ABSTRACT
The porous medium model of Green and Ampt, describing flow in porous media, appeared earlier than the capillary model of Washburn, although both lead to mathematically identical models. Here, the model of Green and Ampt was related to the Washburn model by an examination of the parameters involved in each. Fries et al. [N. Fries, M. Dreyer, J. Colloid Interface Sci. 320 (2008) 259-263] presented an explicit solution to this model. This solution is identical to the explicit solution of the Green and Ampt model presented earlier by Barry et al. [D.A. Barry, J.-Y. Parlange, G.C. Sander, M. Sivaplan, J. Hydrol. 142 (1993) 29-46].
ABSTRACT
A recent paper reported capillary rise and evaporation experiments in metallic wicks, as well as a mathematical model. The authors found a consistent discrepancy between the model predictions and data: The model over-predicted the capillary height rise by about 20%. The model used assumes that the porous medium is either fully wet or dry, an assumption that is particularly unsuited to evaporation from the wick surface. An alternative variable-saturation model is proposed that provides a possible explanation for the 20% discrepancy reported by the authors.
ABSTRACT
Capillary rise in porous media is frequently modeled using the Washburn equation. Recent accurate measurements of advancing fronts clearly illustrate its failure to describe the phenomenon in the long term. The observed underprediction of the position of the front is due to the neglect of dynamic saturation gradients implicit in the formulation of the Washburn equation. We consider an approximate solution of the governing macroscopic equation, which retains these gradients, and derive new analytical formulae for the position of the advancing front, its speed of propagation, and the cumulative uptake. The new solution properly describes the capillary rise in the long term, while the Washburn equation may be recovered as a special case.
ABSTRACT
Contaminant transport in coastal aquifers is complicated partly due to the conditions at the seaward boundary including seawater intrusion and tidal variations of sea level. Their inclusion in modelling this system will be computationally expensive. Therefore, it will be instructive to investigate the consequence of simplifying the seaward boundary condition by neglecting the seawater density and tidal variations in numerical predictions of contaminant transport in this zone. This paper presents a comparison of numerical predictions for a simplified seaward boundary condition with experimental results for a corresponding realistic one including a saltwater interface and tidal variations. Different densities for contaminants are considered. The comparison suggests that the neglect of the seawater intrusion and tidal variations does not affect noticeably the overall migration rate of the plume before it reaches the saltwater interface. However, numerical prediction shows that a more dense contaminant travels further seaward and part of the solute mass exits under the sea if the seawater density is not included. This is not consistent with the experimental result, which shows that the contaminant travels upwards to the shoreline along the saltwater interface. Neglect of seawater density, therefore, will result in an underestimation of the exit rate of solute mass around the coastline and fictitious migration paths under the seabed. For a less dense contaminant, neglect of seawater density has little effect on numerical prediction of migration paths.
