Tortuosity via FDM diffusion solver¶

This example computes the diffusional tortuosity of a synthetic porous medium using the finite difference method (FDM) solver.

In [1]:

import porespy as ps
import matplotlib.pyplot as plt
import poromics

import porespy as ps import matplotlib.pyplot as plt import poromics

Generate a porous medium image¶

In [2]:

im = ps.generators.blobs(shape=[100, 100, 1], porosity=0.6, blobiness=0.5, seed=42)

fig, ax = plt.subplots(figsize=(4, 4))
ax.imshow(im[:, :, 0], cmap="viridis", interpolation="nearest")
ax.set_title(f"Porous medium (porosity = {im.mean():.2f})")
plt.tight_layout()

im = ps.generators.blobs(shape=[100, 100, 1], porosity=0.6, blobiness=0.5, seed=42) fig, ax = plt.subplots(figsize=(4, 4)) ax.imshow(im[:, :, 0], cmap="viridis", interpolation="nearest") ax.set_title(f"Porous medium (porosity = {im.mean():.2f})") plt.tight_layout()

Compute tortuosity¶

In [3]:

result = poromics.tortuosity_fd(im, axis=1, rtol=1e-5)
print(result)
print(f"Tortuosity: {result.tau:.4f}")
print(f"Effective diffusivity (D_eff/D_0): {result.D_eff:.6f}")
print(f"Formation factor: {result.formation_factor:.4f}")

result = poromics.tortuosity_fd(im, axis=1, rtol=1e-5) print(result) print(f"Tortuosity: {result.tau:.4f}") print(f"Effective diffusivity (D_eff/D_0): {result.D_eff:.6f}") print(f"Formation factor: {result.formation_factor:.4f}")

2026-03-09 01:25:36.82 | WARNING  | poromics._metrics:tortuosity_fd:218 - Trimmed 972 non-percolating pore voxels from the image.

TortuosityResult(tau=4.2636, D_eff=0.116124, axis=1)
Tortuosity: 4.2636
Effective diffusivity (D_eff/D_0): 0.116124
Formation factor: 8.6115

Visualize the concentration field¶

The steady-state concentration field shows how species diffuses through the tortuous pore network.

In [4]:

result.plot_concentration(z=0)

result.plot_concentration(z=0)

Out[4]:

(<Figure size 750x400 with 4 Axes>,
 array([<Axes: title={'center': 'Pore structure'}>,
        <Axes: title={'center': 'Concentration field'}>], dtype=object))