Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions

Mingchi Chiou; Chinghuang Chiu

doi:doi:10.11648/j.engmath.20180201.14

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Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions

Mingchi Chiou, Chinghuang Chiu

Published in Engineering Mathematics (Volume 2, Issue 1)

Received: 7 June 2018 Accepted: 27 June 2018 Published: 24 July 2018

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Abstract

Development and applications of the surface rejuvenation model for particle transport towards the surface through turbulent boundary layer involve (1) the introduction of the constitutive equations to establish relations between the fluxes involved in mass transfer processes and the respective driving potentials, (2) the use of definition of the convective velocity to separate the mass transfer flux into diffusive and convective components based on Eulerian models of turbulent deposition proposed by Guha [1] and Young and Leeming [2], (3) the introduction of exponentially distributed functions given by Danckwerts [3] to transform the instantaneous transport properties into the mean domain prior to the solution of the conservation equations, and finally (4) the use of developed relationships for the mean concentration profile and mass transfer flux to obtained an analytical solution for the mean deposition velocity of neutral and charged particles. The deposition velocity of neutral particles with and without including thermophoretic effect is first calculated and then used to clarify the effects caused by the presence of external imposed electric field. A comparison with the experimental data and other theoretical predictions shows that the surface rejuvenation model is logical in finding the combined effect of thermophoresis and turbophoresis on the deposition of neutral particles and confirming the relative independence of deposition velocity upon these drift mechanisms at high values of particle inertia. When both thermophoretic and Coulombic forces operate together, two important conclusions are obtained from this model: (1) the contribution to particle deposition velocities does not represent the sum of these drift mechanisms considered in isolation; (2) the turbophoresis induces an additional drift velocity toward the wall in the vicinity of the wall, alleviating these external forces and enhancing particle deposition onto the wall through reduced build-up of particle concentration adjacent to the wall.

Published in	Engineering Mathematics (Volume 2, Issue 1)
DOI	10.11648/j.engmath.20180201.14
Page(s)	28-49
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Brownian Diffusion, Turbulent Diffusivity of Particles, Turbophoresis, Thermophoresis, Coulombic Force, External Imposed Electric Field

References

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APA Style

Mingchi Chiou, Chinghuang Chiu. (2018). Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Engineering Mathematics, 2(1), 28-49. https://doi.org/10.11648/j.engmath.20180201.14

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ACS Style

Mingchi Chiou; Chinghuang Chiu. Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Eng. Math. 2018, 2(1), 28-49. doi: 10.11648/j.engmath.20180201.14

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AMA Style

Mingchi Chiou, Chinghuang Chiu. Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Eng Math. 2018;2(1):28-49. doi: 10.11648/j.engmath.20180201.14

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@article{10.11648/j.engmath.20180201.14,
  author = {Mingchi Chiou and Chinghuang Chiu},
  title = {Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions},
  journal = {Engineering Mathematics},
  volume = {2},
  number = {1},
  pages = {28-49},
  doi = {10.11648/j.engmath.20180201.14},
  url = {https://doi.org/10.11648/j.engmath.20180201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20180201.14},
  abstract = {Development and applications of the surface rejuvenation model for particle transport towards the surface through turbulent boundary layer involve (1) the introduction of the constitutive equations to establish relations between the fluxes involved in mass transfer processes and the respective driving potentials, (2) the use of definition of the convective velocity to separate the mass transfer flux into diffusive and convective components based on Eulerian models of turbulent deposition proposed by Guha [1] and Young and Leeming [2], (3) the introduction of exponentially distributed functions given by Danckwerts [3] to transform the instantaneous transport properties into the mean domain prior to the solution of the conservation equations, and finally (4) the use of developed relationships for the mean concentration profile and mass transfer flux to obtained an analytical solution for the mean deposition velocity of neutral and charged particles. The deposition velocity of neutral particles with and without including thermophoretic effect is first calculated and then used to clarify the effects caused by the presence of external imposed electric field. A comparison with the experimental data and other theoretical predictions shows that the surface rejuvenation model is logical in finding the combined effect of thermophoresis and turbophoresis on the deposition of neutral particles and confirming the relative independence of deposition velocity upon these drift mechanisms at high values of particle inertia. When both thermophoretic and Coulombic forces operate together, two important conclusions are obtained from this model: (1) the contribution to particle deposition velocities does not represent the sum of these drift mechanisms considered in isolation; (2) the turbophoresis induces an additional drift velocity toward the wall in the vicinity of the wall, alleviating these external forces and enhancing particle deposition onto the wall through reduced build-up of particle concentration adjacent to the wall.},
 year = {2018}
}

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TY  - JOUR
T1  - Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions
AU  - Mingchi Chiou
AU  - Chinghuang Chiu
Y1  - 2018/07/24
PY  - 2018
N1  - https://doi.org/10.11648/j.engmath.20180201.14
DO  - 10.11648/j.engmath.20180201.14
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 28
EP  - 49
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20180201.14
AB  - Development and applications of the surface rejuvenation model for particle transport towards the surface through turbulent boundary layer involve (1) the introduction of the constitutive equations to establish relations between the fluxes involved in mass transfer processes and the respective driving potentials, (2) the use of definition of the convective velocity to separate the mass transfer flux into diffusive and convective components based on Eulerian models of turbulent deposition proposed by Guha [1] and Young and Leeming [2], (3) the introduction of exponentially distributed functions given by Danckwerts [3] to transform the instantaneous transport properties into the mean domain prior to the solution of the conservation equations, and finally (4) the use of developed relationships for the mean concentration profile and mass transfer flux to obtained an analytical solution for the mean deposition velocity of neutral and charged particles. The deposition velocity of neutral particles with and without including thermophoretic effect is first calculated and then used to clarify the effects caused by the presence of external imposed electric field. A comparison with the experimental data and other theoretical predictions shows that the surface rejuvenation model is logical in finding the combined effect of thermophoresis and turbophoresis on the deposition of neutral particles and confirming the relative independence of deposition velocity upon these drift mechanisms at high values of particle inertia. When both thermophoretic and Coulombic forces operate together, two important conclusions are obtained from this model: (1) the contribution to particle deposition velocities does not represent the sum of these drift mechanisms considered in isolation; (2) the turbophoresis induces an additional drift velocity toward the wall in the vicinity of the wall, alleviating these external forces and enhancing particle deposition onto the wall through reduced build-up of particle concentration adjacent to the wall.
VL  - 2
IS  - 1
ER  -

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Author Information

Mingchi Chiou

Department of Vehicle Engineering, National Formosa University, Yunlin, Taiwan
Chinghuang Chiu

Department of Vehicle Engineering, National Formosa University, Yunlin, Taiwan

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Mingchi Chiou, Chinghuang Chiu. (2018). Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Engineering Mathematics, 2(1), 28-49. https://doi.org/10.11648/j.engmath.20180201.14

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ACS Style

Mingchi Chiou; Chinghuang Chiu. Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Eng. Math. 2018, 2(1), 28-49. doi: 10.11648/j.engmath.20180201.14

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AMA Style

Mingchi Chiou, Chinghuang Chiu. Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions. Eng Math. 2018;2(1):28-49. doi: 10.11648/j.engmath.20180201.14

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@article{10.11648/j.engmath.20180201.14,
  author = {Mingchi Chiou and Chinghuang Chiu},
  title = {Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions},
  journal = {Engineering Mathematics},
  volume = {2},
  number = {1},
  pages = {28-49},
  doi = {10.11648/j.engmath.20180201.14},
  url = {https://doi.org/10.11648/j.engmath.20180201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20180201.14},
  abstract = {Development and applications of the surface rejuvenation model for particle transport towards the surface through turbulent boundary layer involve (1) the introduction of the constitutive equations to establish relations between the fluxes involved in mass transfer processes and the respective driving potentials, (2) the use of definition of the convective velocity to separate the mass transfer flux into diffusive and convective components based on Eulerian models of turbulent deposition proposed by Guha [1] and Young and Leeming [2], (3) the introduction of exponentially distributed functions given by Danckwerts [3] to transform the instantaneous transport properties into the mean domain prior to the solution of the conservation equations, and finally (4) the use of developed relationships for the mean concentration profile and mass transfer flux to obtained an analytical solution for the mean deposition velocity of neutral and charged particles. The deposition velocity of neutral particles with and without including thermophoretic effect is first calculated and then used to clarify the effects caused by the presence of external imposed electric field. A comparison with the experimental data and other theoretical predictions shows that the surface rejuvenation model is logical in finding the combined effect of thermophoresis and turbophoresis on the deposition of neutral particles and confirming the relative independence of deposition velocity upon these drift mechanisms at high values of particle inertia. When both thermophoretic and Coulombic forces operate together, two important conclusions are obtained from this model: (1) the contribution to particle deposition velocities does not represent the sum of these drift mechanisms considered in isolation; (2) the turbophoresis induces an additional drift velocity toward the wall in the vicinity of the wall, alleviating these external forces and enhancing particle deposition onto the wall through reduced build-up of particle concentration adjacent to the wall.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions
AU  - Mingchi Chiou
AU  - Chinghuang Chiu
Y1  - 2018/07/24
PY  - 2018
N1  - https://doi.org/10.11648/j.engmath.20180201.14
DO  - 10.11648/j.engmath.20180201.14
T2  - Engineering Mathematics
JF  - Engineering Mathematics
JO  - Engineering Mathematics
SP  - 28
EP  - 49
PB  - Science Publishing Group
SN  - 2640-088X
UR  - https://doi.org/10.11648/j.engmath.20180201.14
AB  - Development and applications of the surface rejuvenation model for particle transport towards the surface through turbulent boundary layer involve (1) the introduction of the constitutive equations to establish relations between the fluxes involved in mass transfer processes and the respective driving potentials, (2) the use of definition of the convective velocity to separate the mass transfer flux into diffusive and convective components based on Eulerian models of turbulent deposition proposed by Guha [1] and Young and Leeming [2], (3) the introduction of exponentially distributed functions given by Danckwerts [3] to transform the instantaneous transport properties into the mean domain prior to the solution of the conservation equations, and finally (4) the use of developed relationships for the mean concentration profile and mass transfer flux to obtained an analytical solution for the mean deposition velocity of neutral and charged particles. The deposition velocity of neutral particles with and without including thermophoretic effect is first calculated and then used to clarify the effects caused by the presence of external imposed electric field. A comparison with the experimental data and other theoretical predictions shows that the surface rejuvenation model is logical in finding the combined effect of thermophoresis and turbophoresis on the deposition of neutral particles and confirming the relative independence of deposition velocity upon these drift mechanisms at high values of particle inertia. When both thermophoretic and Coulombic forces operate together, two important conclusions are obtained from this model: (1) the contribution to particle deposition velocities does not represent the sum of these drift mechanisms considered in isolation; (2) the turbophoresis induces an additional drift velocity toward the wall in the vicinity of the wall, alleviating these external forces and enhancing particle deposition onto the wall through reduced build-up of particle concentration adjacent to the wall.
VL  - 2
IS  - 1
ER  -

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