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Taylor dispersion in osmotically driven laminar flows in phloem

Published online by Cambridge University Press:  02 March 2021

M. Nakad Open the ORCID record for M. Nakad [Opens in a new window] ,
T. Witelski Open the ORCID record for T. Witelski [Opens in a new window] ,
J. C. Domec Open the ORCID record for J. C. Domec [Opens in a new window] ,
S. Sevanto Open the ORCID record for S. Sevanto [Opens in a new window]  and
G. Katul Open the ORCID record for G. Katul [Opens in a new window]
M. Nakad*
Affiliation:
Nicholas School of the Environment, Duke University, Durham, NC27708, USA
T. Witelski
Affiliation:
Department of Mathematics, Duke University, Durham, NC27708-0320, USA
J. C. Domec
Affiliation:
Nicholas School of the Environment, Duke University, Durham, NC27708, USA UMR 1391, INRA-ISPA, Bordeaux Sciences Agro, 33175, Gradignan Cedex, France
S. Sevanto
Affiliation:
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM87545, USA
G. Katul
Affiliation:
Nicholas School of the Environment, Duke University, Durham, NC27708, USA Department of Civil and Environmental Engineering, Duke University, Durham, NC27708, USA
*
†Email address for correspondence: mazen.nakad@duke.edu
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Abstract

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 process remains fraught with experimental difficulties, thereby prompting interest in theoretical approaches and laboratory studies. The Münch pressure and mass flow model is one of the accepted hypotheses describing the physics of sucrose transport in the phloem. It is based on osmosis creating 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–Poiseuille equation. This study revisits such osmotically driven flows in tubes with membrane walls by including the effects of Taylor dispersion on mass transport. This effect has been overlooked in phloem flow studies. Taylor dispersion can increase the effective transport of solutes by increasing the apparent diffusion coefficient. It is shown that, in addition to the conventional diffusive correction derived for impermeable tube walls, a new adjustment to the mean advective terms arises because of osmotic effects. Because the molecular Schmidt number is very large for sucrose in water, the sucrose front speed and travel times have a direct dependence on the Péclet number for different ranges of the Münch number. This study establishes upper limits on expected Taylor dispersion enhancement of sucrose transport.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 913 , 25 April 2021 , A44
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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