3. Porous Media Flow

Studying moisture transport in porous media according to Darcy's Law and nonlinear diffusion equations. I am working on a diverse range of applications, including:

1. Sap flow in maple trees: Maple sap is a traditional Canadian agricultural product that has a significant historical and economic importance in eastern Canada. The sap harvest depends very sensitively on temperature, and sap flows only if the temperature fluctuates for several days above and below the freezing point. To explain this phenomenon we are studying a porous medium model for a maple trunk that couples Richards' equation for the sap flow along with a diffusion equation for the temperature. We are also investigating a cell-level model including the effects of freeze/thaw, gas dissolution and osmosis that captures the phenomena of sap exudation and embolism recovery [J21], [J23], [J24], [J30], [J36], [J38]. This work is funded by the North American Maple Syrup Council.

2. Moisture uptake in concrete: We developed a reaction-diffusion model that captures the uptake of water within a hardened concrete sample, as well as the chemical reactions that take place when the water reacts with residual silicates in the porous concrete matrix. Numerical simulations reproduce the stalling of wetting fronts that is observed in experiments. We have published two papers on the modelling and analytical aspects of this problem [J15], [J34], and are currently extending our model to capture the phenomenon of self-desiccation.

   

3. Gravity-driven fingering in water-repellent soils: Hydrophobic soils occur commonly in nature and are characterized by preferential flow, wherein the infiltrating water forms finger-like instabilities that can penetrate much more rapidly into the subsurface than a uniform wetting front. We have studied these instabilities numerically using a model known as the Relaxation Non-Equilibrium Richards Equation (RNERE) [J18] which incorporates both capillary hysteresis and a non-equilibrium term in the capillary pressure-saturation relation. In our current work, we are investigating other nonlinear parabolic PDE models that yield similar instabilities.

4. Membrane transport in porous vesicles.