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    Home : Math Matters - A Brief Look at How Mathematics has Influenced Modern Life : High Performance Materials
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High Performance Materials

A major category of high performance materials is that of synthetic polymers, commonly known as plastics. A new invention of the 20th century, they are now found everywhere in a wide variety of forms.

One application of high performance plastics is the artificial lung. The main component of the artificial lung is a microporous membrane that allows the diffusion of oxygen into the blood, while carbon dioxide diffuses out of the blood into the gas stream and is thereby removed.

Adolf Eugen Fick (German, 1829-1901) introduced Fick’s Laws of Diffusion in 1855, which govern the diffusion of a gas across a fluid membrane. In 1887 he constructed and fitted what was to be considered the first successful model of a contact lens.

The mechanics of this process are defined by Fick’s Laws of Diffusion:

Fick’s First Law of Diffusion:
Steady-state diffusion
Fick’s Second Law of Diffusion:
Non-steady state diffusion

where J is the diffusion flux, D is the diffusion coefficient or diffusivity,  is the concentration, and x is the position.