Flow resistance of phloem sieve plates revisited using an experimental model

Abstract

Sieve plate resistance has been identified as the key to understanding the efficiency of phloem transport of carbohydrates in trees. These plates with small holes connecting sieve tubes are responsible for the largest resistance to flow in the phloem. Their structure determines how fast sugars can be transported through the phloem with certain pressure differences and what the limits for phloem transport in different plants are. Because experiments with the phloem are very challenging, our understanding of sieve plate resistance is mostly based on anatomical studies and hydrodynamic modeling of flow through sieve plates. These models calculate the resistance of the entire sieve tube–sieve plate system using the Hagen–Poiseuille flow resistance for the sieve cell lumen and a combination of the Hagen–Poiseuille resistance and Sampson flow resistance through the sieve pores. The resistance of the entire sieve plate is calculated by summing the Hagen–Poiseuille and Sampson flow resistances of each pore. To test the validity of this model formulation, an experimental model with aspect parameters similar to phloem sieve tubes was built using polyvinyl chloride (PVC) piping and plastic straws of different diameters and lengths. This system was used to measure flow rates and calculate flow resistance at Reynolds numbers 0.5–300. The results suggest that the current models may significantly overestimate the flow resistance caused by sieve plates and that the resistance might be better described by formulations used for perforated plates.