Asymptotic Analysis of Flow in Sieve Tubes with Semi-permeable Walls

The effect of semi-permeable tube walls on the flow in sieve tubes in the phloem is examined by asymptotic analysis of the governing transport equations. The analysis is valid for long, thin tubes, and pertains to regions far from the inlet and outlet where loading and unloading of sugar occurs. It is shown that, under certain conditions, analytical relations governing the concentration, pressure, and velocity fields can be derived in a rigorous fashion. Under other conditions numerical solutions are required. The solutions presented here demonstrate the physical mechanisms that cause the concentration and pressure to decrease and the velocity to increase non-linearly as one moves down the tube in the direction of flow. These predictions are interpreted in light of previously reported experimental data for both model systems and living plants.