Effect of inertia on the mass/heat transfer from a neutrally buoyant sphere at finite Reynolds number in simple shear flow

2019 ◽  
pp. 83-86
Author(s):  
Chao Yang ◽  
Donald L. Koch
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Neutrally Buoyant

Mass/heat transfer from a neutrally buoyant sphere in simple shear flow at finite Reynolds and Peclet numbers

AIChE Journal ◽  
2010 ◽  
Vol 57 (6) ◽  
pp. 1419-1433 ◽  
Author(s):  
Chao Yang ◽  
Jingsheng Zhang ◽  
Donald L. Koch ◽  
Xiaolong Yin
Keyword(s):  
Heat Transfer ◽  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Neutrally Buoyant

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 → ∞.

Heat/mass transfer from a neutrally buoyant sphere by mixed natural and forced convection in a simple shear flow

AIChE Journal ◽  
2018 ◽  
Vol 64 (7) ◽  
pp. 2816-2827 ◽  
Author(s):  
Bing Yuan ◽  
Chao Yang ◽  
Zai‐Sha Mao ◽  
Xiaolong Yin ◽  
Donald L. Koch
Keyword(s):  
Mass Transfer ◽  
Shear Flow ◽  
Forced Convection ◽  
Simple Shear ◽  
Heat Mass Transfer ◽  
Simple Shear Flow ◽  
Neutrally Buoyant

Three-dimensional calculations of the simple shear flow around a single particle between two moving walls

1995 ◽  
Vol 283 ◽  
pp. 273-285 ◽  
Author(s):  
H. Nirschl ◽  
H. A. Dwyer ◽  
V. Denk
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Simple Shear ◽  
Particle Surface ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Number Range ◽  
Grid Scheme

Three-dimensional solutions have been obtained for the steady simple shear flow over a spherical particle in the intermediate Reynolds number range 0.1 [les ] Re [les ] 100. The shear flow was generated by two walls which move at the same speed but in opposite directions, and the particle was located in the middle of the gap between the walls. The particle-wall interaction is treated by introducing a fully three-dimensional Chimera or overset grid scheme. The Chimera grid scheme allows each component of a flow to be accurately and efficiently treated. For low Reynolds numbers and without any wall influence we have verified the solution of Taylor (1932) for the shear around a rigid sphere. With increasing Reynolds numbers the angular velocity for zero moment for the sphere decreases with increasing Reynolds number. The influence of the wall has been quantified with the global particle surface characteristics such as net torque and Nusselt number. A detailed analysis of the influence of the wall distance and Reynolds number on the surface distributions of pressure, shear stress and heat transfer has also been carried out.

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.

Rigid ring-shaped particles that align in simple shear flow

2013 ◽  
Vol 722 ◽  
pp. 121-158 ◽  
Author(s):  
Vikram Singh ◽  
Donald L. Koch ◽  
Abraham D. Stroock
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Shear Flow ◽  
Simple Shear ◽  
Low Reynolds Number ◽  
Simple Shear Flow ◽  
Rigid Ring ◽  
Axis Of Symmetry ◽  
Low Reynolds ◽  
Axes Of Symmetry

AbstractMost rigid, torque-free, low-Reynolds-number, axisymmetric particles undergo a time-periodic tumbling motion in a simple shear flow, with their axes of symmetry following a set of closed Jeffery orbits. We have identified a class of rigid, ring-like particles whose axes of symmetry instead reach a permanent alignment near the velocity gradient direction with the plane of the particle aligning near the flow–vorticity plane. An asymptotic analysis for small particle aspect ratio (ratio of length parallel to the axis of symmetry to diameter perpendicular to the axis) shows that an appropriate asymmetry of the ring cross-section with a thinner outer edge and thicker inner edge leads to a tendency to rotate in a direction opposite to the vorticity; this tendency can balance the usual rotation rate associated with the finite thickness of the particle. Boundary integral computations for finite particle aspect ratios are used to determine the conditions of aspect ratio and degree of asymmetry that lead to the aligning behaviour and the final orientation of the axis of symmetry of the aligned particles. The aligning particle follows an equation of motion similar to the Leslie–Erickson equation for the director of a small-molecule nematic liquid crystal. However, whereas the alignment of the director arises from intermolecular interactions, the ring-like particle aligns solely due to its intrinsic rotational motion in a low-Reynolds-number flow.

An orientational order transition in a sheared suspension of anisotropic particles

2016 ◽  
Vol 811 ◽  
Author(s):  
Navaneeth K. Marath ◽  
Ruchir Dwivedi ◽  
Ganesh Subramanian
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Orientational Order ◽  
Thermal Fluctuations ◽  
Simple Shear Flow ◽  
Two Phase ◽  
Physics Literature ◽  
Dilute Suspension ◽  
Neutrally Buoyant

Under Stokesian conditions, a neutrally buoyant non-Brownian spheroid in simple shear flow rotates indefinitely in any of a one-parameter family of closed (Jeffery) orbits characterized by an orbit constant $C$. The limiting values, $C=0$ and $C=\infty$, correspond to spinning and tumbling modes respectively. Hydrodynamics alone does not determine the distribution of spheroid orientations across Jeffery orbits in the absence of interactions, and the rheology of a dilute suspension of spheroids remains indeterminate. A combination of inertia and stochastic orientation fluctuations eliminates the indeterminacy. The steady-state Jeffery-orbit distribution arising from a balance of inertia and thermal fluctuations is shown to be of the Boltzmann equilibrium form, with a potential that depends on $C$, the particle aspect ratio ($\unicode[STIX]{x1D705}$), and a dimensionless shear rate ($Re\,Pe_{r}$, $Re$ and $Pe_{r}$ being the Reynolds and rotary Péclet numbers), and therefore lends itself to a novel thermodynamic interpretation in $C{-}\unicode[STIX]{x1D705}{-}Re\,Pe_{r}$ space. In particular, the transition of the potential from a single to a double-well structure, below a critical $\unicode[STIX]{x1D705}$, has similarities to a thermodynamic phase transition, and the small-$C$ and large-$C$ minima are therefore identified with spinning and tumbling phases. The hysteretic dynamics within the two-phase tumbling–spinning envelope renders the rheology sensitively dependent on the precise shear rate history, the signature in simple shear flow being a multivalued viscosity at a given shear rate. The tumbling–spinning transition identified here is analogous to the coil–stretch transition in the polymer physics literature. It should persist under more general circumstances, and has implications for the suspension stress response in inhomogeneous shearing flows.

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