Mass and heat transfer from or to a single sphere in simple extensional creeping flow

Zhang, Jingsheng; Yang, Chao; Mao, Zai‐Sha

doi:10.1002/aic.12811

Cited by 23 publications

(21 citation statements)

References 27 publications

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“…The transfer of mass around spherical bubbles, drops, and particles in a linear ( E = 0) extensional creeping flow and at large Peclet numbers was analytically studied by Gupalo and Riazantzev and Gupalo et al, Morrison, Batchelor and numerically explored by Zhang et al In general, for bubbles and drops, the mass transfer rate is proportional to Pe 1/2 , while for particles the rate follows the Pe 1/3 structure, due to the differences between the thin concentration boundary layers of mobile and immobile interfaces . As bubbles and drops subjected to an extensional flow tend to deform, Favelukis and Lavrenteva extended the linear mass transfer spherical results ( Ca = 0), to slightly deformed prolate (uniaxial) and oblate (biaxial) spheroids, which represent the next order of deformation ( Ca ≪ 1).…”

Section: Introductionmentioning

confidence: 99%

Mass transfer around bubbles, drops, and particles in uniaxial and biaxial nonlinear extensional flows

Favelukis

2018

AIChE Journal

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Mass transfer around spherical bubbles, drops, and solid particles in uniaxial and biaxial nonlinear extensional creeping flows at large Peclet numbers is the subject of this theoretical report. The fluid mechanics problem is governed by the viscosity ratio (λ) and the nonlinear intensity of the flow (E). The flow outside such bodies reveals a different picture than the linear case (E = 0) such as separating surfaces or closed circulations. There is a range: −1.04 < E < 0 (bubbles and drops) and −0.490 < E < 0 (particles) where the mass transfer rate is lower than the linear case. Outside these ranges, the mass transfer rate is higher than the linear case and in general it increases as |E| increases. Same mass transfer rates are expected in uniaxial and biaxial flows, except in the presence of external closed circulations where the biaxial flow overcomes the uniaxial flow.

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Section: Introductionmentioning

confidence: 99%

Mass transfer around bubbles, drops, and particles in uniaxial and biaxial nonlinear extensional flows

Favelukis

2018

AIChE Journal

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“…The internal circulation is assumed quick enough to assure that concentration is equilibrated, and mass transfer does not lower the solute concentration in the sphere. The dimensionless concentration is defined by

C_{1} = (c_{1} - c_{\infty}) / (c_{1}^{s} - c_{\infty})

, and the boundary conditions are

r = 1, C_{1} = C_{1}^{s} = 1

r \to \infty, C_{1} = C_{\infty} = 0

…”

Section: Model Descriptionmentioning

confidence: 99%

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

et al. 2013

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A numerical method is utilized to examine the steady and transient mass/heat transfer processes that involve a neutrally buoyant liquid sphere suspended in simple shear flow at low Reynolds numbers is described. By making use of the known Stokes velocity field, the convection‐diffusion equations are solved in the three‐dimensional spherical coordinates system. For the mass transfer either outside or inside a liquid sphere, Sherwood number Sh approaches an asymptotic value for a given viscosity ratio at sufficiently high Peclet number Pe. In terms of the numerical results obtained in this work, two new correlations are derived to predict Sh at finite Pe for various viscosity ratios. © 2013 American Institute of Chemical Engineers AIChE J, 60: 343–352, 2014

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“…Gupalo et al 6 and Batchelor 7 analytically investigated mass transfer from a solid sphere immersed in a uniaxial extensional flow for asymptotically large and small Peclet numbers. Zhang et al 8,9 numerically investigated mass and heat transfer both outside and inside a solid or liquid sphere immersed in a uniaxial extensional flow for a larger range of Peclet numbers (1-100,000).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2018

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Building on the work of Yang et al. in 2011, the finite difference method and the Boussinesq approximation were applied to solve the time‐dependent Navier‐Stokes, convection diffusion and continuity equations in spherical coordinates. An idealized condition, the mass transfer from a neutrally buoyant sphere in a horizontal simple shear flow with natural convection was numerically simulated for the first time in this work. In the hybrid transfer case, the outwardly spiraling streamlines enhanced the transfer process, but the counter‐gravity spiraling streamlines near the sphere hindered the natural convection and the spatial dilution action weakened the natural convection transfer process. These competing effects led to nonmonotonic behavior of the Nusselt number with Reynolds number. Results from these previously undocumented cases were summarized into correlations for predicting Nusselt numbers at finite Reynolds numbers for various Grashof and Prandtl numbers. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2816–2827, 2018

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Mass and heat transfer from or to a single sphere in simple extensional creeping flow

Cited by 23 publications

References 27 publications

Mass transfer around bubbles, drops, and particles in uniaxial and biaxial nonlinear extensional flows

Mass transfer around bubbles, drops, and particles in uniaxial and biaxial nonlinear extensional flows

Numerical study on steady and transient mass/heat transfer involving a liquid sphere in simple shear creeping flow

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

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