Abstract
Laminar dispersion coefficients both in an elliptical pipe and a rectangular pipe have been studied theoretically. Change in laminar dispersion coefficient with respect to cross-sectional shape is discussed for a wide range of aspect ratio Ar.
Non-dimensional dispersion coefficient both in an elliptical pipe and a rectangular pipe attains the minimal value at Ar=1 and is logarithmically symmetrical about it. The behavior of non-dimensional dispersion coefficient for Ar≠1, however, is remarkably different between an elliptical pipe and a rectangular pipe : the former monotonously increasing with Ar→∞ and Ar→0, whereas the latter approaching an asymptotic value as Ar→∞ and Ar→0. The result suggests that material transport in an elliptical pipe flow with very large (or small) aspect ratio can not be described by the one-dimensional dispersion equation based on G. I. Taylor's hypothesis. At Ar=1, non-dimensional dispersion coefficient in a square pipe is greater than that in a circular pipe. Comparison of dispersion coefficient with different cross-sectional shapes reveals that geometrical shape of a pipe decidedly affects the change in laminar dispersion coefficient with the aspect ratio.
