A diffusive flux link between two pathways has two "sides".
The geometry of the flux link is defined by three inputs:
•the diffusive length on the Outflux side of the link;
•the diffusive length on the Influx side of the link; and
•the diffusive area of the link.
In effect, the Cells act as "nodes" and a collection of Cells linked by diffusive mass fluxes is mathematically identical to a finite difference approximation of the system.
A single diffusive mass flux link between two pathways mathematically represents a one-dimensional diffusive process. For example, if you wished to simulate diffusion along a one-dimensional conduit, you would do so as follows:
1. Specify how you wished to discretize the system by defining the number of Cells you use to represent the conduit.
2. Create diffusive mass flux links between adjacent Cells. The diffusive area would be the same for all mass flux links, and would be equal to the cross-sectional area of the conduit. The diffusive length for each side of each diffusive mass flux link would be equal to half the effective “length” of each Cell. Hence, if you were simulating a 10 m conduit using 5 Cells, each Cell would have an effective length of 2 m, and the diffusive length on each side of each diffusive mass flux link would be specified as 1m.
Note: The amount of media in each Cell
(i.e., the size of the Cell) should be defined in a manner that is consistent
with the diffusive lengths and areas. For example, in a one-dimensional
system simulated using equal sized Cells (filled only with water), the volume of
water in each Cell would be equivalent to twice the diffusive length multiplied
by the diffusive area.
By linking multiple Cells together via diffusive mass flux links and defining the size (volume) of the Cells and the diffusive lengths and areas appropriately, nearly any geometry can be numerically represented by such a network of cells. For example, to represent the diffusion from the center of a sphere outward, you would do the following:
1. Divide the sphere into a number of “shells”, with the volume between the shells defining each Cell:
2. Create diffusive mass flux links between adjacent Cells. For each link, the diffusive area would be computed as the surface area of the shell separating the two Cells:
Similarly, the diffusive length for each side of each diffusive mass flux link would be computed as the distance from the “midpoint” of the Cell to the shell shared by the two Cells:
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