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The relative importance of advection and diffusion in the distribution or mixing of a chemical species like hydrogen may be derived through non-dimensioning the general advection-diffusion equation of transport. This dominance is a function of flow velocity u, species diffusivity D and time t, and may be expressed in terms of the non-dimensional Péclet number:

$$ Pe = {D \over {u^2 t}} = {D \over {uL}} $$

(1)

where D is the diffusion coefficient, u is the velocity, t is time and L is a characteristic length scale. Diffusion is the dominant mechanism when Whereby diffusion is dominant for Pe>>1 and transport by advection transport dominates for Pe<<1. It is important to note that, whenever large times, t, or characteristictravelled lengthscale, L = ut, are considered, the advection transport would always dominate. The Péclet number expresses the ratio between the characteristic times of advection and diffusion. The length travelled by a particle is proportional to t for advection and to t^1/2 for diffusion.

Characteristic length and time scales for advection and diffusion transport may be expressed by

$$ L_{advection} = ut $$	(2)
$$ t_{advection} = {L \over u} $$	(3)
$$ L_{diffusion} = \sqrt {Dt} $$	(4)
$$ t_{diffusion} = {{L^2 } \over D} $$	(5)

These expressions are useful as rules of thumb.

References

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