Transport Processes Diffusion and Advection

There does not seem to by anything in the Universe which stays for ever where it has been put once. This also applies to the elements synthesized in the stellar interiors. Classical evolution models assume that an element in a radiative zone, e.g., in the solar center, always stays exactly at the same place, i.e., for the next 10 billions years in the case of the Sun. Such an assumption ignores microscopic diffusion and the fact that stars, especially rotating stars, are subject to many instabilities which contribute to the transport of chemical elements and angular momentum. These processes considerably affect the course of evolution and nucleosynthesis.

We must distinguish between diffusion and advection:

Diffusion is a transport process which results from chaotic motions. It occurs in media with a gradient of one or several quantities, such as a chemical element, pressure, temperature, angular momentum, etc. In diffusion processes arising from hydrodynamical instabilities, only the quantities with a gradient are transported. This is the case of gradients of chemical composition and of angular momentum which are smoothed by diffusion.

Convection acts as a diffusion process, which mixes the elements with a very short timescale (dynamical timescale). Other diffusion processes generally have much longer timescales (thermal timescale). Diffusion may also act on a quantity homogeneously distributed in a medium where there is, for example, a T gradient. This is case of the microscopic or atomic diffusion, which is able to separate the nuclear species and create gradients of elements which were initially uniformly distributed.

An advection is a transport which results from the coherent displacement of relatively large volume elements, such as a stream or a current.

In many stellar models, advection is treated as a diffusion process, this is incorrect and leads to erroneous conclusions. The circulation of money in the world offers an interesting example of advective motions. If it would be a diffusion, the money would smoothly flow from the rich people to the poor ones. This does not seem to be the case, the flows of money is generally going the opposite way! This is typically an advection, i.e., a global transport of something. Treated as a diffusion, the transport of money would even have the wrong sign. Diffusion and advection do not obey to the same equations.

A. Maeder, Physics, Formation and Evolution of Rotating Stars, Astronomy and Astrophysics Library, DOI 10.1007/978-3-540-76949-1-10, "

© Springer-Verlag Berlin Heidelberg 2009

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