Agriculture Reference
In-Depth Information
Once both diameter D and velocity V of impacting drops are known, any physical
quantity X , such as the momentum, impact force or kinetic energy of these drops can
be calculated with the expression:
D β V γ
X =
α
(16.2)
- 3
For drop momentum,
α
=
ρ
π
/6,
β
= 2,
γ
= 1 with
ρ
w water density in kg m ; for the
w
impact force,
α
of the order of
ρ
w
π
/12,
β
= 2,
γ
= 2; for kinetic energy,
α
=
ρ
w
π
/12,
β
= 2. At terminal velocity, using Ulbrich's function for V(D) (Fig. 16.2b),
this expression becomes X =
= 3,
γ
D β′ with
= 0.81 γ
. These
parameters can be used for scaling variables characterising splash droplet production
(volume, horizontal or vertical distance, kinetic energy of droplets, etc).
α′
α′
α
and
β′
=
β
+ 0.67
γ
16.3.2 Mechanics of splashing and trajectories of splash droplets
By solving the equation of motion (Macdonald and McCartney, 1987; Allen,
1988), the trajectories of splash droplets can be modelled, provided that the
relationship C D ( Re ) is known and the initial conditions of the trajectory (ejection
angle and velocity) are given. Classical Newtonian dynamics can provide an
adequate conceptual framework to simulate distances travelled by splash droplets,
with most of the discrepancies arising from the variability of initial conditions. For
example, in strictly defined conditions with drops falling vertically onto a 1 mm-
deep film of water, a narrow range of droplet ejection angles between 45 and 75°
was observed, but there was a wide range of ejection speeds between 1 and 4 m s -1
(Allen, 1988). Excellent experimental work done by Macdonald and McCartney
(1988) illustrates the relationship existing between initial ejection speed and angle
of ejection for splash droplets on bean leaves. Since the pioneering work of
Gregory et al . (1959), most work on the horizontal distance travelled by splash
droplets has been done under windless rain conditions. Field experiment results on
splash dispersal of conidia of Mycocentrospora acerina on caraway show that
turbulence contributes to the transportation of splash-dispersed spores at least up
to about 10 m (Evenhuis et al., 1997). In the field with a prevailing wind direction,
distances travelled by splash-dispersed spores can be greater by an order of
magnitude than in controlled conditions. In the spread of the anthracnose disease
on the tropical pasture legume Stylosanthes scabra, , dispersal of Colletotrichum
gloeosporioides conidia by rain-splash including both primary splashes and re-
splash is characterized by half-distances of about 1-10 m in the field in
comparison to 5-15 cm in still air (Pangga et al., 2004). Efforts to study wind-
driven rain were made by soil physicists (Erpul et al ., 2004) investigating the
splash saltation process in which particles are lifted by impacting raindrops and
subsequently transported by wind shear. Knowing that the average velocity of the
splash saltation of soil particles ranges between 3 and 7 ms -1 depending on wind
velocity, such physical processes are expected to be of crucial importance for
spore dispersal by rain-splash.
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