scholarly journals Microstructure and rheology of finite inertia neutrally buoyant suspensions

2014 ◽  
Vol 749 ◽  
pp. 431-459 ◽  
Author(s):  
Hamed Haddadi ◽  
Jeffrey F. Morris
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Volume Fraction ◽  
Spherical Particles ◽  
Simple Shear Flow ◽  
Flow Reynolds Number ◽  
Boltzmann Method ◽  
Neutrally Buoyant ◽  
Boltzmann Model ◽  
Scale Shear

AbstractThe microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $\phi $. The inertia is characterized by the particle-scale shear flow Reynolds number $\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$, where $a$ is the particle radius, $\dot{\gamma }$ is the shear rate and $\rho $ and $\mu $ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for $0.005\leqslant \mathit{Re}\leqslant 5$ and$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied using the pair distribution function $g(\boldsymbol {r})$. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions (PDFs) of linear and angular accelerations are also presented.

Pair-sphere trajectories in finite-Reynolds-number shear flow

2008 ◽  
Vol 596 ◽  
pp. 413-435 ◽  
Author(s):  
PANDURANG M. KULKARNI ◽  
JEFFREY F. MORRIS
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Rigid Spheres ◽  
Newtonian Dynamics ◽  
Flow Reynolds Number ◽  
Boltzmann Method ◽  
Neutrally Buoyant

The pair trajectories of neutrally buoyant rigid spheres immersed in finite-inertia simple-shear flow are described. The trajectories are obtained using the lattice-Boltzmann method to solve the fluid motion, with Newtonian dynamics describing the sphere motions. The inertia is characterized by the shear-flow Reynolds number ${\it Re} \,{=}\,\rho\dot{\gamma}a^2/\mu$, where μ and ρ are the viscosity and density of the fluid respectively, $\dot{\gamma}$ is the shear rate and a is the radius of the larger of the pair of spheres in the case of unequal sizes; the majority of results presented are for pairs of equal radii. Reynolds numbers of 0 ≤ Re ≤ 1 are considered with a focus on inertia at Re = O(0.1). At finite inertia, the topology of the pair trajectories is altered from that predicted at Re = 0, as closed trajectories found in Stokes flow vanish and two new forms of trajectories are observed. These include spiralling and reversing trajectories in addition to largely undisturbed open trajectories. For Re = O(0.1), the limits of the various regions in pair space yielding open, reversing and spiralling trajectories are roughly defined.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

The inertial migration of non-neutrally buoyant spherical particles in two-dimensional shear flows

1994 ◽  
Vol 272 ◽  
pp. 285-318 ◽  
Author(s):  
Andrew J. Hogg
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Chemical Engineering ◽  
Practical Importance ◽  
Spherical Particles ◽  
Lateral Motion ◽  
Order Unity ◽  
Inertial Migration ◽  
Induced Motion ◽  
Neutrally Buoyant

The inertial migration of a small rigid spherical particle, suspended in a fluid flowing between two plane boundaries, is investigated theoretically to find the effect on the lateral motion. The channel Reynolds number is of order unity and thus both boundary-induced and Oseen-like inertial migration effects are important. The particle Reynolds number is small but non-zero, and singular perturbation techniques are used to calculate the component of the migration velocity which is directed perpendicular to the boundaries of the channel. The particle is non-neutrally buoyant and thus its buoyancy-induced motion may be either parallel or perpendicular to the channel boundaries, depending on the channel alignment. When the buoyancy results in motion perpendicular to the channel boundaries, the inertial migration is a first-order correction to the magnitude of this lateral motion, which significantly increases near to the boundaries. When the buoyancy produces motion parallel with the channel boundaries, the inertial migration gives the zeroth-order lateral motion either towards or away from the boundaries. It is found that those particles which have a velocity exceeding the undisturbed shear flow will migrate towards the boundaries, whereas those with velocities less than the undisturbed flow migrate towards the channel centreline. This calculation is of practical importance for various chemical engineering devices in which particles must be filtered or separated. It is useful to calculate the forces on a particle moving near to a boundary, through a shear flow. This study may also explain certain migration effects of bubbles and crystals suspended in molten rock flow flowing through volcanic conduits.

The influence of the inertially dominated outer region on the rheology of a dilute dispersion of low-Reynolds-number drops or rigid particles

2011 ◽  
Vol 674 ◽  
pp. 307-358 ◽  
Author(s):  
GANESH SUBRAMANIAN ◽  
DONALD L. KOCH ◽  
JINGSHENG ZHANG ◽  
CHAO YANG
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Simple Shear ◽  
Stokes Equations ◽  
Outer Region ◽  
Simple Shear Flow ◽  
Dispersed Phase ◽  
Leading Order ◽  
Normal Stress Differences ◽  
Neutrally Buoyant

We calculate the rheological properties of a dilute emulsion of neutrally buoyant nearly spherical drops at O(φRe3/2) in a simple shear flow(u∞ = x211, being the shear rate) as a function of the ratio of the dispersed- and continuous-phase viscosities (λ = /μ). Here, φ is the volume fraction of the dispersed phase and Re is the micro-scale Reynolds number. The latter parameter is a dimensionless measure of inertial effects on the scale of the dispersed-phase constituents and is defined as Re = a2ρ/μ, a being the drop radius and ρ the common density of the two phases. The analysis is restricted to the limit φ, Re ≪ 1, when hydrodynamic interactions between drops may be neglected, and the velocity field in a region around the drop of the order of its own size is governed by the Stokes equations at leading order. The dominant contribution to the rheology at O(φRe3/2), however, arises from the so-called outer region where the leading-order Stokes approximation ceases to be valid. The relevant length scale in this outer region, the inertial screening length, results from a balance of convection and viscous diffusion, and is O(aRe−1/2) for simple shear flow in the limit Re ≪ 1. The neutrally buoyant drop appears as a point-force dipole on this scale. The rheological calculation at O(φRe3/2) is therefore based on a solution of the linearized Navier–Stokes equations forced by a point dipole. The principal contributions to the bulk rheological properties at this order arise from inertial corrections to the drop stresslet and Reynolds stress integrals. The theoretical calculations for the stresslet components are validated via finite volume simulations of a spherical drop at finite Re; the latter extend up to Re ≈ 10.Combining the results of our O(φRe3/2) analysis with the known rheology of a dilute emulsion to O(φRe) leads to the following expressions for the relative viscosity (μe), and the non-dimensional first (N1) and second normal stress differences (N2) to O(φRe3/2): μe = 1 + φ[(5λ+2)/(2(λ+1))+0.024Re3/2(5λ+2)2/(λ+1)2]; N1=φ[−Re4(3λ2+3λ+1)/(9(λ+1)2)+0.066Re3/2(5λ+2)2/(λ+1)2] and N2 = φ[Re2(105λ2+96λ+35)/(315(λ+1)2)−0.085Re3/2(5λ+2)2/(λ+1)2].Thus, for small but finite Re, inertia endows an emulsion with a non-Newtonian rheology even in the infinitely dilute limit, and in particular, our calculations show that, aside from normal stress differences, such an emulsion also exhibits a shear-thickening behaviour. The results for a suspension of rigid spherical particles are obtained in the limit λ → ∞.

Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

Orientational Distributions of a Ferromagnetic Spherocylinder Particle in a Simple Shear Flow

2002 ◽  
Author(s):  
Masayuki Aoshima ◽  
Akira Satoh ◽  
Geoff N. Coverdale ◽  
Roy W. Chantrell
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Shear Flow ◽  
Flow Field ◽  
Simple Shear ◽  
Applied Magnetic Field ◽  
Spherical Particles ◽  
Simple Shear Flow ◽  
Microstructure Formation ◽  
Base Liquid

A ferrofluid is a suspension of ferromagnetic spherical particles in a base liquid (1), and is well known as a functional fluid which responds to an external magnetic field to give a large increase in the viscosity. Such a significant increase in the viscosity is due to the fact that chain-like clusters are formed owing to magnetostatic interactions between particles in an applied magnetic field. The microstructure formation offers a large resistance to a flow field that gives rise to a significant increase of the apparent viscosity (2).

ON BOUNDARY CONDITIONS IN THE FINITE VOLUME LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES

1999 ◽  
Vol 10 (06) ◽  
pp. 1003-1016 ◽  
Author(s):  
GONGWEN PENG ◽  
HAOWEN XI ◽  
SO-HSIANG CHOU
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Unstructured Meshes ◽  
Simple Shear Flow ◽  
Boltzmann Method

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

An Application of Distributed Computing to the Finite Element Investigation of Lift Force on a Freely-Rotating Sphere in Simple Shear Flow

1999 ◽  
Author(s):  
Gustavo C. Buscaglia ◽  
Hugo E. Ferrari ◽  
Pablo M. Carrica ◽  
Enzo A. Dari
Keyword(s):  
Finite Element ◽  
Shear Flow ◽  
Simple Shear ◽  
Lift Force ◽  
Cluster Computing ◽  
Low Cost ◽  
Lift Coefficient ◽  
Angular Acceleration ◽  
Spherical Particles ◽  
Simple Shear Flow

Abstract An application of “cluster computing” in finite element CFD is reported, demonstrating the feasibility of solving relevant 3D problems on low-cost architectures (PC’s connected by fast Ethernet network). The main ingredients of our implementation are described. The results concern the lift force on a solid particle in simple shear flow. It is shown that, if the particle is allowed to rotate freely about its center, the self-established rotation significantly alters the lift coefficient. in particular, the lift force points away from a wall for any Re (≤ 100), while if the particle does not rotate the lift changes sign. Suitable estimates for the typical time involved in the angular acceleration of solid spherical particles are derived.

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