Dispersion (hydrology)

In hydrology, dispersion is a process that, similar to diffusion , balances concentration gradients in the water.

In the pore space of a body of groundwater there is a very heterogeneous distribution of the flow velocities. Near the edge of a pore these are z. B. due to the viscosity of the water and the friction on the matrix lower than in the middle of the pore. Likewise, different flow velocities prevail in adjacent pores of different geometry.

Water particles that are directly neighboring at the beginning move apart due to the different speeds at which they are transported. This process is intensified by the tortuosity of the pore space, which causes the particles to take different paths through the pore space.

As a result of these processes, analogous to diffusion , but to a greater extent by orders of magnitude, there is an equalization of concentration gradients. Formerly sharp gradients are flattened. Tracer breakthrough curves show gentle increases in concentrations and no steep jumps, such as those found in e.g. B. would be expected in purely advective processes.

Most of this flattening occurs in the direction of the water flow, but a smaller part is also perpendicular to it. At the same time, however, there is also a further flattening due to diffusion . Since the two processes cannot be separated, the sum of the two is usually referred to as hydrodynamic dispersion .

The mathematical description of this process is analogous to diffusion in one dimension as follows:

${\displaystyle J=-D_{Disp}{\frac {dC}{dx}}}$

in which

${\displaystyle D_{Disp}}$is the dispersion coefficient . ${\displaystyle [cm^{2}/s]}$

J is the particle flux density .

In contrast to the diffusion coefficient, the dispersion coefficient is a function of the medium in which the transport takes place. It also has different values ​​in the various spatial directions.

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• J. Bear, A. Verruijt: Modeling groundwater flow and pollution. D. Reidel Publishing Company, Dordrecht 1998, ISBN 1-55608-015-8 .