https://phys.org/news/2018-07-mathematical-analysis-transpiration-driven-sap-coniferous.html

In an article publishing this week in the SIAM Journal of Applied Mathematics, Bebart M. Janbek and John M. Stockie present a multidimensional porous medium model that measures sap flow within a tree stem. "I became interested in tree sap flow about seven years ago when I started studying the freeze-thaw mechanism that governs exudation—a fancy name for oozing—of maple sap from sugar maple trees during harvest season in late winter," Stockie said. "I grew up in Ontario and visited sugar bushes as a child, so I was thrilled by the opportunity to apply mathematical techniques to the study of the iconic sugar maple." His work with Janbek expands upon an existing one-dimensional model, and notably includes a nonlinear parabolic partial differential equation (PDE) with a transpiration source term.

Researchers frequently use mathematical models to study the flow of sap within conductive sapwood. Electric circuit analogy and porous medium models—which model sap flow quite well due to the simple, repeating microstructure of sapwood—are both popular approaches. Unfortunately, most PDE-based porous models are one-dimensional, thus ignoring the radial variations within plant stems that make sapwood anisotropic.