonian fluids

Therminal settling velocities of single particles, both spherical and non-spherical, were measured in various non-Newtonian fluids. The shear rheology of each fluid was determined using a Weissenberg rheogoniometer. The spherical particles varied in radius and density, and the non-spherical particles were marble chippings selected such that their volume was within the range of sphere volumes. Terminal settling velocities were analysed using a method for determining the drag force on a sphere falling in a power law fluid. A particle falling through a fluid generates a localised shear rate in the fluid surrounding it. The analysis for the drag force was limited to the region bounded by slow particle settling, generating a shear rate within the first Newtonian region, and a rapid particle settling giving rise to inertial affects with Reynolds numbers greater than 0.1. Within the bounds of these constraints it was found to be difficult to obtain a polymer fluid which behaved as a power law fluid at the shear rates generated by the falling spheres. The sensitivity of a falling particle to a fluids shear history, and thus to a viscosity regime governed by an “effective shear rate” which itself generates, was demonstrated using a thixotropic fluid. The results indicate that the settling velocities of particles of irregular shape could be approximated by that of a sphere of equivalent volume and density.

The motion of small particles in non-Newtonian fluids

There are many problems in which the motion of a small particle, bubble or drop in a non-Newtonian fluid differs in an important qualitative way from its corresponding motion in a Newtonian fluid. From a theoretical point of view such problems are conveniently separated into two groups. In the first, some aspect of the particle's motion only exists, for small Reynolds number, because the suspending fluid is non-Newtonian. Examples of this class include the cross-stream (or lateral) motion of spherical particles in a unidirectional shear flow, rotational motion of an orthotropic particle in sedimentation (leading to a deterministic equilibrium orientation), and cross-orbital drift in the rotation of an axisymmetric particle in shear flow. In these cases, a major change in the orientation or position of the particle can result from small instantaneous contributions of non-Newtonian rheology to the particle's motion, provided that these act “cumulatively” over a sufficiently long period of time. An analytical description of the fluid mechanics relevant to this process may thus be based on the asymptotic limit of a nearly-Newtonian fluid using the so-called “retarded-motion” expansion, and a relevant constitutive model for viscoelastic materials is the Rivlin—Ericksen nth-order fluid. Comparison between theory and experiment shows excellent qualitative (and frequently quantitative) agreement for such problems even when the flow is too rapid, in a rheological sense, for strict adherence to the requirements of a retarded-motion expansion. The second major class of problems is that in which the observed difference between Newtonian and non-Newtonian behavior is due to an important, O(1) change in the fluid motion at all times. In this case, the only possible theoretical description which is valid in more than an asymptotic sense is one based on a full non-linear constitutive model, including “memory”, and thus a solution of the equations of motion is generally possible only via numerical methods. Unlike the first class of problems, an important determining factor in successful match between experiment and theory is therefore a judicious (fortunate?) choice of the constitutive model. In the second part of this paper, I shall discuss some examples of numerical and experimental studies which pertain to particle motions in the regime of strongly viscoelastic flows.

Tensile stress contribution of flow-oriented slender particles in non-newtonian fluids

A formula is derived for the intrinsic stress contribution from closely-spaced, rod-like rigid particles suspended in a non-Newtonian liquid subject to a simple extensional flow. The present results indicate that, compared to the Newtonian-fluid result given previously by Batchelor [1], a much smaller particle-stress effect may occur in non-Newtonian fluid, owing to shear thinning and possible tensile stiffening in the fluid itself. While unsubstantiated by any critical experimental test, this prediction appears to agree qualitatively with some recent experimental observations of Charrier and Rieger [29] on glass fibers in polymer melts. Further work is suggested for the relevant slender-body theory, particularly the far-field body influence in non-linear fluids.

The effect of finite boundaries on the motion of particles in non-Newtonian fluids

A general formula is derived for the effect of container boundaries on the motion of a particle immersed in a non-Newtonian fluid. The result is similar to the corresponding formula of Brenner[1] for Newtonian fluids except that it is valid only for the correction of the velocity and not of the force. For a sphere falling axially in a cylinder, a formula is given which is the non-Newtonian equivalent of the Faxen wall correction formula. The experimental results of Turian[14] are analyzed with this formula and the value of the zero-shear viscosity of his polymer solution is found by an extrapolation based on the theory of third order Rivlin-Ericksen fluids.