Splitting Dynamics of Liquid Slugs at a T‐Junction

Abstract

Understanding the mechanisms of liquid movement through fracture intersections is important for prediction of fluid flow and solute transport in unsaturated fractured media. Here we present a quasi‐static model to predict the dynamic splitting behavior of liquid slugs at a T‐junction, as a simplified representation of a fracture intersection and consisting of a main channel and a branch channel. The proposed model is validated against carefully controlled visualization experiments. We find that there exists a critical initial slug length at which the splitting behavior shifts from flow dominated by the main channel to that dominated by the branch. The influence of key parameters, including the inclination angle of the junction, the channel widths, and the dynamic contact angles, on the splitting dynamics is systematically investigated. We show that the splitting ratio depends nonmonotonically on the relative width of the branch channel to the main channel. Furthermore, it is demonstrated that the dynamic contact angles have a profound impact on the splitting ratios and meniscus velocities. It is shown that taking velocity‐dependent contact angle into account is essential to predict the meniscus velocities and the dynamic flow process.

Numerical and Analytical Modeling of Flow Partitioning in Partially Saturated Fracture Networks

“…Furthermore, we assume that flow on the vertical surfaces takes the shape of rivulets. This assumption is often made in soil systems for preferential flows (Bogner & Germann, 2019;Germann & Hensel, 2006;Nimmo, 2010) and has been shown to also hold under laboratory conditions (Noffz et al, 2019), yet, more complex flow-rate-dependent modes (droplet, slugs) may occur (Ghezzehei, 2004;Kordilla et al, 2017) that trigger early partitioning at intersections (T. R. Wood et al, 2005;Xue et al, 2020;Yang et al, 2019) and are different from the sequential approach considered in this work.…”

“…For the former case, a single fracture intersection of a horizontal and a vertical fracture is often "constructed," for example, by breaking glass plates, which results in a quasi-two-dimensional setup (Ji et al, 2006). Modifications to this setup include experiments with a slight offset at the fracture intersection or T-shaped intersections at various degrees of rotation (T. R. Wood et al, 2005;Xue et al, 2020;Yang et al, 2019). Intersections resembling an inverted Y-structure have been studied by Dragila and Weisbrod (2004), M. Liu et al (2007) and Tartakovsky and Meakin (2005a).…”

“…This assumption is often made in studies related to preferential flow in soil systems and the respective macropore structure (Bogner & Germann, 2019;Germann et al, 2007;Nimmo, 2010Nimmo, , 2012Nimmo & Perkins, 2018). However, other flow modes such as flow-rate-dependent droplets (slugs) and rivulets are likely to occur on fracture surfaces (Dippenaar & Van Rooy, 2016;Dragila & Weisbrod, 2003, 2004Ghezzehei & Or, 2005;Jones et al, 2017) and are known to affect partitioning at intersections (Kordilla et al, 2017; T. R. Wood et al, 2005;Xue et al, 2020). While droplets are more likely to bypass intersections due to their extended height (as compared to films) and hence gravitational impact (Kordilla et al, 2017), we have also demonstrated that consecutive routing of droplet flows through arrays of horizontal fractures will nearly always facilitate the formation of film (rivulet) flows on the vertical wide-aperture surfaces after the first partitioning (Noffz et al, 2019).…”

“…For contact angles in the range of 25° to 75° droplet heights (neglecting the dynamic flattening due to movement) would be on the order of 0.75-2.4 mm, therefore setting a lower limit where one-sided flow would persist. Studies focusing on "narrow" vertical fractures often observe a slightly wider range of partitioning patterns that stem from the erratic uptake and emittance of potentially chaotic droplet patterns from T-type (Xue et al, 2020;Yang et al, 2019) and X-type intersections (e.g., Glass et al, 2003;T. R. Wood et al, 2005;T.…”

“…v would be more difficult to derive. Inclusion of more complex partitioning of different flow mode dynamics, (e.g., droplets; Xue et al, 2020;Yang et al, 2019) would be an interesting, yet highly challenging extension because the uptake and release of such flows at intersections introduces a highly erratic and chaotic component.…”