Doctoral defense
Dynamics of bodies small compared to the mean free path
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| Defendant |
Main Advisor |
Extra Advisor |
Date |
| Karl Borg |
Lars Söderholm |
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2003-06-11 |
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| Opponent |
| Kazuo Aoki, University of Kyoto
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| Evaluation committee |
Johan Grundberg, Mälardalens högskola
Alexei Heintz, Department of Mathematics, Chalmers
Bo Thidé, Swedish Institute of Space Physics, Uppsala
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AbstractIn the present thesis, aspects of the dynamics of bodies immersed in gases are investigated. The bodies under consideration are small compared to the mean free path in the gas. The study comprises both gases in equilibrium and gases subject to gradients in the temperature or the flow velocity. For the description of the inhomogeneous gas, the Chapman-Enskog distribution function is used. In the case of an inhomogeneous gas, the dynamics of axially symmetric bodies is studied. The total force and torque exerted on the small body by the gas are calculated. The equations of motion are obtained, and the resulting transport, corresponding to stationary solutions, is investigated. For the case of a gas subject to a temperature gradient, the well-known thermophoresis phenomenon is recovered, where the bodies are transported towards the cooler parts of the gas. Previously known results for spherical bodies are generalised to axially symmetric bodies. For a gas subject to a velocity gradient, a new transport mechanism, "Shearing Phoresis", is obtained, that transports the small bodies along the eigen directions of the shearing tensor. In the case of a gas at equilibrium, the forces and torques acting on a spinning sphere are calculated. First, a sphere of finite thermal conductivity moving with a small speed is considered. A heat equation for the rotating sphere is solved, and the temperature field of the body surface is obtained. The total force acting on the spinning sphere is calculated, which is found to have three different components: a friction force, a force parallel to the angular velocity, and a transverse force of opposite direction compared to the corresponding force appearing in the continuum limit, the so-called Magnus force. Finally, the total force and torque acting on a spinning sphere of high thermal conductivity are obtained for arbitrary speeds. The result is applied to a spinning sphere in a Kepler orbit. In doing this, perturbation theory is employed. It is shown that the force and torque, apart from slowly contracting the orbit radius, also slowly rotates the orbital plane.
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