Randomly distributed fast diffusion phase

Another two DFE simulations are also carried out with different distributions of the fast diffusion phase in order to discover the upper bound and lower bound of the relation between the effective coefficient and the volume fraction. Figure 8.11 describes the two cross-sections of the two cases in the first case, the heterogeneous system is composed of two phases in parallel, while in the second case the system is composed of a centrally located fast diffusion phase and a surrounding slow diffusion phase. Figure 8.12 illustrates three relations between the normalised effective diffusion coefficients obtained from the randomly distributed, the parallel distributed and the centtal distributed fast diffusion phase. It can be seen clearly in Figure 8.12 that the Dj, - Vf relation calculated from the first case yields the upper bound while that from the second case yields the lower bound. 

Firstly, a series of random porous structures of different porosities are represented by generating a number of cubic finite elements in a representative volume. Figure 8.7 illustrates a cubic representative volume containing nxnxn sub-cubes, n is the number of elements in each dimension. Each of the sub-cubic volumes has been assigned a material property of either a fast diffusion phase or a slow diffusion phase with different diffusion coefficients. Two phases can be either uniformly or randomly distributed in a representative unit. This is achieved by assigning different material properties uniformly or randomly on selected sub-cubes with a desired volume fraction. In this section, three geometry cases will be introduced (1) the fast diffusion phase is randomly distributed ... 

A series of randomly distributed two-phase composites with different volume fractions from V = 0.1 to Fy = 0.9 are shown in Figure 8.8. Black blocks indicate a fast diffusion phase with p =, while white blocks represent a slow diffusion phase with p = 0. 

Reaction (2) represents ionisation and electronic excitation of water molecules this occurs on the timescale of an electronictransition. The positive radical ion H2O is believed to undergo the ion molecule reaction (3) in 10" s. The electronically excited states H2O are known to dissociate in the vapour phase in reaction (4),and theelectron released in reaction(l) is known to be solvated by 10 s. At this time, for low LET radiation such as °Co y-rays and fast electrons from an accelerator, the products of reactions (3) - (5) are clustered together in small widely separated spurs, which on average contain 2 to 3 ion pairs. Next, these products begin to diffuse randomly, with the result that a fraction of them encounter one another and react to form molecular and secondary radical products, while the remainder escape into the bulk liquid and effectively become homogeneously distributed with respect to... 

---