What are the best methods to measure effective diffusivity in porous media?

1 Steady-state method

One of the simplest and most widely used methods to measure effective diffusivity is the steady-state method. It involves applying a constant concentration gradient across a sample of porous medium, and measuring the steady-state flux of the solute through the sample. The effective diffusivity can then be calculated from Fick's law, which relates the flux to the concentration gradient and the cross-sectional area of the sample. The steady-state method is suitable for homogeneous and isotropic media, and for solutes that do not react or adsorb in the medium.

2 Transient method

Another common method to measure effective diffusivity is the transient method. It involves applying a step change in the concentration of the solute at one end of a sample of porous medium, and monitoring the concentration change at the other end over time. The effective diffusivity can then be determined from the solution of the diffusion equation, which describes how the concentration profile evolves in the sample. The transient method is more versatile than the steady-state method, as it can handle heterogeneous and anisotropic media, and solutes that react or adsorb in the medium.

3 Sorption method

A more advanced method to measure effective diffusivity is the sorption method. It involves exposing a sample of porous medium to a gas or vapor that can sorb in the medium, and measuring the mass uptake or release of the sorbate over time. The effective diffusivity can then be extracted from the sorption kinetics, which depend on the diffusion and sorption mechanisms in the medium. The sorption method is especially useful for measuring effective diffusivity in microporous and nanoporous media, where the sorption isotherm is nonlinear and the diffusivity is concentration-dependent.

4 NMR method

A novel method to measure effective diffusivity is the nuclear magnetic resonance (NMR) method. It involves applying a magnetic field gradient to a sample of porous medium that contains a solute with a nuclear spin, and measuring the attenuation of the NMR signal over time. The effective diffusivity can then be inferred from the diffusion coefficient, which reflects the mobility of the solute molecules in the medium. The NMR method is non-invasive and non-destructive, and can provide spatially resolved information on the effective diffusivity in complex and heterogeneous media.

5 Numerical method

A complementary method to measure effective diffusivity is the numerical method. It involves simulating the diffusion process in a porous medium using a computational model, and adjusting the effective diffusivity until the simulated results match the experimental data. The numerical method can account for the effects of the pore structure, the tortuosity, the porosity, and the boundary conditions on the effective diffusivity. The numerical method can also be used to validate and refine the analytical solutions and empirical correlations used in the other methods.

6 Here’s what else to consider

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