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Dynamics of the motion of a phase change boundary to changes in pressure

O'Connell, Richard J. and Wasserburg, G. J. (1967) Dynamics of the motion of a phase change boundary to changes in pressure. Reviews of Geophysics, 5 (4). pp. 329-410. ISSN 0096-1043.

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Because of the significance of both shallow and deep phase changes to geophysical problems, the dynamical response of a phase change to pressure loading was investigated. It was found that the characteristic behavior of the system may be analyzed in terms of simple parameters of the system by using analytic expressions that apply for the initial part and the final part of the motion of the phase boundary. These expressions are obtained from approximations based on generalizations of Neumann's solution for melting at a constant temperature or from simple physical approximations based on the over-all geometry of the model. The range of applicability of the approximations can be obtained from the approximations themselves. The analytic results compare very favorably with exact numerical solutions. The distribution of heat sources and convective heat transport are shown to be generally of minor importance on the motion of the phase boundary; the effect of convective heat transport can be estimated from the analytic approximation. The important parameters are the latent heat of the phase change and the difference in slope between the Clapeyron curve and the temperature distribution in the earth. In addition, the long-term motion depends primarily on the over-all geometry of the model and the boundary condition at depth. The analytic results indicate the time at which thermal blanketing by sediments becomes important and the effect of the rate of sedimentation on the response of the system; they also define slow and fast sedimentation and secular equilibrium. The effect of isostasy in conjunction with a shallow phase change is shown to be of major importance, and for certain cases the sediment thickness that can accumulate in a sedimentary basin may depend only on the sedimentation rate and not the initial depth of the basin. The analytic results permit a more physical discussion of the problem, since the functional dependence of the solution on the parameters may be seen. In addition, important results for a variety of models can be obtained by relatively simple calculations, without resorting to separate numerical solutions for each model considered.

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Wasserburg, G. J.0000-0002-7957-8029
Additional Information:Copyright © 1967 by the American Geophysical Union. (Manuscript received May 8, 1967; revised July 12, 1967.) We wish to acknowledge helpful discussions with M. Lees who suggested the method of numerical solution in appendix 2 and some of the mathematical results in appendix 1. Some of the initial investigations of the steady-state aspects were done by A. Ramo. We wish to thank C. Chase for his careful efforts in the calculation and tabulation of the special functions used in this work. This work was supported by the National Science Foundation.
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Caltech Division of Geological and Planetary Sciences1494
Issue or Number:4
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Official Citation:O'Connell, R. J., and G. J. Wasserburg (1967), Dynamics of the motion of a phase change boundary to changes in pressure, Rev. Geophys., 5(4), 329–410, doi:10.1029/RG005i004p00329.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51344
Deposited By: George Porter
Deposited On:06 Nov 2014 16:40
Last Modified:09 Mar 2020 13:19

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