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David C. Silverman |
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Sorption and Diffusion Effect on Sample Size and Test Duration One of the critical variables in the Sequential Immersion Test is the duration of each portion of the test. Though the final equilibrium state or possible steady state movement of components between the environment and the interior of the material is not necessary, the mass change at the end of the soak portion and mass change at the end of the drying portion should be close enough to the "final" mass change that the values extracted from the curves provide enough of a reasonable estimate of the final state that a prediction can be made. The question is how close is close. The following discussion provides a framework for making a gross estimate of the test time. Note that by including additional information on the final curvature, SEQEXPERT allows some leeway in the choice possibly decreasing test time.The process of migration can be divided into two main steps, adsorption onto or desorption from the surface and diffusion between the surface and the interior. The assumption is that diffusion of species between the bulk environment and the surface of the nonmetallic material is rapid so that the amount of material adsorbed on the surface is in equilibrium with the bulk environment. This assumption is reasonable because the diffusion coefficient within the material should be several orders of magnitude lower than diffusion in the bulk fluid. Under these circumstances the concentration difference between the surface and the interior creates the concentration driving force for migration into and out of the nonmetallic material. The surface concentration becomes a boundary condition. The migration, then, is governed by Fick’s laws of diffusion. Though diffusion is three dimensional, by appropriate choice of geometry one can force one dimensional diffusion in Cartesian (rectangular x,y,z) coordinates. To do so, the dimension in the direction of diffusion must be much less than the other dimensions. This choice is shown in this figure This figure 
where D is the
diffusion coefficient, t is the time, and l is the dimension in the direction of
diffusion (in this case one-half of the total thickness). This quantity is a
dimensionless time. It is the ratio of the actual time to the time that a diffusing
species would travel a distance of radius l or carve out an area of radius l.
This non-dimensional time is the important variable for estimating the needed exposure
time.
One possible method of making this estimate is built on information found in E. M. Rosen and D. C. Silverman, "Sorption/Diffusion Prediction in Non-metallics Using Fick’s Law", Corrosion, Volume 46, p. 945, 19901  (450k).
The procedure is as follows. The equation shown in the previous figure above provides
the outline. The assumption is made that the test duration of the soak cycle and the drying
cycle have to be long enough so that if the test time is inserted into
the above equation that equation when solved by regression provide predictions of
the diffusion coefficient and the final mass change at infinite time that are within
a certain defined error of the actual values. This figure The required thickness as function of soak time and diffusion coefficient or required soak time as a function of thickness and diffusion coefficient might be estimated from a plot such as that above. The assumption is that appropriate soaking times are those that would enable the diffusion coefficient and mass gain at infinite time to be estimated reasonably well by regression of the analytical solution to the experimental mass gain data versus time. In other words, the diagonal line in the above figure would form a minimum for each tolerance. Appropriate test times would lie above and to the right of the diagonal line. An example is as follows. Suppose the desire is to design a test so that if a regression were performed against the measured data using the analytical solution, the error in the diffusion coefficient and in the mass gain at infinite time would be 10%. In addition, the estimated total mass gain is 10%. The lower diagonal line would become the minimum boundary. That line could be used to solve for the thickness as a function of test time and diffusion coefficient. The results are shown in this figure. This analysis is limited to
A quantitative analysis such as that above is far more complicated for a real system. Very often, more than one species is diffusing into and out of the sample simultaneously. The result can be an acceleration or deceleration of diffusion depending on the interaction and motion of the species relative to each other. Nonmetallic materials may not be uniform meaning that diffusion coefficients may vary across the specimen. And since the mass loss in a real system is usually caused by migration of more than one species, the diffusion coefficient estimated from the total mass loss is probably a composite diffusion coefficient at best which may have only a limited relationship to the diffusion coefficients of the individual components. These impediments to designing a quantitative framework within which to interpret individual tests led to the development of SEQEXPERT as a way to make predictions from this type of data without needing mathematical analysis or a full understanding of what components are migrating into or out of the specimen. Previous Page: Using SEQEXPERT-a step-by-step procedure Next Page: Features Useful for Interpreting Results 1 © NACE International publication and year shown in citation above. All rights reserved. Displayed with permission from NACE International, Houston, TX (http://www.nace.org). Published in Corrosion, in the month and year shown in the citation above. |
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David C. Silverman, Ph.D. - Primary Consultant |
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