Water and Solute Permeability of Plant Cuticles: Measurement and ...

172 6 Diffusion of Non-Electrolytes
If researchers manage to distinguish between solutes in and on the leaves, the best
result of such experiment is fractional penetration during some arbitrary time after
droplet application.
Even in this case it is generally not realised that the velocity of penetration
depends on size of droplets, more precisely on the ratio droplet volume (Vdroplet)
over area of contact (Acontact) between droplet and leaf surface. The situation can be
demonstrated assuming a hemispherical droplet positioned on a leaf. This means
that the leaf is difficult to wet and the contact angle is 90 ◦ . It is assumed that
Vdroplet, Acontact P and Cdonor are constant and do not vary with time. Hence, the
droplet must not dry up. Our starting point is (2.25), which is repeated here with
appropriate subscripts:
−P× Acontact ×t
Vdroplet
= ln Cdonor
. (6.11)
C0
C0 is the initial donor concentration (t = 0) and Cdonor is the concentration at any
later time. If penetration occurs, C0 decreases with time and we want to calculate
the time needed for 50% of the dose to penetrate into the leaf, that is Cdon/C0 = 0.5
or ln Cdon/C0 = 0.693. Rearranging (6.11), we see that the half-time
t1/2 = 0.693 Vdroplet
×
P Acontact
(6.12)
depends on the volume of the droplet and the contact area. For a hemispherical
droplet Vdroplet/Acontact = (2/3)×rdroplet. We have calculated half-times for frequent
values of permeances of cuticles and droplet sizes produced by conventional spraying
equipment (Fig. 6.11). Such spherical droplets have mean diameters ranging
from 100 to 500µm, which corresponds to volumes of 0.5–65 nl.
When droplet radii increase from 33 to 133µm, half-times increase by a factor
of 1,000; and depending on permeance, half-times were in the range of minutes
to 280 h. If permeance is very high (10 −7 m s −1 ) it might be possible to maintain
Vdroplet/Acontact fairly constant, but with lower P this is impossible. Contact angles on
leaves vary greatly, and they depend on surface tension of the donor solutions. Both
factors greatly affect half-times because they affect Vdroplet/Acontact. Better wetting
leads to smaller Vdroplet/Acontact, even with constant droplet volumes, and this greatly
reduces half times.
These purely physical considerations have consequences for spray applications.
Loss of agrochemicals by rain and volatilisation can be minimised by using a larger
number of small droplets. There is a limit to this strategy because very small droplets
can be lost by drift. However, for rapid penetration it is a good strategy to deliver a
constant dose with more droplets of small size, or use higher concentrations instead
of low concentrations and large droplets.
Apart from these practical aspects, it should be clear that experiments with
small droplets are extremely difficult to analyse, and misinterpretations of cause and
effect are unavoidable. However, such experiments can be meaningful if fractional