text: We use z as an axial coordinate and r as the radial
  coordinate, and assume axisymmetry. The pipe has radius a, and
  the fluid velocity is:
  The concentration of the diffusing species is denoted c and its
  diffusivity is D. The concentration is assumed to be governed by
  the linear advection–diffusion equation:
  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:
  Under some assumptions (see below), it is possible to derive an equation just involving the average quantities:
  Observe how the effective diffusivity multiplying the derivative on the right hand side is greater than the original value of diffusion coefficient, D. The effective diffusivity is often written as:
  where  is the Péclet number, based on the channel radius . The interesting result is that for large values of the Péclet number, the effective diffusivity is inversely proportional to the molecular diffusivity. The effect of Taylor dispersion is therefore more pronounced at higher Péclet numbers.
  In a frame moving with the mean velocity, i.e., by introducing , the dispersion process becomes a purely diffusion process,
  with diffusivity given by the effective diffusivity.
  The assumption is that  for given , which is the case if the length scale in the  direction is long enough to smooth the gradient in the  direction. This can be translated into the requirement that the length scale  in the  direction satisfies:
  Dispersion is also a function of channel geometry. An interesting phenomenon 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. Here the very small side walls of the rectangular channel have an enormous influence on the dispersion.
  While the exact formula will not hold in more general circumstances, the mechanism still applies, and the effect is stronger at higher Péclet numbers. Taylor dispersion is of particular relevance for flows in porous media modelled by Darcy's law.