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We present a theoretical analysis of the capillary driven transport of liquid in porous media that undergoes a sudden expansion. The use of appropriate coordinates allows for exactly and analytically solving different cases in two and three dimensions. The time dependence of liquid front motion in an expanding porous media is shown to be different from the one dimensional Lucas-Washburn (Kolloid Z., 1918 Xiao et al. (Langmuir, 2012. 28: p. 4208). These cases appear as asymptotic limits of our solutions. We also observe that capillary flow in expanding three dimensional porous materials exhibits a steady state solution for the bulk flow rate at the entrance of the expansion.

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Laboratory experiments and numerical simulations were utilized in this study to assess the impact of aquifer stratification on saltwater intrusion. Three homogeneous and six layered aquifers were investigated. Image processing algorithms facilitated the precise calculation of saltwater wedge toe length, width of the mixing zone, and angle of intrusion. It was concluded that the length of intrusion in stratified aquifers is predominantly a function of permeability contrast, total aquifer transmissivity and the number of heterogeneous layers, being positively correlated to all three. When a lower permeability layer overlays or underlays more permeable zones its mixing zone widens, while it becomes thinner for the higher permeability strata. The change in the width of the mixing zone (WMZ) is positively correlated to permeability contrast, while it applies to all strata irrespectively of their relative vertical position in the aquifer. Variations in the applied hydraulic head causes the transient widening of WMZ.These peak WMZ values are larger during saltwater retreat and are negatively correlated to the layer's permeability and distance from the aquifer's bottom. Moreover, steeper angles of intrusion are observed in cases where low permeability layers overlay more permeable strata, and milder ones in the inverse aquifer setups. The presence of a low permeability upper layer results in the confinement of the saltwater wedge in the lower part of the stratified aquifer. This occurs until a critical hydraulic head difference is applied to the system. This hydraulic gradient value was found to be a function of layer width and permeability contrast alike.