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https://hdl.handle.net/2142/55617
Description
Title
Topics in fluid phase transitions
Author(s)
Swift, Jack Bernard
Issue Date
1968
Director of Research (if dissertation) or Advisor (if thesis)
Kadanoff, Leo Philip
Doctoral Committee Chair(s)
Kadanoff, Leo Philip
Committee Member(s)
Bardeen, John
Langebartel, Ray G.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D. (doctoral)
Degree Level
Dissertation
Keyword(s)
Fluid Systems
Language
en
Abstract
Dynamic critical point phenomena in fluid systems are studied first by means of models and then with the aid of the scaling laws for critical exponents. Two models whose equilibrium distribution functions reduce to the standard Ising model density matrices and whose time dependences are governed by master equations are introduced. The first model gives spin and heat diffusion and a proof similar to that of Kawasaki that the transport coefficients are finite near the critical point holds. The second model, which gives sound waves and heat and transverse momentum diffusion, admits the possibility of infinite transport coefficients. A perturbation theory for the determination of transport coefficients near the critical point if presented. This perturbation theory is based upon processes in which one transport mode decays into several low wave-number modes. Scaling law concepts are used to calculate the order of magnitude of the matrix elements and frequency denominators which appear in this theory. This permits the estimation of the order of magnitude of the transport coefficients near the critical point. The perturbation theory is applied to estimating the anomalous part of the transport coefficients of a liquid-gas near its critical point and of a binary liquid mixture near its consolute temperature. Specific predictions of the singularities in the transport coefficients are given in terms of the critical exponents which describe the behavior of thermodynamic and static correlation functions. The connection between these reactions and the scaling of frequencies is discussed.
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