Sucrose transport inside the phloem: Bridging hydrodynamic and geometric characteristics

The delivery of the products of photosynthesis is achieved through a hydraulic system called the phloem. This semi-permeable plant tissue consists of living cells that contract and expand in response to fluid pressure fluctuations. The M$\ddot{u}$nch pressure flow theory, which is based on osmosis providing the necessary pressure gradient to drive the mass flow of carbohydrates, is currently the most accepted model of sucrose transport. When this hypothesis is combined with the conservation of fluid mass and momentum as well as sucrose mass, many simplifications must be invoked to mathematically close the problem. The work to be presented will focus on describing this mass flow using the Navier-Stokes and the sucrose continuity equations in cylindrical coordinates inside an elastic membrane with a concentration-dependant viscosity. It is demonstrated that the interaction between the hydrodynamic and geometrical characteristics of the phloem has a significant effect on the speed of flow. These results offer a novel perspective about the evolutionary adaptation of plant hydraulic traits to optimize phloem carbohydrate transport efficiency.