Thermophoretic motion of slightly deformed aerosol spheres

Chang, Yi‐Chung; Keh, Huan J.

doi:10.1016/j.jaerosci.2009.10.004

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…43 The asymptotic formula for the thermophoretic velocity of a spheroidal particle correct to the second order in the small parameter characterizing the deformation, =1−͑a / b͒, was obtained in a closed form. The values of the normalized thermophoretic mobility U / U 0 of a prolate spheroid ͑with Ͻ0͒ perpendicular to its axis of revolution calculated from this approximate formula are also listed in Table II for comparison.…”

Section: Solution For the Thermophoresis Of A Prolate Spheroidmentioning

confidence: 99%

“…4͑b͔͒. Because the effects of the four parameters k ‫ء‬ , C t ‫ء‬ , C m ‫ء‬ , and a / b on the thermophoretic velocity of a spheroid interact one another in a quite complicated manner, 43 it would be difficult to provide detailed physical analysis for the above observations from Figs. 2-4.…”

Section: Solution For the Thermophoresis Of A Prolate Spheroidmentioning

confidence: 99%

“…Recently, the thermophoresis of a slightly deformed sphere with the effects of temperature jump, thermal slip, and frictional slip at its surfaces was investigated, and an explicit expression for the thermophoretic velocity was obtained to the second order in the small parameter characterizing the deformation. 42,43 The thermophoretic motions of a general axisymmetric particle 44 and a prolate or oblate spheroid 45 with the effects of temperature jump, thermal slip, and frictional slip along their axes of revolution were also examined analytically and numerically to some extent by using the methods of internal singularity distributions, separation or semiseparation of variables in spheroidal coordinates, and boundary collocations. However, the problem of thermophoresis of a general particle of revolution with the jump/slip conditions at its surface in an arbitrary direction has not been analytically or numerically solved yet, mainly due to the fact that, if the temperature jump and/or frictional slip is included, a separable solution of the temperature and/or fluid velocity fields is not feasible for most orthogonal curvilinear coordinate systems, such as the prolate and oblate spheroidal ones.…”

Section: Introductionmentioning

confidence: 99%

“…15,40 For the cases of a spheroid in general conditions whose shape deviates slightly from that of a sphere, our results also agree quite well with the approximate analytical solution in the literature. 43 Because the governing equations and boundary conditions concerning the general problem of thermophoretic motion of a particle of revolution with fore-and-aft symmetry caused by a prescribed moderate temperature gradient in an arbitrary direction are linear, its solution can be obtained as a superposition of the solutions for its two subproblems: motion along the axis of revolution of the particle, which was previously examined, 44,45 and motion normal to the axis, which is treated in this work.…”

Section: Introductionmentioning

confidence: 99%

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Thermophoresis of axially and fore-and-aft symmetric aerosol particles

Chang

Keh

2010

Physics of Fluids

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The thermophoretic motion of an aerosol particle of revolution with fore-and-aft symmetry in a uniformly prescribed temperature gradient normal to its axis of revolution is studied theoretically. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model. A method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the temperature and fluid velocity fields. The temperature jump and fluid slip conditions at the particle surface are satisfied by applying a boundary collocation technique to these general solutions to determine the unknown coefficients. The thermophoretic velocity of the particle is calculated with good convergence behavior for various cases, and the agreement between our results and the available analytical solutions is very good. It is found that the normalized thermophoretic velocity of a prolate or oblate spheroid perpendicular to its axis of revolution decreases monotonically with an increase in its axial-to-radial aspect ratio. For most practical cases of a spheroid with a specified aspect ratio, its thermophoretic mobility is not a monotonic function of its relative thermal conductivity. For the general problem of a particle with axial and fore-and-aft symmetry undergoing thermophoresis in a temperature gradient oriented arbitrarily with respect to its axis of revolution, the solution of the particle velocity can be obtained as a superposition of the solution obtained previously for the axisymmetric motion of the particle and the current result.

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Section: Solution For the Thermophoresis Of A Prolate Spheroidmentioning

confidence: 99%

Section: Solution For the Thermophoresis Of A Prolate Spheroidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermophoresis of axially and fore-and-aft symmetric aerosol particles

Chang

Keh

2010

Physics of Fluids

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“…This analysis has been generalized to the motion of a spheroid with an arbitrary orientation relative to the imposed thermal gradient (Keh and Ou, 2004). Recently, the thermophoresis of an isolated particle which departs slightly in shape from a sphere with the effects of temperature jump, thermal slip and frictional slip was examined, and an explicit expression for the thermophoretic velocity was obtained to the second order in the small parameter characterizing the deformation (Chang and Keh, 2010). However, the boundary effect on thermophoresis of particles of a nonspherical shape has not been investigated yet.…”

Section: Introductionmentioning

confidence: 99%