Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube

A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are approp...

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Vydané v:Journal of experimental botany Ročník 53; číslo 373; s. 1411
Hlavní autori: Henton, S M, Greaves, A J, Piller, G J, Minchin, P E H
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: England 01.06.2002
Predmet:
Algorithms
Biological Transport
Carbohydrate Metabolism
Computer Simulation
Diffusion
Diffusion Chambers, Culture - instrumentation
Models, Biological
Osmotic Pressure
Plant Structures - physiology
Sucrose - metabolism
Time Factors
Water - chemistry
Water - metabolism
ISSN:0022-0957
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Shrnutí:A mathematical model of the Münch pressure-flow hypothesis for long-distance transport of carbohydrates via sieve tubes is constructed using the Navier-Stokes equation for the motion of a viscous fluid and the van't Hoff equation for osmotic pressure. Assuming spatial dimensions that are appropriate for a sieve tube and ensuring suitable initial profiles of the solute concentration and solution velocity lets the model become mathematically tractable and concise. In the steady-state case, it is shown via an analytical expression that the solute flux is diffusion-like with the apparent diffusivity coefficient being proportional to the local solute concentration and around seven orders of magnitude greater than a diffusivity coefficient for sucrose in water. It is also shown that, in the steady-state case, the hydraulic conductivity over one metre can be calculated explicitly from the tube radius and physical constants and so can be compared with experimentally determined values. In the time-dependent case, it is shown via numerical simulations that the solute (or water) can simultaneously travel in opposite directions at different locations along the tube and, similarly, change direction of travel over time at a particular location along the tube.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-0957
DOI:10.1093/jexbot/53.373.1411