Thermophoresis of axisymmetric aerosol particles along their axes of revolution

Abstract

in Wiley InterScience (www.interscience.wiley.com).The axisymmetric thermophoretic motion of an aerosol particle of revolution in a uniformly prescribed temperature gradient 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 distribution and fluid velocity field. The jump/slip conditions on the particle surface are satisfied by applying a boundarycollocation technique to these general solutions. Numerical results for the thermophoretic velocity of the particle are obtained with good convergence behavior for various cases. For the axisymmetric thermophoresis of an aerosol spheroid with no temperature jump and frictional slip at its surface, the agreement between our results and the available analytical solutions is very good. The thermophoretic velocity of a spheroid along its axis of revolution in general increases with an increase in its axial-to-radial aspect ratio, but there are exceptions. For most practical cases of a spheroid with a specified aspect ratio, its thermophoretic mobility is not a monotonic function of its relative jump/slip coefficients and thermal conductivity.

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

“…That is, the effects of the four parameters k ‫ء‬ , C t ‫ء‬ , C m ‫ء‬ , and a / b on the thermophoretic mobility of a spheroid along its axis of revolution are opposite to those on the thermophoretic mobility of a spheroid normal to the axis. For the general problem of thermophoresis of a particle of revolution with fore-and-aft symmetry caused by a uniform temperature gradient in an arbitrary direction with respect to its axis of revolution, which is linear in its governing equations and boundary conditions, the solution of the thermophoretic velocity can be obtained by the vectorial addition of these previous results for the axial movement 44,45 and the present result for the transverse migration. …”

“…The thermophoresis of an axisymmetric aerosol particle with a temperature jump, a thermal slip, and a frictional slip at its surface along its axis of revolution was investigated by using a similar method of internal singularity distributions 44 and the corresponding motion of a prolate or oblate spheroid was also analyzed by using a method of separation or semiseparation of variables in spheroidal coordinates, 45 and analytical and numerical results of the thermophoretic mobil- ity for the particles with various values of aspect ratio were obtained. It was found that, for specified values of k ‫ء‬ , C t ‫ء‬ , and C m ‫ء‬ , the value of the normalized axisymmetric thermophoretic mobility U / U 0 of a spheroid in general increases with an increase in a / b, since the fraction of the thermal slip of the fluid at the particle surface in the direction along its axis of revolution increases with the increase of a / b.…”

“…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.…”

“…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.…”

Efficient simulation of rarefied gas flow past a particle: A boundary element method for the linearized G13 equations

“…In the remainder of the paper, for the sake of compactness, we will refer to this model simply as the 'NSF model with slip and jump'. In this case, for a spheroid of aspect ratio near one, an approximate solution was obtained by Senchenko and Keh (2007) with perturbation techniques and, for a spheroid of arbitrary aspect ratio, by Chang and Keh (2009a) using the singularity-collocation method. Two works for rarefied, confined flows in the plane are worthy of mention.…”