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Amy Heaton's Project SummaryPermeability of Fluid and Gas Through Natural IcesI am interested in the connection between the microstructure of natural ice, both sea and glacial, and the permeability of fluid and gas through these media. I am using mathematical models to understand the effective transport properties of these composite media. Models are chosen that are similar geometrically to the ice microstructure, as this is key in correctly correlating the transport properties of ice to the mathematical properties of the model. I have constructed a program in Matlab that mathematically represents the process of bubble-trapping in the formation of glacial ice. The program, based on the properties of a Swiss Cheese continuum model, generates a series of two-dimensional images, each representing a progressive stage in the bubble-trapping process. I am looking to mathematically characterize the point at which the solid phase (ice) cuts off the second phase (air) from percolating. This point, namely the firn-ice transition, is represented as an infinite cluster in the model. Further work will allow the computer to characterize this point more thoroughly. A similar problem mathematically is that of characterizing the permeability of fluid through natural ices. I am investigating the properties of sea ice in particular. Several techniques in approaching this problem are siginificant: the use of theoretical bounds and the use of network models. I have been investigating the theory of bounds and have identified several that are relevant to the fluid permeability of sea ice. Once experimental data is collected, these theoretical bounds can be evaluated as to how well they capture the data and to what degree a more detailed analysis needs to be constructed. I am also looking at a parallel pipe model to capture the behavior. The microstruacture of sea ice is very similar to this model and, given a brine volume fraction in sea ice, optimal geometries can be constructed to give an upper bound to the problem. A second approach in addressing this problem is the use of network models. I have begun to examine the Random Shrinking Pipe Model for this approach. The model was created to characterize the physics of porous rocks, fluid flow in particular. The model microstructure is similar to that of sea ice, and the process by which the model shrinks bonds as opposed to removing them is characteristic of sea ice microstructure as well as temperature changes. These properties give siginificant promise to this approach. My summer months of 2002 with REU were complemented by a book entitled Random Walks and Electrical Networks by Doyle and Snell. Sections of the book were read and presented at weekly meetings by each REU student under Ken Golden. Theories of transport in composite media were then discussed and related to the research undertaken by each student. |
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VIGRE Steering Committee Department of Mathematics University of Utah 155 South 1400 East; Room 233 Salt Lake City, UT 84112 email: viscom@math.utah.edu |
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