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$10 R^2/D$
(
$R$
is the radius of the pipe and 
$D$
is the molecular diffusivity) is suggested to characterize the transition to transverse uniformity, in contrast to the time scale of 
$0.1 R^2/D$
estimated by Taylor for the initial stage of dispersion, and that of 
$1.0 R^2/D$
by Chatwin for longitudinal normality.
