Production Practices and Quality Assessment of Food Crops. Vol. 1

52 M. Génard and F. Lescourret
4.1.1.1. SWAF principles
The change in the amount of water within the fruit with time (dW water/dt) is the
algebraic sum of the water income from xylem (U x) and phloem (U p) minus the water
outcome due to fruit transpiration (T f).
dW water = Ux + U p – T f (1)
dt
Fruit transpiration leading to mass loss is assumed to be proportional to the fruit
area and to surface conductance to water vapour (Lescourret et al., 2001), and to
be driven by the difference of relative humidity in the air-filled space of the fruit
and in the ambient atmosphere.
Using the subscripts x, p and f for xylem, phloem and fruit variables respectively,
the total phloem and xylem flows into the fruit tissues are:
U x = A x L x [P x – P f – σ x (p x – p f)]
and (2)
U p = A p L p [P p – P f – σ p (p p – p f)]
L is the hydraulic conductivity coefficient of vascular network membranes, P and
p are the hydrostatic and osmotic pressures and σ is a measure of impermeability
of the membrane to the solute, ranging from 1 (fully impermeable membrane) to
0. It is known that p x = 0 and σ x = 1 (Nobel, 1974). A is the vascular network
area assumed to be proportional to the fruit area. The water potentials in the xylem
and phloem are assumed equal to the water potential measured in the stem, �.
This gives P x = � and P p = � + p p.
The change in the amount of dry matter (dW dry/dt) is the difference of assimilate
uptake from phloem (U dry) and dry matter loss due to the fruit respiration (R f).
dW dry = Udry – R f (3)
dt
Dry matter loss due to fruit respiration is divided into growth respiration, which
is proportional to the rate of dry matter income, and maintenance respiration,
which is proportional to dry mass (Thornley and Johnson, 1990).
If s p < 1, part of the sugar can be transported from the phloem to the fruit by mass
flow. Total uptake of carbohydrates is
U dry = U a + (1 – σ p)
( ) Cp + Cf 2
U p
where U a is the rate of uptake due to active or facilitated transport obeying the
Michaelis-Menten equation and C p and C f are the mean concentrations of the solute
in the phloem and the fruit respectively.
Osmotic pressure is calculated from the sugar content according to Nobel (1974).
(4)