title: Multiscale model of a freeze-thaw process for tree sap exudation.
abstract: Sap transport in trees has long fascinated scientists, and a vast literature exists on experimental and modelling studies of trees during the growing season when large negative stem pressures are generated by transpiration from leaves. Much less attention has been paid to winter months when trees are largely dormant but nonetheless continue to exhibit interesting flow behaviour. A prime example is sap exudation, which refers to the peculiar ability of sugar maple (Acer saccharum) and related species to generate positive stem pressure while in a leafless state. Experiments demonstrate that ambient temperatures must oscillate about the freezing point before significantly heightened stem pressures are observed, but the precise causes of exudation remain unresolved. The prevailing hypothesis attributes exudation to a physical process combining freeze-thaw and osmosis, which has some support from experimental studies but remains a subject of active debate. We address this knowledge gap by developing the first mathematical model for exudation, while also introducing several essential modifications to this hypothesis. We derive a multiscale model consisting of a nonlinear system of differential equations governing phase change and transport within wood cells, coupled to a suitably homogenized equation for temperature on the macroscale. Numerical simulations yield stem pressures that are consistent with experiments and provide convincing evidence that a purely physical mechanism is capable of capturing exudation.
authors.affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6.
authors.forename: Isabell
authors.initials: I
authors.lastname: Graf
authors.affiliation: Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo 'Mauro Picone', via dei Taurini 19, Rome 00185, Italy.
authors.forename: Maurizio
authors.initials: M
authors.lastname: Ceseri
authors.affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia, Canada V5A 1S6 stockie@math.sfu.ca.
authors.forename: John M
authors.initials: JM
authors.lastname: Stockie
mesh_terms: D031002:Acer / Q000502:physiology*; D000465:Algorithms; D001692:Biological Transport; D003198:Computer Simulation; D005615:Freezing; D008962:Models, Theoretical; D009991:Oscillometry; D009995:Osmosis; D018515:Plant Leaves / Q000502:physiology; D018517:Plant Roots / Q000502:physiology; D018547:Plant Stems / Q000502:physiology*; D018526:Plant Transpiration; D012621:Seasons; D013696:Temperature; D014197:Trees / Q000502:physiology*; D014867:Water; D014934:Wood / Q000502:physiology; D052584:Xylem / Q000502:physiology
chemical_list: D014867:Water
keywords: differential equations; multiphase flow and transport; periodic homogenization; phase change; sugar maple; tree sap exudation