Mass transfer to freely suspended particles at high Péclet number

Lawson, John M.

doi:10.1017/jfm.2020.1177

Cited by 2 publications

(14 citation statements)

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“…A phenomenon known as the partial suppression of convection by rotation then emerges, whereby the preferential alignment and rotation of the particle with respect to its surroundings alters the mean flow field it perceives. For small spherical and spheroidal particles embedded in rotation-dominated linear shear |ω 0 | |E 0 |, the transfer rate is shown to scale with a Péclet number based on the rate of vortex stretching Pe ω = E ω r 2 /κ, where (Batchelor 1979;Lawson 2021), since particles spin aligned with the vorticity. More generally, for axisymmetric particles spinning along a fixed direction p, the transfer rate scales with the strain rate E p = E 0 ij p i p j perceived in that direction (Lawson 2021).…”

Section: Introductionmentioning

confidence: 97%

“…For small spherical and spheroidal particles embedded in rotation-dominated linear shear |ω 0 | |E 0 |, the transfer rate is shown to scale with a Péclet number based on the rate of vortex stretching Pe ω = E ω r 2 /κ, where (Batchelor 1979;Lawson 2021), since particles spin aligned with the vorticity. More generally, for axisymmetric particles spinning along a fixed direction p, the transfer rate scales with the strain rate E p = E 0 ij p i p j perceived in that direction (Lawson 2021). Therefore, orientation dynamics plays an important role in determining the transfer rate from small particles.…”

Section: Introductionmentioning

confidence: 97%

“…Here, the Péclet number is suitably redefined in terms of some characteristic strain rate E of the steady flow problem. Depending upon the particle geometry and relative flow field, various asymptotic expressions are available for the coefficient α and subsequent corrections (Acrivos & Taylor 1962;Acrivos & Goddard 1965;Sehlin 1969;Gupalo, Polianin & Riazantsev 1976;Poe & Acrivos 1976;Batchelor 1979;Acrivos 1980;Myerson 2002;Dehdashti & Masoud 2020;Lawson 2021). This is supplemented by a wealth of experimental and numerical data at finite Reynolds and Péclet numbers (Clift et al 1978;Sparrow, Abraham & Tong 2004;Kishore & Gu 2011;Ke et al 2018;Ma & Zhao 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Analytical expressions for the transfer rate are available only in the low-Péclet-number regime (Pozrikidis 1997;Feng & Michaelides 1998;Michaelides 2003). At high Péclet number, Batchelor (1979) and later Lawson (2021) showed that, for time-periodic motion of small particles in a steady linear shear u(x) = E 0 x + 1 2 ω 0 × x, unsteady concentration fluctuations arise due to the periodic motion of the particle under the action of the strain E 0 and vorticity ω 0 . Here, in a frame of reference co-rotating with the particle, the particle surface appears stationary but is subject to an unsteady velocity field v( y, t), periodic in time t, where y is the spatial coordinate in the co-rotating body frame.…”

Section: Introductionmentioning

confidence: 99%

“…As such, the mean flow field in the body frame of the particle ṽ(t) = (1/T) T 0 v dt determines the mean transfer rate. Classical asymptotic methods for steady flows can then be applied to determine the mean transfer rate (Acrivos & Goddard 1965;Leal 2012;Lawson 2021). A phenomenon known as the partial suppression of convection by rotation then emerges, whereby the preferential alignment and rotation of the particle with respect to its surroundings alters the mean flow field it perceives.…”

Section: Introductionmentioning

confidence: 99%

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Mass transfer from small spheroids suspended in a turbulent fluid

Lawson

Ganapathisubramani

2021

J. Fluid Mech.

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By coupling direct numerical simulation of homogeneous isotropic turbulence with a localised solution of the convection–diffusion equation, we model the rate of transfer of a solute (mass transfer) from the surface of small, neutrally buoyant, axisymmetric, ellipsoidal particles (spheroids) in dilute suspension within a turbulent fluid at large Péclet number, $\textit {Pe}$ . We observe that, at $\textit {Pe} = O(10)$ , the average transfer rate for prolate spheroids is larger than that of spheres with equivalent surface area, whereas oblate spheroids experience a lower average transfer rate. However, as the Péclet number is increased, oblate spheroids can experience an enhancement in mass transfer relative to spheres near an optimal aspect ratio $\lambda \approx 1/4$ . Furthermore, we observe that, for spherical particles, the Sherwood number $\textit {Sh}$ scales approximately as $\textit {Pe}^{0.26}$ over $\textit {Pe} = 1.4\times 10^{1}$ to $1.4\times 10^{4}$ , which is below the $\textit {Pe}^{1/3}$ scaling observed for inertial particles but consistent with available experimental data for tracer-like particles. The discrepancy is attributed to the diffusion-limited temporal response of the concentration boundary layer to turbulent strain fluctuations. A simple model, the quasi-steady flux model, captures both of these phenomena and shows good quantitative agreement with our numerical simulations.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mass transfer from small spheroids suspended in a turbulent fluid

Lawson

Ganapathisubramani

2021

J. Fluid Mech.

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Mechanisms of mass transfer to small spheres sinking in turbulence

Lawson

Ganapathisubramani²

2023

J. Fluid Mech.

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Using laboratory experiments and numerical simulations, we examine the transfer of soluble material from small, spherical particles sinking in homogeneous turbulence at large Péclet number. A theoretical analysis predicts two distinct mechanisms of convective mass transfer: strain due to turbulence and slip due to gravitational settling. Their relative strength is parametrised by the sinking ratio, ${Sr} = w_0 \tau _\eta /a$ , where $w_0$ is the quiescent settling velocity, $a$ is the particle radius and $\tau _\eta$ is the Kolmogorov time scale. This analysis predicts that the topology of the concentration wake changes from a symmetric topology at ${Sr} \ll 1$ to an asymmetric topology at ${Sr} \gg 1$ as the dominant mechanism of mass transfer changes. Particle tracking flow visualisations of small spheres releasing dye in turbulence confirm the existence of this change in mechanism at ${Sr} = O(1)$ . We complement these experiments with numerical simulations of the mass transfer from sinking particles. The transfer rate predicted by the simulation is found to be in good agreement with literature data for mass transfer to turbulent suspensions of solid particles and is consistent with asymptotic expressions for mass transfer in uniform flow when ${Sr} \gg 1$ . A decomposition of the convective fluxes confirms the transition in the transfer mechanism. At ${Sr} = O(1)$ , both mechanisms provide comparable contributions to the transfer rate. Cross-correlation analysis reveals that particle-scale knowledge of both the recent strain and velocity history is required to predict the instantaneous transfer rate. Turbulence-induced particle rotation has a modest suppression effect upon convective transfer by sinking.

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Mass transfer to freely suspended particles at high Péclet number

Abstract: Abstract

Cited by 2 publications

References 32 publications

Mass transfer from small spheroids suspended in a turbulent fluid

Mass transfer from small spheroids suspended in a turbulent fluid

Mechanisms of mass transfer to small spheres sinking in turbulence

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