The speed of osmotically driven laminar flow within elastic semi-permeable tubes*

The phloem provides the pathway for the products of photosynthesis to be transported to different parts of the plant for consumption or storage. The Munch pressure flow theory is currently the most accepted to mathematically represent sucrose transport. It is based on osmosis that provides the pressure gradient to drive the flow within the phloem. Due to experimental challenges, mathematical models are used to complement and assist interpreting plant responses to environmental stresses that reduce the efficiency of phloem transport. One of these simplifications is to geometrically represent the phloem as a rigid semi-permeable tube. However, the phloem consists of living cells that contract and expand in response to pressure fluctuations. The effect of membrane elasticity on sucrose front speed frames the scope of the talk. Laboratory experiments are first conducted to elucidate the pressure-radius relation in membranes. The findings are then incorporated into 2-D numerical simulations. It is demonstrated that the speed of the flow is decreased when the tube is allowed to expand. These results offer a novel perspective about the role of sieve plates evenly spaced throughout the phloem.