Thermophoresis and Creeping Motion of Non-Spherical Aerosol Particles
Date Issued
2010
Date
2010
Author(s)
Chang, Yu-Chen
Abstract
In this thesis, the steady thermophoresis and creeping motion of non-spherical particles in a gaseous medium are theoretically studied. Either the applied uniform temperature gradient driving the thermophoresis of the particle or the external force driving the creeping motion of the particle in the absence of the temperature gradient can be in an arbitrary direction. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the surface of the particle. In the limit of small Peclet and Reynolds numbers, the appropriate energy and momentum equations governing the systems are solved for some general cases of non-spherical particles, including the slightly deformed spheres, the axisymmetric particles, and the spheroidal particles.
In Chapter 2, the thermophoresis, translation, and rotation of a slightly deformed aerosol sphere in an arbitrary direction are analyzed. The energy and momentum equations governing the system are solved asymptotically using a method of perturbed expansions. To the second order in the small parameter characterizing the deformation of the aerosol particle from the spherical shape, the thermal and hydrodynamic problems are formulated for the general case, and explicit expressions for the thermophoretic velocity of the particle and the drag and torque exerted on the particle by the fluid due to its isothermal creeping motion are obtained for the special cases of prolate and oblate spheroids. The agreement between our asymptotic results for a spheroid and the relevant analytical and numerical solutions in the literature is quite good, even if the particle deformation from the spherical shape is not very small.
In Chapter 3, the thermophoresis and translation of a spheroidal particle along the axis of revolution of the particle are studied. The general solutions in prolate and oblate spheroidal coordinates can be expressed in infinite-series forms of separation of variables for the temperature distribution and of semi-separation of variables for the stream function. The jump/slip boundary conditions on the particle surface are applied to these general solutions to determine the unknown coefficients of the leading orders, which can be numerical results obtained from a boundary collocation method or explicit formulas derived analytically. Numerical results for the thermophoretic velocity of the particle and the drag force exerted on the particle translating in an isothermal fluid are obtained in a broad range of its aspect ratio with good convergence behavior for various cases. The agreement between our results and the available numerical results in the literature and those in the previous chapter is very good.
In Chapter 4, the thermophoresis of an axisymmetric particle along its axis of revolution is analyzed. 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 boundary-collocation technique to these general solutions. Numerical results for the thermophoretic velocity are obtained with good convergence behavior for the spherical and spheroidal particles. The results agree quite well with the available solutions in the literature and in the previous chapters.
In Chapter 5, the thermophoresis and translation of a particle of revolution with fore-and-aft symmetry perpendicular to the axis of revolution are explored using the same method of the distribution of spherical singularities combined with the boundary-collocation technique. The thermophoretic velocity of the particle and the drag force acting on the particle by the fluid are calculated with good convergence behavior for various cases, including the spherical and spheroidal particles. The results show excellent agreement with the relevant analytical solutions in the literature and in Chapter 2 for a spheroid whose shape deviates slightly from that of a sphere.
It is found that the thermophoretic mobility of the spheroid normalized by the corresponding value for a sphere with equal equatorial radius in general is a monotonic function of the aspect ratio of the spheroid, but there are some exceptions. For most practical cases of a spheroid with a specified aspect ratio, the thermophoretic mobility of the particle is not a monotonic function of its relative jump/slip coefficients and thermal conductivity. Depending on the value of the slip parameter, the hydrodynamic drag force and torque acting on a moving spheroid normalized by the corresponding values for a no-slip sphere with equal equatorial radius are not necessarily monotonic functions of the aspect ratio of the spheroid. For a moving spheroid with a fixed aspect ratio, its normalized hydrodynamic drag force and torque decrease monotonically with an increase in the slip capability of the particle.
Subjects
Thermophoresis
Creeping motion
Temperature jump
Thermal slip
Frictional slip
Axisymmetric aerosol particle
Slightly deformed aerosol sphere
Type
thesis
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