The exact science of tree sap transport has puzzled plant physiologists for many years. Sap’s migration throughout tree trunks and branches is linked heavily to transpiration, the movement and subsequent evaporation of moisture from plants. As carbon dioxide diffuses inward from the air to plant leaves, a vapor pressure deficit between the leaf interior and surrounding atmosphere causes evaporation. This generates tension within leaf cell walls that is then transmitted via sap to tracheids — conductive hollow wood cells with vertical grooves that comprise the trunk, stem, and branches of trees and are collectively called sapwood. The resulting negative sap pressure draws water from roots to leaves, sometimes to heights of over 300 feet.
The exact science of tree sap transport has puzzled plant physiologists for many years. Sap’s migration throughout tree trunks and branches is linked heavily to transpiration, the movement and subsequent evaporation of moisture from plants. As carbon dioxide diffuses inward from the air to plant leaves, a vapor pressure deficit between the leaf interior and surrounding atmosphere causes evaporation. This generates tension within leaf cell walls that is then transmitted via sap to tracheids — conductive hollow wood cells with vertical grooves that comprise the trunk, stem, and branches of trees and are collectively called sapwood. The resulting negative sap pressure draws water from roots to leaves, sometimes to heights of over 300 feet.
Tracheids are the primary conductive elements in coniferous trees, and resemble tubes with small holes (or pits) that connect them both vertically and radially. Substances travelling in the radial direction must pass through many of these pits; thus, radial travel is more difficult than vertical travel. As a result, hydraulic conductivity is highly anisotropic (direction-dependent) and liquid movement is easier in the vertical direction.
In an article publishing today 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.
Read more at Society for Industrial and Applied Mathematics
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