Rheology of suspensions with high particle inertia and moderate fluid inertia

2003 ◽  
Vol 480 ◽  
pp. 95-118 ◽  
Author(s):  
JONATHAN J. WYLIE ◽  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Fluid Inertia ◽  
Particle Inertia ◽  
High Particle

Dense, bounded shear flows of agitated solid spheres in a gas at intermediate Stokes and finite Reynolds numbers

2009 ◽  
Vol 618 ◽  
pp. 181-208 ◽  
Author(s):  
HAITAO XU ◽  
ROLF VERBERG ◽  
DONALD L. KOCH ◽  
MICHEL Y. LOUGE
Keyword(s):  
Shear Flows ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Solid Volume Fraction ◽  
Reynolds Numbers ◽  
Fluid Inertia ◽  
Particle Inertia ◽  
Dissipation Term ◽  
Solid Spheres ◽  
Fluctuation Energy

We consider moderately dense bounded shear flows of agitated homogeneous inelastic frictionless solid spheres colliding in a gas between two parallel bumpy walls at finite particle Reynolds numbers, volume fractions between 0.1 and 0.4, and Stokes numbers large enough for collisions to determine the velocity distribution of the spheres. We adopt a continuum model in which constitutive relations and boundary conditions for the granular phase are derived from kinetic theory, and in which the gas contributes a viscous dissipation term to the fluctuation energy of the grains. We compare its predictions to recent lattice-Boltzmann (LB) simulations. The theory underscores the role played by the walls in the balances of momentum and fluctuation energy. When particle inertia is large, the solid volume fraction is nearly uniform, thus allowing us to treat the rheology using unbounded flow theory with an effective shear rate, while predicting slip velocities at the walls. When particle inertia decreases or fluid inertia increases, the solid volume fraction becomes increasingly heterogeneous. In this case, the theory captures the profiles of volume fraction, mean and fluctuation velocities between the walls. Comparisons with LB simulations allow us to delimit the range of parameters within which the theory is applicable.

Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow

2013 ◽  
Vol 738 ◽  
pp. 563-590 ◽  
Author(s):  
T. Rosén ◽  
F. Lundell ◽  
C. K. Aidun
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Aspect Ratio ◽  
Shear Flow ◽  
Stokes Number ◽  
Spheroidal Particle ◽  
Fluid Inertia ◽  
Prolate Spheroidal ◽  
Particle Inertia ◽  
Neutrally Buoyant

AbstractThe basic dynamics of a prolate spheroidal particle suspended in shear flow is studied using lattice Boltzmann simulations. The spheroid motion is determined by the particle Reynolds number (${\mathit{Re}}_{p} $) and Stokes number ($\mathit{St}$), estimating the effects of fluid and particle inertia, respectively, compared with viscous forces on the particle. The particle Reynolds number is defined by ${\mathit{Re}}_{p} = 4G{a}^{2} / \nu $, where $G$ is the shear rate, $a$ is the length of the spheroid major semi-axis and $\nu $ is the kinematic viscosity. The Stokes number is defined as $\mathit{St}= \alpha \boldsymbol{\cdot} {\mathit{Re}}_{p} $, where $\alpha $ is the solid-to-fluid density ratio. Here, a neutrally buoyant prolate spheroidal particle ($\mathit{St}= {\mathit{Re}}_{p} $) of aspect ratio (major axis/minor axis) ${r}_{p} = 4$ is considered. The long-term rotational motion for different initial orientations and ${\mathit{Re}}_{p} $ is explained by the dominant inertial effect on the particle. The transitions between rotational states are subsequently studied in detail in terms of nonlinear dynamics. Fluid inertia is seen to cause several bifurcations typical for a nonlinear system with odd symmetry around a double zero eigenvalue. Particle inertia gives rise to centrifugal forces which drives the particle to rotate with the symmetry axis in the flow-gradient plane (tumbling). At high ${\mathit{Re}}_{p} $, the motion is constrained to this planar motion regardless of initial orientation. At a certain critical Reynolds number, ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, a motionless (steady) state is created through an infinite-period saddle-node bifurcation and consequently the tumbling period near the transition is scaled as $\vert {\mathit{Re}}_{p} - {\mathit{Re}}_{c} {\vert }^{- 1/ 2} $. Analyses in this paper show that if a transition from tumbling to steady state occurs at ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $, then any parameter $\beta $ (e.g. confinement or particle spacing) that influences the value of ${\mathit{Re}}_{c} $, such that ${\mathit{Re}}_{p} = {\mathit{Re}}_{c} $ as $\beta = {\beta }_{c} $, will lead to a period that scales as $\vert \beta - {\beta }_{c} {\vert }^{- 1/ 2} $ and is independent of particle shape or any geometric aspect ratio in the flow.

Motion of spheroid particles in shear flow with inertia

2014 ◽  
Vol 749 ◽  
pp. 145-166 ◽  
Author(s):  
Wenbin Mao ◽  
Alexander Alexeev
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Shear Flow ◽  
Rotation Period ◽  
Reynolds Numbers ◽  
Stokes Number ◽  
Simple Shear Flow ◽  
Fluid Inertia ◽  
Particle Rotation ◽  
Particle Inertia

AbstractIn this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.

An ellipsoidal particle in tube Poiseuille flow

2017 ◽  
Vol 822 ◽  
pp. 664-688 ◽  
Author(s):  
Haibo Huang ◽  
Xi-Yun Lu
Keyword(s):  
Phase Diagram ◽  
Poiseuille Flow ◽  
Stable State ◽  
Major Axis ◽  
Fluid Inertia ◽  
Initial State ◽  
Particle Inertia ◽  
Ellipsoidal Particle ◽  
Rolling Mode ◽  
Particle Geometry

A suspended ellipsoidal particle inside a Poiseuille flow with Reynolds number up to 360 is studied numerically. The effects of tube diameter ($D$), inertia of the particle and the flow, and the particle geometry (both prolate and oblate ellipsoids) are considered. When a prolate particle with $a/b=2$ is inside a wider tube (e.g. $D/A>1.9$), where $A=2a$ is the length of the major axis of the particle, the terminal stable state is tumbling. When the prolate particle is inside a narrower tube ($1.0<D/A<1.9$), log-rolling or kayaking modes may appear. Which mode occurs depends on the competition between fluid and particle inertia. When the fluid inertia is dominant, the log-rolling mode appears, otherwise, the kayaking mode appears. Inclined and spiral modes may appear when $D/A<1$ and $D/A=1$, respectively. For a prolate ellipsoid with $a/b=4$, if $1<D/A<1.9$, there is only the kayaking mode and the log-rolling mode is not observed. When an oblate particle is inside a wider tube (e.g. $D/A>3.5$), it may adopt the log-rolling mode. Inclined and intermediate modes are firstly identified in narrower tubes. The phase diagram of the modes is also provided. The modes in the phase diagrams were not found to be affected by the initial state of the particle based on limited observation.

The dynamical states of a prolate spheroidal particle suspended in shear flow as a consequence of particle and fluid inertia

2015 ◽  
Vol 771 ◽  
pp. 115-158 ◽  
Author(s):  
T. Rosén ◽  
M. Do-Quang ◽  
C. K. Aidun ◽  
F. Lundell
Keyword(s):  
Shear Flow ◽  
External Boundary ◽  
Full Description ◽  
Spheroidal Particle ◽  
Fluid Inertia ◽  
Prolate Spheroidal ◽  
Particle Inertia ◽  
Inertia Effects ◽  
Rotational States ◽  
Neutrally Buoyant

The rotational motion of a prolate spheroidal particle suspended in shear flow is studied by a lattice Boltzmann method with external boundary forcing (LB-EBF). It has previously been shown that the case of a single neutrally buoyant particle is a surprisingly rich dynamical system that exhibits several bifurcations between rotational states due to inertial effects. It was observed that the rotational states were associated with either fluid inertia effects or particle inertia effects, which are always in competition. The effects of fluid inertia are characterized by the particle Reynolds number $\mathit{Re}_{p}=4Ga^{2}/{\it\nu}$, where $G$ is the shear rate, $a$ is the length of the particle major semi-axis and ${\it\nu}$ is the kinematic viscosity. Particle inertia is associated with the Stokes number $\mathit{St}={\it\alpha}\,\mathit{Re}_{p}$, where ${\it\alpha}$ is the solid-to-fluid density ratio. Previously, the neutrally buoyant case ($\mathit{St}=\mathit{Re}_{p}$) was studied extensively. However, little is known about how these results are affected when $\mathit{St}\neq \mathit{Re}_{p}$, and how the aspect ratio $r_{p}$ (major axis/minor axis) influences the competition between fluid and particle inertia in the absence of gravity. This work gives a full description of how prolate spheroidal particles in the range $2\leqslant r_{p}\leqslant 6$ behave depending on the chosen $\mathit{St}$ and $\mathit{Re}_{p}$. Furthermore, consequences for the rheology of a dilute suspension containing such particles are discussed. Finally, grid resolution close to the particle is shown to affect the quantitative results considerably. It is suggested that this resolution is a major cause of quantitative discrepancies between different studies. Thus, the results of this work and previous direct numerical simulations of this problem should be regarded as qualitative descriptions of the physics involved, and more refined methods must be used to quantitatively pinpoint the transitions between rotational states.

Negative Staining: a Valuable Technique for Studying Subcellular Components

1997 ◽  
Vol 3 (S2) ◽  
pp. 341-342
Author(s):  
Sara E. Miller
Keyword(s):  
Negative Staining ◽  
Cell Organelles ◽  
Preparation Time ◽  
Nucleic Acid Probes ◽  
Virus Identification ◽  
High Particle ◽  
Thin Sectioning ◽  
Particle Counts ◽  
Selection Of

Negative staining is the most frequently used procedure for preparing particulate specimens, e.g., cell organelles, macromolecules, and viruses, for electron microscopy (Figs. 1-4). The main advantage is that it is rapid, requiring only minutes of preparation time. Another is that it avoids some of the harsh chemicals, e.g., organic solvents, used in thin sectioning. Also, it does not require advanced technical skill. It is widely used in virology, both in classification of viruses as well as diagnosis of viral diseases. Notwithstanding the necessity for fairly high particle counts, virus identification by negative staining is advantageous in not requiring specific reagents such as antibodies, nucleic acid probes, or protein standards which necessitate prior knowledge of potential pathogens for selection of the proper reagent. Furthermore, it does not require viable virions as does growth in tissue culture. Another procedure that uses negative contrasting is ultrathin cryosectioning (Fig. 5).In 1954 Farrant was the first to publish negatively stained material, ferritin particles.

scholarly journals Settling of an asymmetric dumbbell in a quiescent fluid

2016 ◽  
Vol 802 ◽  
pp. 174-185 ◽  
Author(s):  
F. Candelier ◽  
B. Mehlig
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Size Difference ◽  
Fluid Inertia ◽  
Horizontal Orientation ◽  
Vertically Aligned ◽  
Rigid Rod ◽  
Quiescent Fluid

We compute the hydrodynamic torque on a dumbbell (two spheres linked by a massless rigid rod) settling in a quiescent fluid at small but finite Reynolds number. The spheres have the same mass densities but different sizes. When the sizes are quite different, the dumbbell settles vertically, aligned with the direction of gravity, the largest sphere first. But when the size difference is sufficiently small, then its steady-state angle is determined by a competition between the size difference and the Reynolds number. When the sizes of the spheres are exactly equal, then fluid inertia causes the dumbbell to settle in a horizontal orientation.

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