Scaling laws refer to variables that change drastically depending on the scale considered. Simple laws state that volume increases with the cube of linear dimensions, while complex laws are found in micro and nanotechnology. Scale-invariant phenomena occur on all magnitude scales. Most physical properties vary with scale.
Scaling laws are a scientific and engineering concept. It refers to variables that change drastically depending on the scale (dimension) considered. For example, if you try to build a 50-ton mining vehicle using the same engineering assumptions as a 2-ton car, you’ll likely end up with a vehicle that doesn’t even work. The term “laws of scaling” often appears when considering the design of a construct that is unusually large or small, so careful thought is required to extend the principles of typically sized constructs to unusually sized constructs.
Some scaling laws are simple. For example, “for a three-dimensional construct, the volume increases with the cube of linear dimensions.” This simply means that for every 10x increase in linear size, the volume of the construct increases by a factor of 1000. This is significant for machine or structure design: if you wanted to double the capacity of a water tower, you would only increase the its linear dimensions by a few dozen percent, rather than doubling them. Simple but true.
There are more complex variations of the scaling laws. Some of the most interesting manifestations of the scaling laws are found in the areas of microtechnology and nanotechnology, where engineers must address and exploit unusual properties resulting from small scales. In microfluidics, some of these unusual properties include laminar flow, surface tension, electrohumidification, rapid thermal relaxation, surface electric charges, and diffusion. For example, in fluid chambers smaller than about half a millimeter, the flow is laminar, meaning that two converging channels cannot mix by turbulence, as on the macroscale, and must instead mix by diffusion. There are many more examples of scaling laws here.
When certain properties hold regardless of scale, it is called scale invariant. Examples include anything that occurs on all magnitude scales, including avalanches, the wear of electrical insulators, the percolation of fluids through disordered media, and the diffusion of molecules in solution. As we learn more about physics and mechanics, we discover new interesting scale-invariant phenomena. In general, most physical properties vary with scale.
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