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# What are Scaling Laws?

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• Written By: Michael Anissimov
• Edited By: Bronwyn Harris
• Last Modified Date: 16 October 2019
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2003-2019
Conjecture Corporation
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Scaling laws are a concept in science and engineering. It refers to variables which change drastically depending on the scale (size) being considered. For example, if you tried to build a 50-ton mining vehicle using the same engineering assumptions as a 2-ton car, you would probably end up with a vehicle that doesn't even run. The term "scaling laws" often appears when considering the design of a construct that is unusually large or small, so that careful thought is necessary to extend principles of typical-sized constructs to unusually-sized constructs.

Some scaling laws are simple. For instance, "for a three-dimensional construct, volume increases with the cube of linear dimensions." This simply means that for every 10 times increase in linear dimensions, the construct's volume increases by a factor of 1000. This is significant for designing machines or structures: if you wanted to double the capacity of a water tower, you'd only increase its linear dimensions by a few dozen percent, rather than doubling them. Simple but true.

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There are more complex variations of scaling laws. Some of the most interesting manifestations of scaling laws are being found in the areas of microtechnology and nanotechnology, where engineers must both cope with and exploit unusual properties resulting from small scales. In microfluidics, some of these unusual properties include laminar flow, surface tension, electrowetting, fast thermal relaxation, electrical surface charges, and diffusion. For instance, in fluid chambers with sizes smaller than about half a millimeter, the flow is laminar, meaning that two converging channels cannot mix through turbulence, as on the macro-scale, and must instead mix through diffusion. There are many other examples of scaling laws here.

When certain properties are retained regardless of the scale, it is called scale invariant. Examples include anything that occurs on all size scales, including the phenomenon of avalanches, wear and tear in electrical insulators, percolation of fluids through disordered media, and the diffusion of molecules in solution. As we learn more about physics and mechanics, we discover interesting new scale-invariant phenomena. In general, most physical properties vary with scale.

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