Figure 1 illustrates the microstructural features captured by the x-ray microtomography for the two types of FRMs. For the gypsum-based material on the left, one can easily observe plate-like vermiculite particles surrounded by a porous gypsum binder. For the fiber/cement-based FRM on the right, substantially larger pores are observed. The bright "particles" observed in this image are most likely agglomerations of the cement particles that are bonding together fibrous subregions of the microstructure. As observed more clearly in the three-dimensional representations of microstructure provided in Figures 2 and 3, while the pores in the gypsum-based FRM definitely appear to be comprised of closed roughly spherical shapes, those in the fiber/cement-based FRM may be interconnected across large regions of the microstructure. These differences in pore shape/connectivity would also be expected to influence the thermal conductivities of these two materials, particularly at elevated temperatures.
Figure 1. Two-dimensional x-ray microtomography images from a gypsum-based FRM (left: 28 mm by 28 mm) and a fiber/cement-based FRM (right: 30 mm by 30 mm), illustrating some of the differences in microstructural features.
Figure 2. Renderings of the three-dimensional x-ray microtomography original data sets (100 by 200 by 200 voxels with a 100 by 100 by 100 voxel volume removed for increased visual clarity) for a gypsum-based FRM (left) and a fiber/cement-based FRM (right). Pores are dark and "solid" regions are bright.
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Figure 3. False color renderings of the individual pores isolated using the watershed segmentation algorithm in a gypsum-based FRM (left: 120 by 120 by 120 voxels) and a fiber/cement-based FRM (right: 200 by 200 by 200 voxels).
The thermal conductivity predictions and measurements for the gypsum-based FRM are provided in Figure 4. While good agreement between the experimental results and the computational predictions is observed for temperatures below 300 ºC, above this temperature the gypsum-based predictions underestimate the measured values while the anhydrite-based predictions generally overestimate the measured values, although providing a reasonable fit for temperatures above 600 ºC. This could indicate that (during the experimental measurement of its thermal conductivity) in the intermediate temperature range of 300 ºC to 600 ºC, the FRM possibly contained a mixture of gypsum (hemihydrate) and anhydrite. These results highlight one of the inherent difficulties in equitably measuring the thermal conductivity of FRMs at elevated temperatures, the fact that their mass, their chemical composition, and their microstructure may all be changing during the course of the measurement.
Figure 4. Measured and predicted thermal conductivities for a gypsum-based FRM as a function of temperature, for the case where individual pores were identified using a watershed segmentation algorithm (Russ and Russ, 1988).
The importance of pore size in controlling high temperature thermal conductivity is indicated by the results shown for the first of the fiber/cement-based FRMs in Figure 5. Here, because of the non-spherical shape of many of the pores, the watershed segmentation algorithm subdivided the largest porous "regions" into two or more individual pores. In this case, better agreement with the experimental data was observed for the three-dimensional microstructure where the pores were identified by the simple application of a burning algorithm without any application of erosions/dilations to the binary image subvolume. As illustrated in Figure 6, similar results were observed for the second fiber/cement-based FRM, where larger thermal conductivities are observed at the highest measured temperatures due to both an increased porosity and a generally larger pore size.
Figure 5. Measured and predicted thermal conductivities for the first fiber/cement-based FRM as a function of temperature.
Figure 6. Measured and predicted thermal conductivities for a second fiber/cement-based FRM as a function of temperature.
A large degree of anisotropy in the three-dimensional subvolumes was observed for these FRMs, as indicated by the large difference between the computed thermal conductivities for the (x and y) directions and the z direction. In Figure 3, several large flat plate-like porous regions oriented in the xy (spraying) plane are clearly observed to comprise a major fraction of the subvolume. It should be noted that the three-dimensional box in Figure 3 has been rotated to better view these pores and that the z-direction moves from left to right in the labeled subvolume. Furthermore, for these materials, it must also be noted that some of the underestimation of the experimental results is likely due to energy transfer through the FRMs by radiation transmission and scattering (Flynn and Gorthala, 1997), due to their overall fibrous nature and likely percolated three-dimensional pore networks. The theory of Loeb (Loeb, 1954) does not account for this mode of radiation transport through the porous material, as it assumes a porous solid comprised of isolated (not interconnected) pores.