Grain porosity models

grains2 provides support for grain porosity models. Porosity may be a function of grain radius. A commonly used model is the fractal porosity, described by the fractal dimension \(D\), and the basic unit radius, \(a_0\):

\[P = 1.0 - (a / a_0)^{D - 3}\]

Note that \(D=3\) is solid for all \(a\).

Calculate the porosity of a 1.0 μm grain, given \(D=2.8\) and \(a_0=0.1\) μm:

>>> from grains2 import FractalPorosity
>>>
>>> a0 = 0.1
>>> D = 2.8
>>>
>>> porosity = FractalPorosity(a0, D)
>>> porosity.P(1.0)
0.369042655519807

Plot the same porosity model for grains of size 0.1 μm to 1 mm:

(Source code, png, hires.png, pdf)