  We investigate the distributions of residence time for in-line chaotic
mixers; in particular, we consider the Kenics, the F-mixer and the Multi-level
laminating mixer, and also a synthetic model that mimics their behavior and
allows exact mathematical calculations. We show that whatever the number of
elements of mixer involved, the distribution possesses a $t^{-3}$ tail, so that
its shape is always far from Gaussian. This $t^{-3}$ tail also invalidates the
use of second-order moment and variance. As a measure for the width of the
distribution, we consider the mean absolute deviation and show that, unlike the
standard deviation, it converges in the limit of large sample size. Finally, we
analyze the performances of the different in-line mixers from the
residence-time point of view when varying the number of elements and the shape
of the cross-section.
