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

Zheng, Lizhi, Wang, Lichun, Wang, Tiejun, Singh, Kuldeep, Wang, Zhong-Liang, Chen, Xi
Journal of hydrology 2020 v.581 pp. 124385
dispersibility, hydrology, mathematical models, prediction
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.