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Permeability is a property that describes the ease with which a substance can pass through a material or medium. In science and engineering, permeability is contextualized for different transport processes and typically depends on the medium, the transported species, and environmental conditions.

Magnetic permeability (mu) measures how a material responds to a magnetic field. It is often expressed as relative permeability (mu_r = mu/mu0) and indicates whether a material is diamagnetic, paramagnetic, or ferromagnetic. Magnetic permeability can vary with frequency and field strength, influencing the behavior of inductors, transformers, and other magnetic devices.

Hydraulic permeability characterizes fluid flow through porous media and is described by Darcy’s law. The intrinsic permeability of the medium, often denoted k, reflects the ease with which a fluid can move through its pore structure and is influenced by porosity, pore size distribution, tortuosity, and fluid viscosity. Units commonly used include darcies or square meters.

Gas and vapor permeability concerns the transmission of gases through solids, particularly polymers and films. The permeability P equals the product of diffusivity D and solubility S (P = D·S). This measure is critical for packaging, barrier coatings, and membrane design, with P depending on temperature, pressure, thickness, and material composition.

Biological membranes exhibit permeability to water and solutes, governed by concentration gradients, osmotic pressure, and the presence of channels or transport proteins. Permeability is measured in various ways, including flow rates, time-lag methods for gases, and diffusion assays for membranes.

Overall, permeability bridges material structure and transport behavior, informing applications across soils, energy, materials science, and biotechnology.