Xylem anisotropy and water transport--a model for the double sawcut experiment

Early experiments with overlapping cuts to the stems of trees demonstrated that lateral flow within the stem must be possible to allow such trees to maintain water flow to their leaves. We present a mathematical approach to considering lateral flow in stems by treating the xylem as an anisotropic medium for flow and develop an expression of its conductivity in the form of a tensor. In both 3D models of tracheid-bearing stems with cuts (incorporating this tensor analysis) and experimental stems with steadily deepening cuts, it is shown that flow can continue despite the presence of even strongly overlapping cuts through 90% of the stem. Such remaining conducting ability was, however, strongly dependent on values for radial and tangential conductivity (conductivity to lateral flow across the stem either radially with respect to the central axis or tangentially to the stem surface). Furthermore, the lateral flow around obstructing cuts was more dependent on tangential flow around the stem upstream and downstream of the cuts than on radial flow across the stem. The relative importance of tangential flow could be accounted for by a greater tangential conductivity, perhaps related to the predominance of pits on radial walls of tracheids, and the presence of non-conducting pith and early growth rings in the stems. These results demonstrate that a consideration of anisotropy in transport properties of the xylem will be important for future studies of flow in stems around naturally occurring geometric features such as branching points.