ABSTRACT
For many engineering materials, it has been known since long time ago that there is a rather weak correlation between the properties of the ingredients and those of the resulting products, as revealed by the pioneer works of Grifœth1 on material strength, and independently of Peirce2 on the weakest link theorem. That is, constituents with improved quality cannot assure a better product, and the internal structure-the way the constituents are arranged in the material system-is just as, if not more, important. On the other hand, the inclusion of different components into a material can be beneœcial, acting as reinforcement or supplements to improve the performance of the materialalloys and œber-reinforced composite are just such examples. Nevertheless, analysis and prediction of behaviors of composites are in general much more intricate. Once mixed together, the components of different types will more or less interact with each other, and the properties at the interfacial
9.1 Introduction .......................................................................................................................... 357 9.2 Theoretical Models and Challenges ..................................................................................... 359 9.3 Numerical Methods .............................................................................................................. 361
9.3.1 Structure Characterization and Reproduction Algorithms ....................................... 361 9.3.1.1 Granular Structure ..................................................................................... 363 9.3.1.2 Fibrous Structure .......................................................................................366 9.3.1.3 Netlike Structure ........................................................................................ 367
9.3.2 Solutions of the Governing Laws.............................................................................. 367 9.3.2.1 Governing Equations ................................................................................. 368 9.3.2.2 Lattice Boltzmann Method ........................................................................ 369 9.3.2.3 Benchmarks ............................................................................................... 372
9.4 Modeling Results and Discussion ......................................................................................... 373 9.4.1 Effective Transport Properties Compared with Experiments .................................. 373
9.4.1.1 Thermal Conductivity ................................................................................ 374 9.4.1.2 Electric Conductivity ................................................................................. 377 9.4.1.3 Dielectric Permittivity ............................................................................... 378 9.4.1.4 Elastic Moduli ............................................................................................ 379
9.4.2 Structure Effects ....................................................................................................... 381 9.4.2.1 Size Effects ................................................................................................ 381 9.4.2.2 Anisotropy Effects ..................................................................................... 382 9.4.2.3 Morphology Effects ................................................................................... 383
9.5 Conclusions ...........................................................................................................................384 Acknowledgments .......................................................................................................................... 385 References ...................................................................................................................................... 385
region will exhibit a transition from one component to the other.3-6 Such effects usually turn even more complicated when the components are at different phase states, such as in a semifrozen soil system.7,8 The porous multiphase materials are increasingly used in various œelds, but analysis and investigation efforts are severely lagging behind.9,10
The challenges in studying porous media come mainly from the inherent variety and randomness of their internal microstructures and the coupling between the components of different phases.11 Figure 9.1 shows three typical such material structures having extensive and important applications. Figure 9.1a shows a typical cross section of sand soil with granular structure.12-14 For soil, the black stands for the solid phase and the white is the void. The similar structures can be found in wood15,16 or food.17-20 For some cases of food, like the bread, since there are lots of granular pores in the “our, the white becomes the solid frame and the black is the pore/voids. The next type is a œbrous structure as shown in Figure 9.1b of another solid-void mixture with the solid in a slender and oriented form, usually existing in polymeric and biomaterials.21 For a long time, the porous transport layer (PTL) in PEM fuel cell has been thought to possess a granular porous structure; however, very recent investigations have demonstrated that the PTL actually possesses a œbrous structure that exhibits quite different transport behaviors from those with granular structures.22,23 Another example of œbrous materials is the advanced œber-reinforced composites where œbers are utilized to enhance the mechanical and thermal properties of the composites up to surprisingly high levels.24-28 Figure 9.1c shows a cross section of an open-cell foam material.29-32 It has a netlike porous structure that leads, for metal-foam materials, to the interesting combination of high porosity and low density yet very high thermal and electric conductivities. Such foam materials, typically two-phase systems of solid and void, have played critical roles in advanced aircraft designs, for instance, to improve the catalytic surfaces and enhance the heat exchanger systems.
