Vascular plants rely on differences of osmotic pressure to export sugars from
regions of synthesis (mature leaves) to sugar sinks (roots, fruits). In this
process, known as M\"unch pressure flow, the loading of sugars from
photosynthetic cells to the export conduit (the phloem) is crucial, as it sets
the pressure head necessary to power long-distance transport. Whereas most
herbaceous plants use active mechanisms to increase phloem concentration above
that of the photosynthetic cells, in most tree species, for which transport
distances are largest, loading seems to occur via passive symplastic diffusion
from the mesophyll to the phloem. Here, we use a synthetic microfluidic model
of a passive loader to explore the nonlinear dynamics that arise during export
and determine the ability of passive loading to drive long-distance transport.
We first demonstrate that in our device, phloem concentration is set by the
balance between the resistances to diffusive loading from the source and
convective export through the phloem. Convection-limited export corresponds to
classical models of M\"unch transport, where phloem concentration is close to
that of the source; in contrast, diffusion-limited export leads to small phloem
concentrations and weak scaling of flow rates with the hydraulic resistance. We
then show that the effective regime of convection-limited export is predominant
in plants with large transport resistances and low xylem pressures. Moreover,
hydrostatic pressures developed in our synthetic passive loader can reach
botanically relevant values as high as 10 bars. We conclude that passive
loading is sufficient to drive long-distance transport in large plants, and
that trees are well suited to take full advantage of passive phloem loading
strategies
