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Theses Doctoral

Near-field Radiative Momentum, Energy and Entropy Transfer in Fluctuational Electrodynamics

Zheng, Yi

Quantum and thermal fluctuations of electromagnetic fields, which give rise to Planck's law of blackbody radiation, are also responsible for van der Waals and Casimir forces, as well as near-field radiative energy transfer between objects. Electromagnetic waves transport energy, momentum, and entropy. For classical thermal radiation, the dependence of the above mentioned quantities on the temperature is well-known mainly due to Planck's work. When near-field effects, namely the collective influence of diffraction, interference, and tunneling of waves, become important, Planck's theory is no longer valid. Of momentum, energy, and entropy transfer, the role of near-field effects on momentum transfer between two half-spaces separated by a vacuum gap (van der Waals pressure in the vacuum gap) was first determined by Lifshitz, using Rytov's theory of fluctuational electrodynamics in 1956. Subsequently, Dzyaloshinskii, Lifshitz, and Pitaevskii, employing sophisticated methods from quantum field theory, generalized Lifshitz' result for van der Waals pressure in a vacuum layer to the case of van der Waals pressure in a dissipative layer between two half-spaces. The influence of near-field effects on radiative transfer was appreciated only in the late 1960s and, subsequently, in the last two decades because of the enhancement in radiative transfer due to electromagnetic surface waves. The role played by near-field effects on entropy transfer has not been investigated so far, at least when the temperature distribution is non-uniform.
In this thesis, I investigate the transport of momentum, energy, and entropy due to electromagnetic fluctuations with near-field effects taken into consideration. For momentum transfer, I give a new perspective to the theory of van der Waals pressure by obtaining the results of Dzyaloshinskii, Lifshitz, and Pistaevskii without having to use any quantum field theory. I show that the computation of van der Waals pressure between objects on the imaginary frequency axis is only a numerical/mathematical convenience, not a physical necessity. For energy transfer, I identify some of the similarities and differences between energy and momentum transfer. I solve a problem in near-field radiative transfer between two half-spaces to identify the differences, mainly with an aim of identifying features that make it likely that the proximity approximation for computing near-field radiative transfer between two curved objects is as valid as the proximity approximation for van der Waals forces between curved surfaces. The analysis shows qualitative differences between energy and momentum transfer. Finally, I solve for the first time the entropy transfer between half-spaces at different temperatures taking near-field effects into account.
I wanted to calculate the momentum and entropy transfer between two half-spaces in order to solve the more complicated problem of van der Waals pressure in a layer of dissipative material between two half-spaces at different temperatures, namely the problem of Dzyaloshinskii, Lifshitz, and Pitaevskii but under conditions of thermal non-equilibrium. My hypothesis was that the knowledge of non-equilibrium entropy transfer in a vacuum gap would furnish us the solution. I have not been successful in that endeavor, though.
This work is focused on three aspects of momentum, energy and entropy transfer in fluctuational electrodynamics: (1) a transparent formalism of determining the van der Waals and Casimir force in a dissipative planar multilayered system, (2) a formalism of surface integrals of dyadic Green's functions for radiative energy and momentum transfer between objects of arbitrary shapes and sizes at different temperatures, and (3) a theory of evaluating entropy density and entropy flux at both thermal equilibrium and non-equilibrium while taking into account the influence of near-field effects. My doctoral research is devoted to establishing a general theory of momentum and energy transfer between arbitrarily shaped objects at thermal non-equilibrium and at a microscopic length scale, which urges a more careful, deeper, and complete thermodynamic study of near-field radiative heat transfer.

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More About This Work

Academic Units
Mechanical Engineering
Thesis Advisors
Narayanaswamy, Arvind
Degree
Ph.D., Columbia University
Published Here
August 19, 2014
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