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

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 Munch 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(-1/3)t(-2/3) with time t and dimension less number M similar to eta kappa L(2)r(-3) for tubes of length L, radius r, permeability kappa and fluid viscosity eta. 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 Munch mechanism can account only for the short distance transport of sugar in plants.