An empirical correlation of the longitudinal and transverse dispersion coefficients for flow through random particle packs

We propose an empirical correlation describing the interplay of the asymptotic longitudinal and transverse solute dispersion behaviors for flow through random particle packs. The correlation is consistent with currently available theoretical results when the Peclet number approaches zero and infinity. The correlation is validated in terms of asymptotic dispersion coefficients reported in the literature for both Stokes and inertial flows through random particle packs and dispersion coefficients calculated numerically for flow through numerically constructed fixed beds. The correlation agrees well with experimental data and numerical results for Stokes flow (the Reynolds number is less than 1) through homogeneous random particle packs and spatially periodic fixed beds when the Peclet number is less than 1000. Reasonable agreements are also observed when compared with scattered experimental data including possible macroscopic flow heterogeneities for both Stokes and inertial flows through random particle packs. In spite of its empirical shortcomings, the correlation provides a universal understanding of the dispersion behaviors in open channels and random particle packs and a new understanding of the coupling behavior of diffusion and convection in particle packs. In addition, current numerical simulation shows that the longitudinal dispersion coefficient decreases while the transverse dispersion coefficient increases with increasing Reynolds number when the Peclet number is fixed. Current empirical correlation explains this behavior with fair accuracy.