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A Theory for the Hugoniot of Condensed Media


Salzman, Paul Klenett (1971) A Theory for the Hugoniot of Condensed Media. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/7nnp-4m89.


A shock model is developed that leads to an analytical expression for the Hugoniot of condensed media. In the analysis the final state is selected to coincide with the end of the shock transition so that the total energy change across the shock front is evaluated from changes in configurational energy only using an n-6 pair potential (shown to be valid for all n > 0) and a given lattice structure. Thermal energy changes are ignored because the dwell time of the molecules in the shock transition region is less than the thermal relaxation time. The total energy change is equated to the Hugoniot energy change in the Rankine-Hugoniot conservation relations. This together with the assumption of linear compression across the shock transition gives the desired expression for the Hugoniot.

In the "weak form" (WF) solution the Hugoniot depends on molecular (atomic) weight M and initial density ρo as well as the collision diameter σ, depth of the potential well ε and repulsive exponent n of the pair potential. Extrapolation of this solution, under certain conditions, yields an expression for the sound velocity Uo dependent on M, ε and n. In the "strong form" (SF) solution the Hugoniot depends only on Uo and n.

The shock data for 13 liquids and 23 metals are compiled and a selection process used to eliminate poor data and data affected by phase transitions. Using σ from the literature and ε from a melting point correlation, the WF solution Hugoniot is applied to the liquids and the "best" values of n determined using numerical fitting techniques. Excellent fits are obtained with values of n from 6.2 to 11.7. A common value of 9.2 is found to fit the shock data for argon at four different initial states. Failure of the theory is noted only for (di-)ethyl ether and water. The results are generally concluded to support the validity of the shock model. Values of n for argon, mercury and nitrogen compare favorably with values reported in the literature. The WF solution does not yield accurate values of Uo.

The SF solution is expanded in Taylor series to eliminate singularities and applied to the shock data for 10 fcc and 13 bcc metals and the "best" values of n determined. For the fcc metals excellent fits are found for values of n from 4.0 to 6.3. Based on the "pseudo-atom" concept, it is concluded that metals have "softer" potentials than liquids. The results for the fcc metals are concluded to generally support the validity of the shock model. For the bcc metals excellent fits are found for n = 0.1 to 4.6 and it is concluded that bcc metals are "softer" than fcc metals. Since σ is "not defined" for all n < 3 it is speculated that the Hugoniot might not be "well defined" in these cases. The theory is found to be not applicable to Cs and Ba. The values of n found for Cu, Al and Pb agree well with values in the literature. The n for metals are found to roughly correlate with the Grüneisen coefficient γ.

The major assumption of the theory, that the transition region is "sufficiently thin," is analyzed and found to be reasonable. The mean number of molecular layers in the transition region is ~ 7 and the mean residence time ~ 2 x 10-12sec. In addition the n-6 potential is judged to be adequate for the present study.

The SF solution Hugoniot is shown to be compatible with the classical linear U-µ relation (U = A + Bu) when x-1 « 1. Values of the slope B from experimental data are found to agree closely with the derived relation B ≃ (n + 5)/6 for the corresponding metals. Recommendations for further studies with liquids, fcc and bcc metals are made, including an evaluation of an explicit expression generally relating the pair potential to the shock data.

In several subsidiary studies a new method of computing temperatures along the Hugoniot is found, two statistical approaches to the definition of "nearest neighbor distance" and its use as a measure of liquid structure are developed and the effect of phase transitions on the shock model is determined.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Chemical Engineering
Degree Grantor:California Institute of Technology
Division:Chemistry and Chemical Engineering
Major Option:Chemical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Pings, Cornelius J.
Thesis Committee:
  • Unknown, Unknown
Defense Date:28 May 1971
Funding AgencyGrant Number
General DynamicsUNSPECIFIED
Record Number:CaltechTHESIS:04172018-113351900
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10810
Deposited By: Benjamin Perez
Deposited On:17 Apr 2018 20:40
Last Modified:16 Apr 2021 23:04

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