Steady State Models of Münch Pressure Flow
Since 1972 several papers have appeared that deal with the mathematical modelling of Münch pressure flow systems. The first paper (Eschrich, Evert and Young, 1972) dealt with Münch pressure flow relaxation phenomena in man-made tubular semi-permeable membranes. The next two papers treated models applicable to Münch pressure flow in sieve tubes. Young, Evert and Eschrich (1973) derived the mathematical formalism applicable to steady state translocation in sieve tubes for an arbitrary distribution of solute sources and sinks; while these authors discussed the qualitative behaviour of their equations they published no sample calculations. Christy and Ferrier (1973) published another paper at about the same time in which they independently derived a model that applied to Münch pressure flow for an arbitrary distribution of solute sources and sinks both in the steady state and in the time-dependent state; a number of sample calculations were published for sugar beet. Shortly thereafter, Tyree and Dainty (1975) and Tyree, Christy and Ferrier (1974) derived yet another steady state model that produced numerical results in substantial agreement with Christy and Ferrier (1973). This model had the advantage of being computationally simpler, and it was applied to obtain steady state solutions of translocation over long distances, e.g. 50 meters. Anderson (1974) appears to have independently arrived at a steady state model using the formalism of standing gradient osmotic flow which was applied first to a kind of Münch pressure flow system in animals (Diamond and Bossert, 1967).
KeywordsHydraulic Conductivity Sugar Beet Sucrose Concentration Pressure Flow Time Dependent Behaviour
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