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Osmotically driven pipe flows and their relation to sugar transport in plants

Published online by Cambridge University Press:  25 September 2009

KÅRE H. JENSEN ,
EMMANUELLE RIO ,
RASMUS HANSEN ,
CHRISTOPHE CLANET  and
TOMAS BOHR
KÅRE H. JENSEN
Affiliation:
Center for Fluid Dynamics, Department of Physics, Technical University of Denmark, Building 309, 2800 Kgs. Lyngby, Denmark Center for Fluid Dynamics, Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech Building 345 East, 2800 Kgs. Lyngby, Denmark
EMMANUELLE RIO
Affiliation:
Center for Fluid Dynamics, Department of Physics, Technical University of Denmark, Building 309, 2800 Kgs. Lyngby, Denmark Laboratoire de Physique des Solides, Univ. Paris-Sud, CNRS, UMR 8502, F-91405 Orsay Cedex, France
RASMUS HANSEN
Affiliation:
Center for Fluid Dynamics, Department of Physics, Technical University of Denmark, Building 309, 2800 Kgs. Lyngby, Denmark
CHRISTOPHE CLANET
Affiliation:
IRPHE, Universités d'Aix-Marseille, 49 Rue Frédéric Joliot-Curie BP 146, F-13384 Marseille Cedex 13, France
TOMAS BOHR*
Affiliation:
Center for Fluid Dynamics, Department of Physics, Technical University of Denmark, Building 309, 2800 Kgs. Lyngby, Denmark
*
†Email address for correspondence: tbohr@fysik.dtu.dk
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Abstract

In plants, osmotically driven flows are believed to be responsible for translocation of sugar in the pipe-like phloem cell network, spanning the entire length of the plant – the so-called Münch mechanism. In this paper, we present an experimental and theoretical study of transient osmotically driven flows through pipes with semi-permeable walls. Our aim is to understand the dynamics and structure of a ‘sugar front’, i.e. the transport and decay of a sudden loading of sugar in a water-filled pipe which is closed in both ends. In the limit of low axial resistance (valid in our experiments as well as in many cases in plants) we show that the equations of motion for the sugar concentration and the water velocity can be solved exactly by the method of characteristics, yielding the entire flow and concentration profile along the tube. The concentration front decays exponentially in agreement with the results of Eschrich, Evert & Young (Planta (Berl.), vol. 107, 1972, p. 279). In the opposite case of very narrow channels, we obtain an asymptotic solution for intermediate times showing a decay of the front velocity as M−1/3t−2/3 with time t and dimensionless number M ~ ηκL2r−3 for tubes of length L, radius r, permeability κ and fluid viscosity η. The experiments (which are in the small M regime) are in good quantitative agreement with the theory. The applicability of our results to plants is discussed and it is shown that it is probable that the Münch mechanism can account only for the short distance transport of sugar in plants.

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 371 - 396
Copyright
Copyright © Cambridge University Press 2009

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References

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