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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:02:09 +0000Application of the element potential method to gaseous chemical equilibrium calculation
https://resolver.caltech.edu/CaltechTHESIS:10042012-081149631
Authors: Wrobel, Joseph Richard
Year: 1963
DOI: 10.7907/8D03-R614
The equilibrium state of a mixture of chemically reacting
perfect gases at fixed enthalpy and pressure is formulated
in terms of the Massieu element potentials by the application
of the entropy maximization principle. An iterative solution
technique is presented to obtain the parameters appropriate
to the equilibrium state. A method for obtaining starting
values and a stability criterion based upon the element
potential method are presented. A perturbation technique
is developed to predict the equilibrium state for different
enthalpy, pressure, and atomic mole number constraints, given
the solution for one set of constraints.
https://thesis.library.caltech.edu/id/eprint/7223On the turbulent flow of dilute polymer solutions
https://resolver.caltech.edu/CaltechETD:etd-12082005-140727
Authors: Walsh, Myles Alexander
Year: 1967
DOI: 10.7907/6NTP-AH77
This paper is concerned with the problem of explaining the anomalous decrease in turbulent skin friction observed in the turbulent flow of very dilute polymer solutions.
The experimental evidence for dilute solutions is summarized.
The polymer molecule in solution is examined from a theoretical point of view, using the Rouse model. It is found that the model predicts that the molecule will locally store energy as a function of the local strain rate of the solution.
The experimental evidence is reexamined and it is concluded that the anomalous decrease in turbulent momentum transport results because the molecules manage to alter the energy balance of the small disturbances at the edge of the viscous sublayer. By slightly altering this balance the molecules allow viscous dissipation to destroy disturbances which would have had sufficient energy to grow had the molecules not been present. By decreasing the number of small disturbances which grow per unit area and time and move out from the edge of the viscous sublayer, the addition of polymer molecules ultimately changes the structure of the turbulence in the outer part of the boundary layer. This change results in lower Reynolds stresses and hence lower turbulent momentum transport.
With the help of the relation for local energy storage derived from the Rouse model, parameters are developed to characterize the phenomenon. These parameters appear to be useful in understanding the experimental evidence to date.https://thesis.library.caltech.edu/id/eprint/4865Theoretical Investigation of the Effect of Intramolecular Interactions on the Configuration of Polymeric Chains
https://resolver.caltech.edu/CaltechETD:etd-10072002-145049
Authors: Curro, John Gillette
Year: 1969
DOI: 10.7907/8KEP-R512
<p>A theoretical investigation of the effect of intramolecular interactions on the configurational statistics of a polymer molecule is presented. This problem has been studied by many authors and is known as the "excluded volume problem" in the literature. A statistical mechanical approach is used. Many of the similarities between the theory of "classical fluids" and the excluded volume problem are exploited.</p>
<p>The configurational statistics of 2 and 3 segment chains are computed exactly for the "hard sphere potential". The integrations were performed by introducing bipolar and tripolar coordinate systems. It was found that the mean square end-to-end distance for these cases was n<sup>1.33</sup> where n is the number of segments. These results are of no practical use in predicting the properties of real polymer chains which are much longer. It is instructive, however, to compare these exact results with approximate theories in the limit of short chain length.</p>
<p>A "cluster expansion" is written for the partition function of a polymer chain with the ends of the chain fixed. This is analogous to the cluster expansion for the partition function of an imperfect gas. The first-order term in this expansion is evaluated for the hard core potential. In the limit of small hard core diameters, the first-order term leads to the wellknown first-order perturbation theory for the mean square end-to-end distance. The exact results of this first-order correction term are used to construct higher-order terms of a specified "isolated topology". If only these terms are used in the cluster expansion, incorrect results are obtained for the mean square end-to-end distance. This indicates that higher-order terms of complicated topology are significant for longer chain length.</p>
<p>Various approximate integral equations for the restricted partition function of a polymer chain are presented. The most promising of these equations is the analog of the well-known Percus-Yevick equation in the theory of liquids. In deriving this equation two topologically distinct types of graphs are defined. These are the "nodal and elementary" graphs. An exact equation relating these types of graphs is presented. The analog of the Percus-Yevick approximation is made which leads to an integro-difference equation. This equation is solved exactly using the hard core potential for the special case of the hard core diameter equal to the polymer segment length. Results of numerical calculations are given for other intermediate values of this diameter ranging from zero to the segment length (the "pearl necklace" model). This leads to values of γ ranging correspondingly from 1.0 to 2.0 where <r<sup>2</sup><sub>1N</sub> ∝ M<sup>γ</sup>> with <r<sup>2</sup><sub>1N</sub> the mean square end-to-end distance and M the molecular weight. The numerical results for <r<sup>2</sup><sub>1N</sub> as a function of chain length are in good agreement with the second-order perturbation theory of Fixman for small hard core diameters.</p>https://thesis.library.caltech.edu/id/eprint/3958