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Fluid-flow computation

To determine the permeability of our pore structures we numerically solved the Stokes equation [22]

using a finite difference scheme in conjunction with the artifical compressibility method [23]. The pore space was discretized as a MAC mesh, where MAC stands for "marker and cell" [23]. A node was centered in each pixel, with pressure defined at the nodes, and velocities defined at the pixel boundaries as shown in Fig. 3. No-slip boundary conditions [22] (zero fluid velocity) were imposed at all fluid-solid interfaces. In order to improve the accuracy of our solution, non-centered difference equations were used near the pore surface to force the fluid velocities to be zero exactly at pixel boundaries. This results in velocity profiles across channels being accurate to at least second order. A pressure difference was maintained across the microstructure, in the same way that the voltage gradient was maintained in the electrical algorithm. After the fluid velocities were relaxed to their equilibrium values the fluid permeability was determined via Eq. (1). The 35% porosity models took about 20 minutes of CPU time for each realization, while the 80% porosity models took 2-4 hours [24].

Figure 3: A piece of a pore space-solid interface. The dark lines are pixel boundaries, and the dashed lines are the superimposed MAC mesh for the fluid-flow computation. The arrows show the location where the fluid velocities are determined, and the black circles show the nodes where the pressures are determined.


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