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 Münch 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(-5) mole second(-1) centimeters(-2) (= 18.5 grams hour(-1) centimeters(-2)) over distances in excess of 50 meters. The calculations clearly indicate that a Münch 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 centimeters(2) second(-1) bar(-1)); (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(-1)). 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(2) second(-1) bar(-1). For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 x 10(-7) centimeters second(-1) bar(-1) or greater.