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\begin{document}

\title{Experimental study and analytical modeling of preferential flow and
partitioning dynamics at unsaturated fracture intersections}



\author[1]{Torsten Noffz}%
\author[2]{Marco Dentz}%
\author[1]{Jannes Kordilla}%
\affil[1]{University of Göttingen, Geoscientific Centre (GZG), Göttingen, Germany}%
\affil[2]{Institute of Environmental Assessment and Water Research (IDAEA), Spanish National Research Council (CSIC), Barcelona, Spain}%


\vspace{-1em}



  
  \date{May 24, 2024}


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\begin{abstract}
Unsaturated fractured aquifer systems offer a domain for complex
gravity-driven flow dynamics leading to the development of preferential
flow along fracture networks that often strongly contributes to rapid
mass fluxes. This behaviour is difficult to recover by volume-effective
modeling approaches (e.g. Richards equation) due to the non-linear
nature of free-surface flows and mass partitioning processes at
unsaturated fracture intersections. The application of well-controlled
laboratory experiments enables to isolate single aspects of the mass
redistribution process that ultimately affects travel time distributions
across scales. We use custom-made acrylic cubes (20 cm x 20 cm x 20 cm)
in analogue percolation experiments to create simple fracture networks
with single or multiple horizontal fractures. A high precision
multichannel dispenser produces gravity-driven free surface flow
(droplets; rivulets) at flow rates ranging from 1 ml/min to 5 ml/min.
Hereby, total inflow rates are kept constant while the fluid is injected
via 15 (droplet flow) or 3 inlets (rivulet flow) to reduce the impact of
erratic flow dynamics. Normalized fracture inflow rates (Q\_f/Q\_0) are
calculated and compared for aperture widths d\_f of 1 mm and 2.5 mm. A
higher efficiency in filling an unsaturated fracture by rivulet flow
observed in former studies can be confirmed. The onset of a capillary
driven Washburn-type flow is determined and recovered by an analytical
solution. In order to upscale the dynamics and enable the prediction of
mass partitioning for arbitrary-sized fracture cascades a Gaussian
transfer function is derived that reproduces the repetitive filling of
fractures, where rivulet flow is the prevailing regime. Results show
good agreement with experimental data for all tested aperture widths.%
\end{abstract}%



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