Sugar Transport in a Merging Phloem Vessels: A Hydrodynamic Model

Green plants are the major tappers of the energy from the sun. The collected solar energy in the form of light is used to activate the chemical reaction occurring in matured leaves between carbon dioxide and water, leading to the synthesis of sugar (chemical energy). Two main transport processes are involved in the transport of mineral salt water from the soil through the roots, via the trunk and branches to the leaves where photosynthetic activity occurs, and the translocation of sugar from the leaves to where they are needed and possibly, stored. The xylem vessels bear the absorbed mineral salt water while the phloem vessels bear the manufactured sugar. In this study, neglecting the effects of occlusion and clogging of the phloem channels, we investigate the transport of sugars in the merging phloem vessels using the hydrodynamic approach. The model is designed using the Boussinesq approximation and solved semi-analytically using the regular perturbation series expansion solutions and Mathematica 11.2 computational software. Expressions for the concentration, temperature, and velocity are obtained and presented quantitatively and graphically. The results show among others, that increase in the merging angle causes a reduction in the concentration, temperature, and velocity profiles. However, there exists fluctuations in the concentration and temperature structures.