Abstract
Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed in a plant. According to Münch, the osmotically generated hydrostatic phloem pressure is the force driving the long-distance transport of photoassimilates. Following Thompson and Holbrook[35]'s approach, we develop a mathematical model of coupled water-carbohydrate transport. It is first proven that the model presented here preserves the positivity. The model is then applied to simulate the flow of phloem sap for an organic tree shape, on a 3D surface and in a channel with orthotropic hydraulic properties. Those features represent an significant advance in modelling the pathway for carbohydrate transport in trees.
Highlights
Expanded knowledge of the carbohydrate pathway in trees is critical in agriculture, forestry and ecology
Phloem transport is the process by which carbohydrates produced by photosynthesis in the leaves get distributed within a plant
For over 60 years, it has served as the basis for mathematical models of the phloem transport process [3, 4, 5, 6, 7, 8, 9, 1, 10, 11]
Summary
Expanded knowledge of the carbohydrate pathway in trees is critical in agriculture, forestry and ecology. The difference in hydraulic properties along and across sieve elements as well as the lateral positioning of sources and sinks are essential to understand phloem transport in trees Taking those features into account can be achieved by describing transport as a two-dimensional process [18]. Numerical simulations are presented in a the third section in order to evaluate the model and illustrate some of its capabilities Those simulations include: a comparison and validation with an existing model [1] for the one-dimensional case; a parametric study; the application of the model to an existing tree; a preliminary investigation of the role played by sieve element orientation on carbohydrate distribution; simulating phloem transport on a branched, three-dimensional manifold
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