A steady-state model of solution flow in a tubular semipermeable membrane is developed for an arbitrary distribution of solute sources and sinks along the translocation path. It is demonstrated that the volume-flow mechanism of phloem transport depends only on the two assumptions: 1. that the plasmalemma of the sieve tube is a differentially permeable membrane, and 2. that sugars are actively secreted into and absorbed from the lumen of the sieve tube. It is shown that in the absence of a pressure gradient, there is a negligible concentration gradient over most of the translocation path. However, in the presence of a pressure gradient a small concentration gradient develops as a result of the continually changing chemical potential of water along the direction of solution flow. For Poiseuille flow the concentration gradient is approximately proportional to the mean stream velocity.
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