Taylor Dispersion in Osmotically Driven Flows with Solute Leakage

Jepson, Jacob M.; Band, Leah R.

Abstract

The phloem facilitates the transport of solute from mature leaves throughout the plant for growth and maintenance. Solute is loaded into the phloem, which drives water influx via osmosis, thereby increasing the phloem pressure. The resulting pressure gradient drives the flow of solute-rich sap toward a distant sink region, where sap and solute are unloaded to nearby plant tissues. In this paper, we examine a model which describes solute transport and leakage
throughout a phloem sink region, performing radial averaging as in Taylor dispersion. This approach leads to governing equations that contain additional terms that have not been included in previous modelling descriptions. In addition to new terms in the sink component, we find that the radial averaging introduces an additional term in the sap velocity, in which solute leakage increases the sap velocity, and hence solute advection. Numerical solutions demonstrate how these terms affect the predicted sap velocities and solute concentrations. Further insights into the model solutions are
obtained via an asymptotic analysis which considers two parameter regimes. We conclude that Taylor dispersion can substantially modify predicted dynamics in the phloem sink regions. Furthermore, our study provides insights into how Taylor dispersion results in modified governing equations for solute transport in permeable tubes.

Citation

Jepson, J. M., & Band, L. R. (in press). Taylor Dispersion in Osmotically Driven Flows with Solute Leakage. Physics of Fluids,

• Journal Article Type: Article
• Acceptance Date: May 25, 2025
• Deposit Date: Jun 23, 2025
• Journal: Physics of Fluids
• Print ISSN: 1070-6631
• Electronic ISSN: 1089-7666
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/50707105
• Additional Information: The following article has been submitted to/accepted by Physics of Fluids . After it is published, it will be found at https://pubs.aip.org/aip/pof