Taylor Dispersion in Osmotically Driven Laminar Flow in Phloem

Sucrose is among the main products of photosynthesis that are deemed necessary for plant growth and survival. It is produced in the mesophyll cells of leaves and translocated to different parts of the plant through the phloem. Progress in understanding this transport mechanism remains fraught with experimental difficulties thereby prompting interest in theoretical approaches and laboratory studies. The Munch pressure and mass flow model is one of the commonly accepted hypotheses for describing the physics of sucrose transport in the phloem systems. It is based on osmosis to build an energy potential difference between the source and the sink. The flow responding to this energy potential is assumed laminar and described by the Hagen-Poiseulle equation. This study revisits such osmotically driven flow in tubes by including the effects of Taylor dispersion on mass transport, which has not been considered in the context of phloem flow. Taylor dispersion is an effect in tube flow where shear flow can increase the effective transport of species. It is shown that in addition to the conventional Taylor dispersion diffusive correction derived for closed pipe walls, a new adjustments to the mean advective terms, arise because of osmotic effects. These new terms act as local sources and sinks of sucrose, though their overall average effect is zero. Because the molecular Schmidt number is very large for sucrose in water, the role of a radial Peclet number emerges as controlling the sucrose front speed and travel times above and beyond the much studied Munch number. This study establishes upper limits on expected Taylor dispersion speed-up of sucrose transport.