Numerical simulations of a multiscale model for maple sap exudation

Sap exudation refers to the process whereby trees such as sugar maple (Acer saccharum) and red maple (Acer rubrum) generate elevated stem pressure, which permits maple sap to be harvested as a viable agricultural product. There exists a vast literature on sap exudation and various hypotheses regarding the physical and biological mechanisms for in- ternal pressure generation in trees but very limited mathematical modeling work. Here, we perform a careful parametric study of a model for sap exudation recently published by Graf et al. [J R Soc Interface 12:20150665, 2015] which consists of a nonlinear system of differential equations obtained by homogenizing the equations governing phase change and sap transport at the cellular level. We focus on the influence of realistic daily temperature oscillations on the resulting stem pressure and draw comparisons with experimental mea- surements on red and sugar maple saplings taken during the sap harvest season. This study demonstrates the limitations and capabilities of our model in terms of capturing realistic exudation behaviour.