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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Monday, November 8, 2004 - 04:00

Location:

Gilkey 113

Guest Speaker:

Institution:

University of Colorado at Denver

Abstract:

Here we examine typical experiments performed on soils (swelling and non-swelling porous materials) which can be performed on any liquid-solid porous material and relate them to thermodynamic quantities. Compressibility experiments typically take a porous material sample and control two of the following four parameters: liquid pressure, pressure of the sample, volume of the sample, and volume of liquid leaving the porous sample. The other two variables are measured at equilibrium. In this talk the results of a thermodynamic analysis (with no constitutive assumptions) are presented assuming that the macrscopic properties of the liquid phase are a function of density and volume fraction. The results relate thermodynamic quantities (such as the compressibility of each phase and difference in the solid and liquid phase pressures) to what is practically measurable via compressibility experiments. Because minimal constitutive assumptions are assumed (the behavior of the liquid is a function of the volume fraction as well as other variables) the results apply to many other materials such as swelling soils (such as clay), bio-tissues such as cartilage and cells, and polymers.