Euler characteristic during drying of porous media

Phase Saturation Control on Vorticity Enhances Mixing in Porous Media

“…Recent studies have highlighted the role of the topological complexity inherent to porous media in driving local fluid stretching, ultimately controlling transport, mixing, reactions, and biological processes occurring in porous systems (Lester et al, 2013(Lester et al, , 2016. In order to assess this aspect, we first rely on a geometrical characterization of the wetting liquid phase topology, by means of the Euler characteristic χ, a topological invariant widely used in soil and porous systems research (Armstrong et al, 2019;Lester et al, 2016;Schlüter et al, 2016;Shih et al, 2022). In particular, it can be used to characterize the connectivity of the porous system, with strong implications on the divergence or convergence of streamlines, as it is directly linked to the dynamics of the skin friction field, that is, to the occurrence of separation and reattachment points along boundary surfaces (Lester et al, 2016).…”

“…In these cases, topological indicators such as helicity density, reflecting the effect of vorticity on streamlines deformation, and indexes such as the Okubo‐Weiss parameter (Okubo, 1970; Weiss, 1991) or the Q‐criterion (Hunt et al., 1988), which can be used for characterizing both vorticity‐ and shear‐dominated deformation regions, have been applied with success in mixing analyses. On the contrary, similar studies under unsaturated conditions have mainly drawn attention toward changes in the connectivity of the non‐wetting phase during cycles of imbibition and drainage (Schlüter et al., 2016; Shih et al., 2022), and also during stages of constant saturation as a result of coalescence and snap‐off events of trapped ganglia (Armstrong et al., 2016). The impact of saturation on wetting phase topology both in 2D and 3D model systems and its implications for flow and transport at the pore scale remain unanswered.…”

“…New advances in imaging techniques such as magnetic resonance imaging (Lehoux et al., 2016; Markale et al., 2021), high‐resolution laser imaging (Heyman et al., 2020), and X‐ray micro‐tomography (Boon et al., 2017; Hasan et al., 2020) have allowed expanding these observations to 3D systems, involving both artificial and real porous media. Advances in X‐ray micro‐tomography have increasingly enabled the imaging of rock‐ and soil‐like samples and of flow and transport through them, both for real‐time visualization of the physical processes themselves (Armstrong et al., 2016; Chen et al., 2021; Dobson et al., 2016; Hasan et al., 2020; Schlüter et al., 2016) and for supporting the development and validation of respective numerical investigations (Guédon et al., 2019; Kang et al., 2014; Puyguiraud et al., 2021; Shih et al., 2022). These studies have unveiled important features of pore‐scale flow and transport, such as intermittency of local velocities and accelerations, essential to be taken into account for improved model formulations (Kang et al., 2014).…”