  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. In this paper, we present an experimental and
theoretical study of transient osmotically driven flows through pipes with
semipermeable walls. We extend the experimental work of Eschrich, Evert and
Young \cite[]{Eschrich:1972} by providing a more accurate version of their
experiment allowing for better comparison with theory. In the experiments we
measure the dynamics and structure of a "sugar front", i.e. the transport and
decay of a sudden loading of sugar in a pipe which is closed in both ends. We
include measurements of pressure inside the membrane tube allowing us to
compare the experiments directly with theory and, in particular, to confirm
quantitatively the exponential decay of the front in a closed tube.In a novel
setup we are able to measure the entire concentration profile as the sugar
front moves. In contrast to previous studies we find very good agreement
between experiment and theory.
  In the limit of low axial resistance (valid in our experiments as well as in
many cases in plants) we show that the equations can be solved exactly by the
method of characteristics yielding, in general, an implicit solution. Further
we show that under more general conditions the equations of motion can be
rewritten as a single integro-differential equation, which can be readily
solved numerically. The applicability of our results to plants is discussed and
it is shown that it is probable that the pressure-flow hypothesis can account
for short distance transport of sugar in plants.
