Scaling laws in the macro-, micro- and nanoworlds

The microworld and the nanoworld are now of interest to the public, scientists, engineers and industrialists. Effects negligible at the macroscopic level become important at the micrometre scale, and vice versa . Moreover, at the nanoscale, quantum effects may become dominant. Scaling laws are useful for an understanding of the origin of such differences and/or to generalize results obtained at various scales. It is the aim of this paper to examine scaling laws relevant to mechanics, fluids, electromagnetism, thermodynamics, optics and quantum mechanics. Examples related to biology, micromachines and nanotechnologies are treated to show the usefulness of the scaling laws.