Theoretical considerations of optimal conduit length for water transport in vascular plants

 Summary 196 I.  196 1. The neglected dimension 196 2. Basic concepts 197 (a) The heuristic notion of vessel-tiers 197 (b) Ohm's law 199 (c) Conductances, resistances and resistivities 199 (d) Lumen and pit resistances 199 (e) The importance of conduit radius and length in conductance 199 II.      199 1. Nature and origin of xylem conduits 199 2. Increasing hydraulic conductance with increasing diameter and length 200 (a) Evolutionary trends in tracheid dimensions 200 (b) Origin of the vessel 200 3. Functional limitations to increasing vessel length 201 (a) Safety versus efficiency 201 (b) Containment of cavitation and embolism 202 III.         203 1. Cavitation is linked to the driving force for transport 203 2. Transport models and extreme assumptions about conduit length 203 (a) Unitary cavitation response (n l 1) 203 (b) Infinitely partitioned response (n l _) 204 (c) ∆P and cavitation containment 204 *Author for correspondence (fax j1 607 254 1242 ; e-mail jpc8!cornell.edu). IV.        205 1. Framing questions of optimal conduit length 205 2. A numeric model for flow through n conduit tiers 205 (a) Model structure 205 (b) Model solution 206 3. Optimization when f(P) is linear 206 (a) Isolating the effects of n on cavitation containment 206 (b) Optimal conduit tier-length distributions (OCLDs) 207 (c) Abrupt changes in conduit length 208 (d) Optimal frequency of end walls : incorporating R pit 208 4. Optimization when f(P) is curvilinear 210 V.      :    210 1. Limitations to the concept of conduit tiers 210 (a) Vessel ends are randomly distributed 210 (b) Dispersion around mean length within each ' tier ' 210 2. Is the xylem optimally partitioned ? 211 (a) Optimal number of end walls 211 (b) Conduit length distribution along the pathway 211 3. Hydraulic segmentation 212 (a) Segmentation in hydraulic resistance 212 (b) Segmentation in cavitation vulnerability 212 VI.  212 1. Anatomy 212 2. Modelling flow 213 196 REVIEW J. P. Comstock and J. S. Sperry VII.  :     213 1. Analytic solution for Q max with a single tier 213 2. The general case for n tiers 214 3. Analytic solution for Q max with two tiers 214 4. Matric flux and n l _ 215  Vascular plants …