Can homogeneous slip boundary condition affect effective dispersion in single fractures with Poiseuille flow?

• Published in: Journal of hydrology (Amsterdam) 2020-02, Vol.581, p.124385, Article 124385
• Main Authors: Zheng, Lizhi, Wang, Lichun, Wang, Tiejun, Singh, Kuldeep, Wang, Zhong-Liang, Chen, Xi
• Format: Article
• Language: English
• Subjects: Cubic Law; Fracture; Longitudinal dispersion coefficient; Poiseuille flow; Slip boundary condition; Taylor dispersion
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2019.124385

•We rigorously derive the longitudinal dispersion coefficient for Poiseuille flow with homogeneous slip boundary condition.•The effects of slip boundary condition on dispersion are assessed and validated through direct numerical simulations.•Homogeneous slip boundary condition plays a trivial role in altering the longitudinal dispersion coefficient. The fate of fluid-borne entities depends on flow and transport processes in geological environments. The classical theories for describing flow (Cubic Law) and transport (Taylor dispersion theory) processes within single fractures are based on the Poiseuille flow model (i.e., flow through the parallel plates) and its modifications with more complex surfaces. Nonetheless, the Poiseuille flow model assumes no-slip boundary condition while some natural environments show the otherwise, e.g., fracture walls are slippery with non-zero flow velocity. To better understand the effects of slippery boundaries on transport within Poiseuille flow, we develop a closed-form expression for the longitudinal dispersion coefficient (DL) based on the corrected flow field that considers homogeneous slip boundary condition. Moreover, the reliable direct numerical simulations were implemented to further validate our proposed theory on DL. Both theory and numerical experiments suggest that homogeneous slip boundary condition unsignificantly alters DL, although slippery boundaries can significantly change the mean velocity of Poiseuille flow. Our theory based on mechanistic, albeit simplified, model might shed light on predicting the fate of fluid-borne entities in complex geological environments.