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\author[1,2]{Ali Saeibehrouzi}%
\author[2]{Ran Holtzman}%
\author[1]{Petr Denissenko}%
\author[1]{Soroush Abolfathi}%
\affil[1]{School of Engineering, University of Warwick}%
\affil[2]{Centre for Fluid and Complex Systems, Coventry University}%


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  \date{June 15, 2024}


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\begin{abstract}
Solute transport in unsaturated porous media is of interest in many
engineering and environmental applications. The interplay between
small-scale, local forces and the porous microstructure exerts a strong
control on the transport of fluids and solutes at the larger,
macroscopic scales. Heterogeneity in pore geometry is intrinsic to
natural material across a large range of scales. This multiscale nature,
and the intricate links between two-phase flow and solute transport,
remain far from well understood, by and large. Here, we use Direct
Numerical Simulation (DNS) to quantify the effects of correlated
heterogeneity on solute transport during drainage under an unfavorable
viscosity ratio. We find that increasing spatial correlations in pore
sizes increases the size of the required Representative Elementary
Volume (REV). We also show that increasing the correlation length
enhances solute dispersivity through its impact on the spatial
distribution of low-velocity (diffusion-dominated) and high-velocity
(advection-dominated) regions. Fluid saturation is shown to directly
affect diffusive mass flux among high-and low-velocity zones. Another
indirect effect of correlated heterogeneity on solute transport is
through its control of the drainage patterns via rearrangements of
mobile-immobile zones. Our findings improve quantitative understanding
of solute mixing and dispersion in unsaturated conditions, highly
relevant to some of our most urgent environmental problems.%
\end{abstract}%



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