A Simpler Iterative Steady State Solution of Münch Pressure-Flow Systems Applied to Long and Short Translocation Paths

Abstract

A simple steady state iterative solution of Munch pressure-flow in unbranched sieve tubes containing only water and sucrose is derived. The iterative equations can be solved on a programmable desk calculator. Solutions are presented for steady state transport with specific mass transfer rates up to 1.5 X 10-' mole second-' centimeters-' (= 18.5 grams hour' centimeters-') over distances in excess of 50 meters. The calcu-lations clearly indicate that a Munch pressure-flow system can operate over long distances provided (a) the sieve tube is surrounded by a semipermeable membrane; (b) sugars are actively loaded in one region and unloaded at another; (c) the sieve pores are unblocked so that the sieve tube hydraulic conductivity is high (around 4 centimeters2secon bar-'); (d) the sugar concentration is kept high (around one molar in the source region); and (e) the average sap velocity is kept low (around 20-50 centimeters hour-'). The dimensions of sieve cells in several species of plants are reviewed and sieve tube hydraulic conductivities are calculated; the values range from 0.2 to 20 centimeters'secon bar-'. For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes mnst be about 5 X 10-' centimeters second'