mean¶

poreana.diffusion.mean(diff_data, dens_data, ax_area=[0.2, 0.8], is_print=True)¶

This function uses the diffusion coefficient slope obtained from function poreana.diffusion.bins() and the density slope of function poreana.density.bins() to calculate a weighted diffusion coefficient inside the pore

\[\langle D_\text{axial}\rangle =\frac{\int\rho(r)D_\text{axial}(r)dA(r)}{\int\rho(r)dA(r)}.\]

In a discrete form, following formula is evaluated

\[\langle D_\text{axial}\rangle=\frac{\sum_{i=1}^n\rho(r_i)D_\text{axial}(r_i)A(r_i)}{\sum_{i=1}^n\rho(r_i)A(r_i)}\]

with the partial area

\[A(r_i)=\pi(r_i^2-r_{i-1}^2)\]

of radial bin \(i\). It is assumed that the discretization of the density is finer than the diffusion. Therefore, the diffusion values for each density bin are interpolated between the nearest available diffusion values.

Parameters:

diff_datadictionary: Diffusion data dictionary from function poreana.diffusion.bins()
dens_datadictionary: Density data dictionary from function poreana.density.bins()
ax_arealist, optional: Bin area percentage to calculate the axial diffusion coefficient
is_printbool, optional: True to print mean diffusion

Returns:

diff_weightfloat: Density weighted mean axial diffusion in 10^-9 m^2s^-1