Editing Porous medium (section)

== Laws ==
One of the Laws for porous materials is [[Murray's law|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.<ref>{{Cite journal|last1=Zheng|first1=Xianfeng|last2=Shen|first2=Guofang|last3=Wang|first3=Chao|last4=Li|first4=Yu|last5=Dunphy|first5=Darren|last6=Hasan|first6=Tawfique|author-link6=Tawfique Hasan|last7=Brinker|first7=C. Jeffrey|last8=Su|first8=Bao-Lian|date=2017-04-06|title=Bio-inspired Murray materials for mass transfer and activity|journal=Nature Communications|language=en|volume=8|page=14921|bibcode=2017NatCo...814921Z|doi=10.1038/ncomms14921|issn=2041-1723|pmc=5384213|pmid=28382972}}</ref>

For connecting a parent pipe with radius of '''''r<sub>0</sub>''''' to many children pipes with radius of '''''r<sub>i</sub>''''' , the formula of generalized Murray's law is: <math>r_o^a={1 \over 1-X}\sum_{i=1}^Nr_i^a</math>, 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.