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

Nirschl, Hermann; Dwyer, H. A.; Denk, V.

doi:10.1017/s002211209500231x

Cited by 46 publications

(28 citation statements)

References 5 publications

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“…The difference Ω − Ω 0 is plotted along with the theoretical result appropriate to the geometry of the body, in figure 15(a) for the cylinder and in figure 15(b) for the sphere. The zero-Re values of rotation rate computed for the cylinder are within 0.2% of the theoretical value of Ω 0 = −1/2 for R ∞ > 10 (and always of slightly larger magnitude), while Nirschl, Dwyer & Denk (1995) Figure 16. Rotation rates of the freely suspended circular cylinder and sphere in simple shear flow computed in this work along with results from other numerical and experimental studies.…”

Section: Rotation Rate and Stressletsupporting

confidence: 64%

“…their figure 7a at Re = 10) are inverted in the shear gradient direction. The analogous problem for a sphere in simple shear has been studied by Nirschl, Dwyer & Denk (1995) for a wallbounded geometry at 0.025 < Re < 25 using a finite-volume scheme. The influence of inertial flow upon the rheology of a dilute suspension of disks was performed by Patankar & Hu (2001); from finite-element-based numerical solutions of simple shear Q1 around a circular cylinder, Patankar & Hu extracted the first normal stress difference (the second normal stress difference is undefined in this case) up to Re = 5.…”

Section: Introductionmentioning

confidence: 99%

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Stationary shear flow around fixed and free bodies at finite Reynolds number

2004

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Numerical solutions of stationary flow resulting from immersion of a single body in simple shear flow are reported for a range of Reynolds numbers. Flows are computed using finite-element methods. Comparisons to results of asymptotic low-Reynoldsnumber theory, experimental study, and other numerical techniques are provided. Results are presented primarily for isotropic bodies, i.e. the circular cylinder and sphere, for both of which the two conditions of a torque-free (freely-rotating) and fixed body are investigated. Conditions studied for the sphere are 0 < Re < 100, and for the circular cylinder 0 < Re < 500, with the shear-flow Reynolds number defined as Re =γ a 2 /ν;γ is the shear rate of the Cartesian simple shear flow u = (γ y, 0, 0), a is the cylinder or sphere radius, and ν is the kinematic viscosity of the fluid. In the torque-free case, the rotation rate of the body decreases with increasing Re. Qualitative dependence, seen in the Re = 0 fluid flow field, upon whether the body is fixed against rotation or torque-free vanishes as Re increases and the fluid flow is more similar to that around the fixed body: the influence of rotation of the body and the associated closed streamlines are confined to a narrow layer about the body for Re > O(1). Separation of the boundary layer is observed in the case of a fixed cylinder at Re ≈ 85, and for a fixed sphere at Re ≈ 100; similar separation phenomena are observed for a freely rotating cylinder. The surface stress and its symmetric first moment (the stresslet) are presented, with the latter providing information on the particle contribution to the mixture rheology at finite Re. Stationary flow results are also presented for elliptical cylinders and oblate spheroids, with observation of zero-torque inclinations relative to the flow direction which depend upon the aspect ratio, confirming and extending prior findings.

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Section: Rotation Rate and Stressletsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Stationary shear flow around fixed and free bodies at finite Reynolds number

2004

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“…In this paper, the angular velocity ω is normalized for the shear rate. We compare our results to results of Nirschl, Dwyer & Denk (1995), who carried out comparable computations with a finite-volume numerical scheme, but for a three-dimensional system. Taylor (1932) derived an analytical solution for low-Reynolds-number flow over a rotating sphere in simple shear, which predicts an angular velocity ω of a half.…”

Section: Effects Of Hydrodynamics and Inertia In Particle Suspensionsmentioning

confidence: 86%

Shear-induced self-diffusion and microstructure in non-Brownian suspensions at non-zero Reynolds numbers

et al. 2005

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This paper addresses shear-induced self-diffusion in a monodisperse suspension of non-Brownian particles in Couette flow by two-dimensional computer simulations following the lattice-Boltzmann method. This method is suited for the study of (manyparticle) particulate suspensions and can not only be applied for Stokes flow, but also for flow with finite Reynolds number. At relatively low shear particle Reynolds numbers (up to 0.023), shear-induced diffusivity exhibited a linear dependence on the shear rate, as expected from theoretical considerations. Simulations at shear particle Reynolds numbers between 0.023 and 0.35, however, revealed that in this regime, shear-induced diffusivity did not show this linear dependence anymore. Instead, the diffusivity was found to increase more than linearly with the shear rate, an effect that was most pronounced at lower area fractions of 0.10 and 0.25. In the same shear regime, major changes were found in the flow trajectories of two interacting particles in shear flow (longer and closer approach) and in the viscosity of the suspension (shear thickening). Moreover, the suspended particles exhibited particle clustering. The increase of shear-induced diffusivity is shown to be directly correlated with this particle clustering. As for shear-induced diffusivity, the effect of increasing shear rates on particle clustering was the most intensive at low area fractions of 0.10 and 0.25, where the radius of the clusters increased from about 4 to about 7 particle radii with an increase of the shear Reynolds number from 0.023 to 0.35. The importance of particle clustering to shear-induced diffusion might also indicate the importance of other factors that can induce particle clustering, such as, for example, colloidal instability.

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“…Secondly surface shear can be considered with stresses τ S which are equal to normal stresses τ N = τ S shown at low Reynolds numbers by Taylor [23] and extended to medium Reynolds numbers (1-100) by Nirschl [24]. Here, correspondingly turbulent stresses are characterized by τ = k · νρ f ·γ t = k · ρ f v 2 d using Eqs.…”

Section: Fluid Dynamicsmentioning

confidence: 99%

Turbulent hydrodynamic stress induced dispersion and fragmentation of nanoscale agglomerates

Wengeler

Nirschl

2007

Journal of Colloid and Interface Science

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High pressure dispersion nozzles of 2.5-10 mm length and 125 µm diameter have been characterized in terms of fluid dynamics and dispersion experiments at 100-1400 bar. Elongational stresses at the nozzle entry (5 × 10 5 Pa) and turbulent stresses up to 10 5 Pa at a Reynolds number of 25,000 in turbulent channel flow are identified crucial for desagglomeration and aggregate fragmentation. Maximum stresses are calculated on representative particle tracks and related to agglomerate breakage. Agglomerates in the experimental study are in the range of the Kolmogorov micro scale (100-400 nm) and therefore break due to turbulent energy dissipation in viscous flow. Bond strength distributions could be determined experimentally from particle size distributions and fluid dynamics simulations, with primary particle erosion determined as dispersion mechanism for diffusion flame silica particles. Nanoscale agglomerates show a power law scaling for breakage with scaling exponents diverging from theory of floc dispersion. This is attributed to their strong bonding by sinter necks.

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

Cited by 46 publications

References 5 publications

Stationary shear flow around fixed and free bodies at finite Reynolds number

Stationary shear flow around fixed and free bodies at finite Reynolds number

Shear-induced self-diffusion and microstructure in non-Brownian suspensions at non-zero Reynolds numbers

Turbulent hydrodynamic stress induced dispersion and fragmentation of nanoscale agglomerates

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