Reciprocal theorem for convective heat and mass transfer from a particle in Stokes and potential flows

Vandadi, Vahid; Kang, Saeed Jafari; Masoud, Hassan

doi:10.1103/physrevfluids.1.022001

Cited by 16 publications

(10 citation statements)

References 22 publications

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“…It is also a special case of the reciprocal theorem developed by Vandadi et al . 47 for convection heat and mass transfer from particles in Stokes and potential flows.…”

Section: Droplet Evaporationmentioning

confidence: 99%

Evaporation of a sessile droplet on a slope

Timm

Dehdashti

Darban

et al. 2019

Sci Rep

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We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from the purely diffusive transport of liquid vapor and that the contact line is a pinned circle. For the purposes of the analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the droplet is unperturbed by the effect of gravity and takes the form of a spherical cap, for which the vapor concentration field is already known. Here, the Young-Laplace equation is solved analytically to calculate the first-order correction to the shape of the drop. Knowing the first-order perturbation to the drop geometry and the zeroth-order distribution of vapor concentration, we obtain the leading-order contribution of gravity to the rate of droplet evaporation by utilizing Green’s second identity. The analytical results are supplemented by numerical calculations, where the droplet shape is first determined by minimizing the Helmholtz free energy and then the evaporation rate is computed by solving Laplace’s equation for the vapor concentration field via a finite-volume method. Perhaps counter-intuitively, we find that even when the droplet deforms noticeably under the influence of gravity, the rate of evaporation remains almost unchanged, as if no gravitational effect is present. Furthermore, comparison between analytical and numerical calculations reveals that considering only the leading-order corrections to the shape of the droplet and vapor concentration distribution provides estimates that are valid well beyond their intended limit of very small Bo.

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“…It is also a special case of the reciprocal theorem developed by Vandadi et al . 47 for convection heat and mass transfer from particles in Stokes and potential flows.…”

Section: Droplet Evaporationmentioning

confidence: 99%

Evaporation of a sessile droplet on a slope

Timm

Dehdashti

Darban

et al. 2019

Sci Rep

Self Cite

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“…This is remarkable, since both flows correspond to an axisymmetric strain; only the direction of the flow is reversed. At first glance, this appears to violate Brenner's flow reversal theorem (Brenner 1967; Vandadi, Jafari Kang & Masoud 2016; Masoud & Stone 2019), which states that for an isothermal body in steady flow, the surface flux is preserved under flow reversal . However, we recall that the stable orientation of a free spheroid shifts under flow reversal.…”

Section: Resultsmentioning

confidence: 85%

Mass transfer to freely suspended particles at high Péclet number

Lawson

2021

J. Fluid Mech.

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“…However, most of these studies have assumed uniform and constant boundary conditions at the particle surface, as also pointed out recently in Ref. [7], and do not match my actual problem.…”

Section: Problem Statementmentioning

confidence: 90%

“…This avoids tracking at the same time both the motion of the reservoir and the release of its inner substance, which is not a trivial easy task. This setup is also very close to the case of studying the problem in the particle center-of-mass reference frame while considering an externally applied uniform flow, as usually done analytically [6,7].…”

Section: Problem Statementmentioning

confidence: 99%

Flow and mass transfer around a core-shell reservoir

Kaoui

2017

Phys. Rev. E

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I have developed an alternative numerical approach to study mass transfer from a stationary core-shell reservoir under channel flow conditions. I use the lattice Boltzmann method to compute both the solvent fluid flow and the diffusion and advection of the solute. I have investigated the impact of the flow by reporting mass transfer quantities such as the instantaneous solute concentration and the local Sherwood number at the surface of the reservoir. The flow is found to enhance the release of the encapsulated material, but it prevents the released material from reaching the channel walls.

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Reciprocal theorem for convective heat and mass transfer from a particle in Stokes and potential flows

Cited by 16 publications

References 22 publications

Evaporation of a sessile droplet on a slope

Evaporation of a sessile droplet on a slope

Mass transfer to freely suspended particles at high Péclet number

Flow and mass transfer around a core-shell reservoir

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