Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-20T00:08:00.622Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barenblatt, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press.CrossRefGoogle Scholar
Eschrich, W., Evert, R. F. & Young, J. H. 1972 Solution flow in tubular semipermeable membranes. Planta(Berl.) 107, 279–300.Google ScholarPubMed
Frisch, H. L. 1976 Osmotically driven flow in narrow channels. Trans. Soc. Rheol. 20, 23–27.CrossRefGoogle Scholar
Gurbatov, S. N. Malakhov, A. N. & Saichev, A. I. 1991 Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles. Manchester University Press.Google Scholar
Henton, S. M. 2002 Revisiting the Münch pressure-flow hypothesis for long-distance transport of carbohydrates: modelling the dynamics of solute transport inside a semipermeable tube. J. Exp. Bot. 53, 1411–1419.Google ScholarPubMed
Jonsson, G. 1986 Transport phenomena in ultrafiltration: membrane selectivity and boundary layer phenomena. J. Pure Appl. Chem. 58, 1647–1656.Google Scholar
Jensen, K. H. 2007 Osmotically driven flows and their relation to sugar transport in plants. MSc Thesis, The Niels Bohr Institute, University of Copenhagen.Google Scholar
Knoblauch, M. & van Bel, A. J. E. 1998 Sieve tubes in action. The Plant Cell 10, 35–50.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1980 Statistical Physics. Pergamon Press.Google Scholar
Münch, E. 1930 Die Stoffbewegung in der Pflanze. Verlag von Gustav Fisher.Google Scholar
Niklas, K. J. 1992 Plant Biomechanics – An Engineering Approach to Plant Form and Function. The University of Chicago Press.Google Scholar
Nobel, P. S. 1999 Physicochemical & Environmental Plant Physiology. Academic Press.Google Scholar
Pedley, T. J. 1983 Calculation of unstirred layer thickness in membrane transport experiments: a survey. Quart. Rev. Biophys. 16, 115–150.Google Scholar
Press, W. H. 2001 Numerical Recipes in Fortran 77, Vol. 1 Cambridge University Press.Google Scholar
PubChem–Database 2007 http://pubchem.ncbi.nlm.nih.gov/ National Library of MedicineGoogle Scholar
Schultz, S. G. 1980 Basic Principles of Membrane Transport. Cambridge University Press.Google Scholar
Taiz, L. & Zeiger, E. 2002 Plant Physiology. Sinauer Associates.Google Scholar
Thompson, M. V. & Holbrook, N. M. 2003 a, Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport. J. Theor. Biol. 220, 419–455.CrossRefGoogle Scholar
Thompson, M. V. & Holbrook, N. M. 2003 b, Scaling phloem transport: water potential equilibrium and osmoregulatory flow. Plant, Cell Environ. 26, 1561–1577.Google Scholar
Weir, G. J. 1981 Analysis of Münch theory. Math. Biosci. 56, 141–152.CrossRefGoogle Scholar