6
A. Shaviv
During the lag period, water penetrates the granule and dissolves part of the
internal solid. The driving force for this process is the vapor pressure gradient
across the coating. The volume for the condensed vapor is limited to the voids
inside the solid core and those between the core and the coating. A possible
explanation for the lag period is the time needed to fill the internal voids of the
granule with water until a critical level is reached. Alternatively (and almost
equally), the lag can be attributed to the time needed for the establishment of a
steady state between the flux of water entering the granule and the flux of solute
leaving it. As the steady state is achieved the volume change in the granule in
assumed to be negligible.
Once a critical volume of saturated solution accumulates inside the granule,
the second stage of the constant release rate starts. The rate remains constant as
long as the saturated solution in the granule is equilibrated with the nondissolved
solid fertilizer. The constant, saturation concentration, yields a constant driving
force for fertilizer transport (concentration or pressure gradient).
When the solid fertilizer in the core is dissolved, the concentration of the
internal solution decreases due to the continuing release and the fact that water
continues to flow into the granule due to the water potential gradient driving it.
Accordingly, the driving force for the nutrient release decreases and the release
rate decays. This is the third stage of the release denoted the decay phase.
The above described conceptual model serves as the basis for the mathematical
model of release presented below.
The lag period, t', of release from a single granule is given by Shaviv et al.
(2001):
y rl
/'=_:..-_3P h I1P
(4)
where Ph = water permeability through the coating, y = void volume fraction in
the coated granule, r = granule radius, I = coating thickness and P is the osmotic
pressure in the granule.
The fractional release, g(r, I, t,) during the linear release is given by:
3P. C
g(r,l,t)
s sat (t -t'1t'~ t ~ t *
rl{>s
'
(5)
where Ps = solute permeability, Csat = saturation concentration offertilizer,
Ps = fertilizer density, and t* is the time at which the decay period begins. Finally,
the fractional release during the decay period is given by [symbols as in Eq. (5)]:
C
{3P. J
g(r,l,t)=l ;:t ex ---;f-(t-t*) ,
(6)
A. Shaviv
During the lag period, water penetrates the granule and dissolves part of the
internal solid. The driving force for this process is the vapor pressure gradient
across the coating. The volume for the condensed vapor is limited to the voids
inside the solid core and those between the core and the coating. A possible
explanation for the lag period is the time needed to fill the internal voids of the
granule with water until a critical level is reached. Alternatively (and almost
equally), the lag can be attributed to the time needed for the establishment of a
steady state between the flux of water entering the granule and the flux of solute
leaving it. As the steady state is achieved the volume change in the granule in
assumed to be negligible.
Once a critical volume of saturated solution accumulates inside the granule,
the second stage of the constant release rate starts. The rate remains constant as
long as the saturated solution in the granule is equilibrated with the nondissolved
solid fertilizer. The constant, saturation concentration, yields a constant driving
force for fertilizer transport (concentration or pressure gradient).
When the solid fertilizer in the core is dissolved, the concentration of the
internal solution decreases due to the continuing release and the fact that water
continues to flow into the granule due to the water potential gradient driving it.
Accordingly, the driving force for the nutrient release decreases and the release
rate decays. This is the third stage of the release denoted the decay phase.
The above described conceptual model serves as the basis for the mathematical
model of release presented below.
The lag period, t', of release from a single granule is given by Shaviv et al.
(2001):
y rl
/'=_:..-_3P h I1P
(4)
where Ph = water permeability through the coating, y = void volume fraction in
the coated granule, r = granule radius, I = coating thickness and P is the osmotic
pressure in the granule.
The fractional release, g(r, I, t,) during the linear release is given by:
3P. C
g(r,l,t)
s sat (t -t'1t'~ t ~ t *
rl{>s
'
(5)
where Ps = solute permeability, Csat = saturation concentration offertilizer,
Ps = fertilizer density, and t* is the time at which the decay period begins. Finally,
the fractional release during the decay period is given by [symbols as in Eq. (5)]:
C
{3P. J
g(r,l,t)=l ;:t ex ---;f-(t-t*) ,
(6)