Numerical Modeling of Flow Through Phloem Considering Active Loading

Abstract

Transport through phloem is of significant interest in engineering applications, including selfpowered microfluidic pumps. In this paper we present a phloem model, combining protein level mechanics with cellular level fluid transport. Fluid flow and sucrose transport through a petiole sieve tube are simulated using the Nernst–Planck, Navier–Stokes, and continuity equations. The governing equations are solved, using the finite volume method with collocated storage, for dynamically calculated boundary conditions. A sieve tube cell structure consisting of sieve plates is included in a two dimensional model by computational cell blocking. Sucrose transport is incorporated as a boundary condition through a sixstate model, bringing in active loading mechanisms, taking into consideration their physical plant properties. The effects of reaction rates and leaf sucrose concentration are investigated to understand the transport mechanism in petiole sieve tubes. The numerical results show that increasing forward reactions of the proton sucrose transporter significantly promotes the pumping ability. A lower leaf sieve sucrose concentration results in a lower wall inflow velocity, but yields a higher inflow of water due to the active loading mechanism. The overall effect is a higher outflow velocity for the lower leaf sieve sucrose concentration because the increase in inflow velocity outweighs the wall velocity. This new phloem model provides new insights on mechanisms which are potentially useful for fluidic pumping in selfpowered microfluidic pumps.