Porous medium

In materials science, a porous medium or a porous material is a material containing pores (voids).^[1] The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The skeletal material is usually a solid, but structures like foams are often also usefully analyzed using concept of porous media.

A porous medium is most often characterised by its

Often both the solid matrix and the pore network (also known as the pore space) are continuous, so as to form two interpenetrating continua such as in a sponge. However, there is also a concept of closed porosity and effective porosity, i.e. the pore space accessible to flow.

Many natural substances such as

At the microscopic and macroscopic levels, porous media can be classified. At the microscopic scale, the structure is represented statistically by the distribution of pore sizes, the degree of pore interconnection and orientation, the proportion of dead pores, etc.[4] The macroscopic technique makes use of

Fluid flow through porous media is a subject of common interest and has emerged a separate field of study. The study of more general behaviour of porous media involving deformation of the solid frame is called poromechanics.

The theory of porous flows has applications in inkjet printing^[7] and nuclear waste disposal^[8] technologies, among others.

Numerous factors influence fluid flow in porous media, and its fundamental function is to expend energy and create fluid via the wellbore. In flow mechanics via porous medium, the connection between energy and flow rate becomes the most significant issue. The most fundamental law that characterizes this connection is Darcy's law,^[9] particularly applicable to fine-porous media. In contrast, Forchheimer's law finds utility in the context of coarse-porous media.^[10]

Pore structure models

A representation of the void phase that exists inside porous materials using a set or network of pores. It serves as a structural foundation for the prediction of transport parameters and is employed in the context of pore structure characterisation.^[11]

There are many idealized models of pore structures. They can be broadly divided into three categories:

• networks of capillaries
• arrays of solid particles (e.g., random close pack of spheres)
• trimodal

Porous materials often have a

Laws for porous materials

One of the Laws for porous materials is the generalized Murray's law. The generalized Murray's law is based on optimizing mass transfer by minimizing transport resistance in pores with a given volume, and can be applicable for optimizing mass transfer involving mass variations and chemical reactions involving flow processes, molecule or ion diffusion.^[17]

For connecting a parent pipe with radius of r₀ to many children pipes with radius of r_i , the formula of generalized Murray's law is: ${\displaystyle r_{o}^{a}={1 \over 1-X}\sum _{i=1}^{N}r_{i}^{a}}$, where the X is the ratio of mass variation during mass transfer in the parent pore, the exponent α is dependent on the type of the transfer. For laminar flow α =3; for turbulent flow α =7/3; for molecule or ionic diffusion α =2; etc.

See also

• Cenocell
• Nanoporous materials
• NMR in porous media
• Percolation theory
• Percolation threshold
• Reticulated foam
• Filtration
• Poromechanics
• Reactive transport
• Permeability

References