Abstract
Fluid motion is of fundamental importance for plant survival, growth and development. This distribution of water and nutrients is achieved by hydraulics. Fluid flow also plays a key role in long-distance signalling, allowing plants to adapt to environmental challenges. Fluid dynamics thus maintains plant vitality and health. In this chapter we derive the basic governing equations for fluid motion from first principles and describe the pertinent boundary conditions. Pressure-driven flow in a tube is discussed as a conceptualised model of fluid transport in the plant’s vasculature system. We also discuss solute transport with particular reference to the individual roles played by convection and diffusion and the enhanced dispersive effect that can be achieved when these two effects work in unison.
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Notes
- 1.
In the definition of P, the term nn is a dyadic product. This can be thought of as a matrix so that in index notation nn is interpreted as the matrix with elements n i n j. Note that some authors write this product as n ⊗n.
- 2.
This condition is required to avoid a coordinate singularity at r = 0 which would otherwise result in an unphysical, infinite velocity at the tube axis.
- 3.
The O(𝜖 2) term in (2.21) may be interpreted to mean “terms of typical size 𝜖 2 and smaller”.
- 4.
This has been demonstrated for elastic tubes by Flaherty et al. [5], who also calculated the buckled tube states.
- 5.
This is required to avoid a singularity on the pipe axis. Compare with the calculation for Poiseuille flow in a circular tube in Sect. 2.3.1.1.
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Blyth, M.G., Morris, R.J. (2018). Fluid Transport in Plants. In: Morris, R. (eds) Mathematical Modelling in Plant Biology. Springer, Cham. https://doi.org/10.1007/978-3-319-99070-5_2
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DOI: https://doi.org/10.1007/978-3-319-99070-5_2
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