Exact moment analysis of transient dispersion properties in periodic media

This paper develops a homogenization approach, based on the introduction of exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of point-sized and finite-sized particles in periodic media. The proposed method represents a robust and computationally efficient continuous approach, alternative to stochastic dynamic simulations. As a case study, the exact moment method is applied to analyze transient dispersion properties of point-sized and finite-sized particles in sinusoidal tubes under the action of a pressure-driven Stokes flow. The sinusoidal structure of the tube wall induces a significant variation of the axial velocity component along the axial coordinate. This strongly influences the transient behavior of the effective axial velocity V-z(t) and of the dispersivity D-z(t), both exhibiting wide and persistent temporal oscillations, even for a steady (not-pulsating) Stokes flow. For a pointwise injection of solute particles on the symmetry axis, many interesting features appear: negative values of the dispersion coefficient D-z (t), values of D-z(t) larger than the asymptotic value D-z(infinity), and anomalous temporal scaling of the axial variance of the particle distribution. All these peculiar features found a physical and theoretical explanation by adopting simple transport models accounting for the axial and radial variation of the axial velocity field and its interaction with molecular diffusion. Published under license by AIP Publishing.