permeabilitye

Permeabilitye is a coined term used in some discussions of transport phenomena to describe a generalized permeability that accounts for effects beyond classical formulations. It is not a standardized concept in mainstream literature, and its precise definition and units can vary among authors. In general, permeabilitye is envisioned as a parameter that characterizes how easily a medium accommodates the passage of a quantity—such as fluid, electric current, or magnetic flux—when dissipation, nonlinearity, or time dependence are significant.

In practice, permeabilitye is often treated as a complex or state-dependent quantity. It may be expressed as ke*(ω, T, p) or ke*(f, T), combining a base permeability with corrective factors that capture energy losses, dynamic response, or coupling to other fields. Under simplifying assumptions, permeabilitye reduces to the conventional permeability or tensor k for isotropic, steady-state conditions. The concept is used in contexts such as porous media with frequency-dependent flow, electromagnetic metamaterials, and geophysical models where dissipation and time-varying driving forces influence transport.

Measurement and estimation of permeabilitye typically involve fitting experimental data to constitutive relations that include ke*(ω) or ke*(T). Techniques such as impedance spectroscopy, dynamic permeability testing, or numerical inversion are employed to infer its value and dependence on frequency, temperature, or state variables. Because there is no universal definition, researchers emphasize clarity about the adopted form, range of applicability, and how permeabilitye relates to established parameters like k and μ.

See also: permeability, Darcy’s law, complex permeability, porosity, anisotropy.