I will present a mathematical model for sap exudation, which is the process whereby sugar maple (and a few other tree species) generate a large stem pressure despite the tree being in a leafless, largely dormant state. Numerous bio-physical mechanisms have been proposed over the past century to explain this phenomenon, yet the question of what actually drives maple sap flow remains a controversial one. We incorporate distinctive features of the cellular microstructure of maple sapwood and treat the sap as a two-phase (gas + liquid) mixture whose dynamics are governed by the combined effects of porous media flow, phase change, gas dissolution and osmosis. The governing equations on the microscale consist of a nonlinear differential-algebraic system, which is then averaged through the process of periodic homogenization to obtain a macroscale equation for temperature within the tree stem. I will then present a comparison between numerical simulations and experimental measurements, showing that the sap exudation model reproduces realistic behaviours seen in experimental measurements of pressure and sap flow rate from actual maple trees.
BIO: JS is an applied mathematician with research interests that span scientific computing, fluid mechanics, partial differential equations and asymptotic analysis. JS received PhD in Applied Mathematics from the University of British Columbia in 1997 after which he held a postdoctoral fellowship at Simon Fraser University (SFU). In 2000 JS took up a faculty position at the University of New Brunswick in Fredericton NB and 3 years later moved to the Department of Mathematics at SFU
where he has been ever since. My current research projects involve mathematical modelling of sap flow in trees and numerical simulations for fluid-structure interaction problems involving suspensions of swimming organisms.