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Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions
Engineering Mathematics
Volume 2, Issue 1, June 2018, Pages: 28-49
Received: Jun. 7, 2018; Accepted: Jun. 27, 2018; Published: Jul. 24, 2018
Authors
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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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.
Keywords
Brownian Diffusion, Turbulent Diffusivity of Particles, Turbophoresis, Thermophoresis, Coulombic Force, External Imposed Electric Field
Mingchi Chiou, Chinghuang Chiu, Adaptation of Surface Rejuvenation Model to Turbulent Mass Transfer with Coupling Between Thermophoretic and Coulombic Force Interactions, Engineering Mathematics. Vol. 2, No. 1, 2018, pp. 28-49. doi: 10.11648/j.engmath.20180201.14
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