(1956) On the dispersion of a solute in a fluid flowing through a tube, Proc. Taylor dispersion is of particular relevance for flows in porous media modelled by Darcy's law. While the exact formula will not hold in more general circumstances, the mechanism still applies, and the effect is stronger at higher Péclet numbers.
Here the very small side walls of the rectangular channel have an enormous influence on the dispersion. An interesting phenomena for example is that the dispersion of a flow between two infinite flat plates and a rectangular channel, which is infinitely thin, differs approximately 8.75 times. The effect of Taylor dispersion is therefore more pronounced at higher Péclet numbers.ĭispersion is also a function of channel geometry. Where is the Péclet number, based on the channel diameter d = 2 a. The effective diffusivity is often written as Observe how the effective diffusivity multiplying the derivative on the right hand side is greater than the original value of diffusion coefficient, D. Using the additional assumptions that and that the length scale of axial variation is much greater than a, it is possible to derive an equation just involving the average quantities: The concentration and velocity are written as the sum of a cross-sectional average (indicated by an overbar) and a deviation (indicated by a prime), thus: The concentration is assumed to be governed by The concentration of the diffusing species is denoted c and itsĭiffusivity is D. We use z as an axial coordinate and r as the radialĬoordinate, and assume axisymmetry. Poiseuille flow through a uniform circular pipe with no-flux The canonical example is that of a simple diffusing species in uniform Recognize and detect the effects of electrostatic charges on your balance
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