Microfluidic Networks

A large part of the branching vasculature of the mammalian circulatory and respiratory systems obeys Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. Where this law is obeyed, a functional relationship exists between vessel radius and volumetric flow, average linear velocity of flow, velocity profile, vessel-wall shear stress, Reynolds number, and pressure gradient in individual vessels. In homogeneous, full-flow sets of vessels, a relation is also established between vessel radius and the conductance, resistance, and cross- sectional area of a full-flow set.

Leaves constitute a substantial fraction of the total resistance to water flow through plants. A key question is how hydraulic resistance within the leaf is distributed among petiole, major veins, minor veins, and the pathways downstream of the veins. We partitioned the leaf hydraulic resistance (R(leaf)) for sugar maple (Acer saccharum) and red oak (Quercus rubra) by measuring the resistance to water flow through leaves before and after cutting specific vein orders. Simulations using an electronic circuit analog with resistors arranged in a hierarchical reticulate network justified the partitioning of total R(leaf) into component additive resistances. On average 64% and 74% of the R(leaf) was situated within the leaf xylem for sugar maple and red oak, respectively. Substantial resistance-32% and 49%- was in the minor venation, 18% and 21% in the major venation, and 14% and 4% in the petiole. The large number of parallel paths (i.e. a large transfer surface) for water leaving the minor veins through the bundle sheath and out of the leaf resulted in the pathways outside the venation comprising only 36% and 26% of R(leaf). Changing leaf temperature during measurement of R(leaf) for intact leaves resulted in a temperature response beyond that expected from changes in viscosity. The extra response was not found for leaves with veins cut, indicating that water crosses cell membranes after it leaves the xylem. The large proportion of resistance in the venation can explain why stomata respond to leaf xylem damage and cavitation. The hydraulic importance of the leaf vein system suggests that the diversity of vein system architectures observed in angiosperms may reflect variation in whole-leaf hydraulic capacity.