A concentration dependent viscosity enhances the resilience of phloem hydraulics to sucrose loading

Mazen Nakad, Jean-Christophe Domec and Gabriel G. Katul, Nicholas School of the Environment, Duke University, Durham, NC, Jean-Christophe Domec, Bordeaux Sciences-Agro, University of Bordeaux, Gradignan Cedex, France, Sanna Sevanto, Earth & Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, Gabriel G. Katul, Department of Civil and Environmental Engineering, Duke University, Durham, NC

Background/Question/Methods
Within plants, the delivery of water and nutrients is achieved using two different but highly interconnected hydraulic systems: the xylem and the phloem. While extensive research on xylem water transport and its hydraulic failure has been performed for more than a 100 years, sucrose transport inside the phloem remains relatively under-studied. The work to be presented here will focus on exploring the effect of a variable phloem sap viscosity on transport speed and its role on phloem hydraulic failure. Previous studies showed an optimal range for sucrose concentration exists when invoking a concentration dependent viscosity from a global point of view. This viewpoint is revisited using the Navier-Stokes and the sucrose continuity equations in cylindrical coordinates inside a tube covered by a membrane. This configuration is intended to approximate the hydrodynamics of water and sucrose transport in the phloem. A concentration-dependent viscosity was used thereby allowing concentration variations axially and radially to impact the gradients of the viscous stresses resisting the flow. Numerical simulations were then used to generate radial and axial velocity and sucrose concentration variations in the tube. These solutions were then employed to assess the range of sucrose concentrations admitting near maximum hydraulic transport efficiency.
Results/Conclusions
The results and discussion are presented by contrasting runs that include viscosity gradients when formulating viscous stresses and those that do not. It was found that the variable viscosity case increases the transport speed when compared to a constant viscosity model. This difference between the two cases is enlarged when increasing the tube length (i.e. for long distance phloem transport) due to a higher concentration gradient inside the flow. In addition, the range of sucrose concentrations that allows maximum transport speed appears wider than shown in previous studies, which makes sucrose transport efficiency less sensitive to changes in initial concentrations loaded in the phloem. These findings suggest that passive sucrose transport following the Munch hypothesis can still predict long distance plant water transport. Moreover, phloem hydraulics can be more resilient to variations in sucrose loading when experiencing drought or other ecological stresses.