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## Diffusion equationThe ## Additional recommended knowledgeThe equation is usually written as: where is the density of the diffusing material at location and time also called the heat equation. More generally, when ## DerivationThe diffusion equation can be derived in a straightforward way from the continuity equation, which states that a change in density in any part of the system is due to inflow and outflow of material into and out of that part of the system. Effectively, no material is created or destroyed: - ,
where is the flux of the diffusing material. The diffusion equation can be obtained easily from this when combined with the phenomenological Fick's first law, which assumes that the flux of the diffusing material in any part of the system is proportional to the local density gradient: - .
## See also |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Diffusion_equation". A list of authors is available in Wikipedia. |