1. The document analyzes the kinetic stability of an oil-in-water nanoemulsion system using nanoparticle tracking analysis and principal component analysis to model particle growth via Ostwald ripening. 2. It finds that the rate of particle growth at high dilution is slow, indicating kinetic stability conferred by surface-active agents. 3. Using the particle growth rate and established equations, it estimates the minimal solubility of castor oil in the complex system to be 0.0134 kg/L, around 10 times greater than literature values for pure castor oil due to surfactant effects.

1. 1. Tadros, T., Izquierdo, P., Esquena, J., & Solans, C. (2004, May 20). Formation and stability of
nano-emulsions. Advances in Colloid and Interface Science, 108-109, 303-318.
doi:10.1016/j.cis.2003.10.023
2. Taylor, P. "Ostwald Ripening in Emulsions: Estimation of Solution Thermodynamics of the
Disperse Phase." Advances in Colloid and Interface Science 106 (2003): 261-85. National Center
for Biotechnology Information. 1 Dec. 2003.
3. Fluid Characteristics Chart Table Reference. (n.d.). Retrieved from
http://www.engineersedge.com/fluid_flow/fluid_data.htm
4. Da Silva, N. D., Batistella, C., Filho, R.M., Maciel, M.R.W. (n.d.). Determination of Castor Oil
Molecular Weight by Vapour Pressure Osmometry Technique. Retrieved from
https://www.researchgate.net/publication/267263370_Determination_of_Castor_Oil_Molecular_W
eight_by_Vapour_Pressure_Osmometry_Technique
5. Than, P., Preziosi, L., Josephl, D., & Arney, M. (1988). Measurement of interfacial tension between
immiscible liquids with the spinning road tensiometer. Journal of Colloid and Interface Science,
124(2), 552-559. doi:10.1016/0021-9797(88)90191-9
DISCLAIMER: This scientific publication reflects the views of the authors
and should not be construed to represent FDA’s views or policies
A model was developed to estimate the minimal solubility
of an oil in a complex water-based system using
NTA/PCA and classical diffusion-limited LSW theory. In
this system, the solubility of castor oil was estimated to
be 0.0134 kg/L. The use of a Wilhelmy plate could
provide a more accurate estimate of the interfacial
energy of the complex system. The rate of ripening was
shown to be an insignificant factor in the release of the
lipophilic drug inside an O/W nanoemulsion. Additionally,
the partition coefficient was found to be > 4. Finally,
despite extreme conditions, NTA demonstrated the
kinetic stability of the system, as Ostwald Ripening
occurs slowly in stabilized nanoemulsion systems.
Ostwald Ripening Kinetics Determined by Nanoparticle Tracking Analysis for the Study of
Nanoemulsion System’s Drug Release Mechanisms
Patrick Buoniconti1, Vasanthakumar Sekar2, Xiaoming Xu2
1. University of Virginia,
2. Division of Product Quality Research, CDER/OPQ/OTR, FDA
In the nanometer range, oil in water (O/W) nanoemulsions may
exhibit thermodynamic instability under physiological dilution
because the surface area to volume ratio and the Laplace
pressure of the oil globules are high at the nano-scale. The net
effect is a strained interface between the oil globules and water
phase that works to increase the average size of the oil globule.
This change is commonly due to Ostwald Ripening in
nanoemulsion systems, and is characterized by a decrease in oil
globule concentration as the number average radius cubed
increases linearly with time. The rate of this effect is analyzed
using Nanoparticle Tracking Analysis (NTA) and Principle
Component Analysis (PCA) to estimate its contribution to the
solubilization and uptake of the active ingredient in-vivo, and
partitioning of the lipophilic molecule is also examined.
PURPOSE
Dilutions of a water based ophthalmic emulsion were prepared
and the average particle size and concentration were measured
using Nanoparticle Tracking Analysis (NTA) and principal
component analysis (PCA). The kinetics of particle growth are
modeled by the Ostwald Ripening phenomenon described in
diffusion-limited Lifshitz, Slyozov, & Wagner (LSW) theory and
experimentally determined as the growth rate of the number
average globule radius cubed. PCA was used to ensure that only
the oil globule radius (purple peak) was exclusively considered in
the model. To exaggerate the impact of this phenomenon in
comparison to in-vivo conditions, the LSW zero volume fraction
condition was satisfied by determining the rate of ripening at high
dilution (75kx). Further, stronger instability was coaxed by testing
with 10mM 1x PBS dilution. The partition coefficient was
calculated by allowing the active ingredient to equilibrate between
20 mL of castor oil saturated in water and 20 mL of water
saturated in castor oil, and analyzing the subsequent HPLC data.
METHODS
The experimental rate of ripening was determined to be 4863.1
nm3/hour using the 75kx slope. From this an estimate for castor
oil’s minimal solubility in water at 20°C was derived using
Equations 3 through 5. The diffusion coefficient (D) was
calculated using Equation 3, a modified Stokes-Einstein equation
for a dilute nonelectrolyte in an aqueous environment. Other
parameters were obtained from the literature. The solubility of
castor oil was calculated to be 0.0134 kg/L in the complex
nanoemulsion system, about 10 times greater than the
inequality listed in literature (<.001 kg/L) for pure castor oil. Of
note, the interfacial energy used did not account for the
surfactants in the system. It is anticipated that with a truer value
for the interfacial tension of the complex system, a more accurate
solubility could be obtained. Additionally, after dilution with 10mM
1x PBS, a similar rate of growth was observed despite extreme
conditions. Finally, the partition coefficient was determined to be
greater than four. From this, a dilution curve was obtained.
RESULTS
RESULTS
CONCLUSION
REFERENCES
1) Particle size distribution and concentration will change to reduce surface area to volume ratio
2) Surface active agents confer kinetic stability by lowering the interfacial energy, creating a metastable state
3) The metastable state will be characterized by a measurably slow number average oil globule growth rate
4) The slow rate will suggest that Ostwald Ripening is not the primary release mechanism
5) Dilution testing of such nanoemulsion systems can be reliably performed due to negligible rate of ripening
HYPOTHESIS:
Solubility Equation
75kx Dilution:
Concentration
decreasing with
time and radius
slowly increasing
(1)
(2)
(4)
(5)
𝐷 =
𝑥,𝑦2
4𝑡
𝐷 =
𝑘 𝑏 𝑇
6𝜋 𝜂 𝑟ℎ𝑦𝑑𝑟𝑜𝑑𝑦𝑛𝑎𝑚𝑖𝑐
𝑑 𝑅𝑎𝑑𝑖𝑢𝑠 𝑡
3
𝑑𝑡
=
8 D γ 𝑐∞ M
9 ρ2 𝑅𝑇
𝐷 =
7.4E−12 (2.6∗m).5 T
η 𝑣 2
.6
𝑑 𝑅𝑎𝑑𝑖𝑢𝑠 𝑡
3
𝑑𝑡
= 4863.1
(3)
𝑐∞ =
9 ρ2
𝑅𝑇
8 D γ M
* 4863.1 = 0.0134 kg/L
y = -629412x + 2E+07
R² = 0.7831
2.1E+07
2.2E+07
2.3E+07
2.4E+07
2.5E+07
2.6E+07
0 1 2 3 4 5
Concentration(particles/mL)
Time (Hours)
Identification of
Second Peak
<R^3>
Increasing with
time; stronger
correlation due
to greater
sensitivity
75kx Dilution:
Concentration
decreasing with
time
y = 4863.1x + 74757
R² = 0.8442
0.0E+00
2.0E+04
4.0E+04
6.0E+04
8.0E+04
1.0E+05
1.2E+05
0 1 2 3 4 5
AverageMeanRadius^3
(nm^3)
Particle Size Characterization Ostwald Ripening Data
Partition Coefficient
DLVO Theory:
Ostwald Ripening:
Time (Hours) Dx50 (Radius) Concentration (particles / mL)
0 42.56 2.33E+07
0.5 42.90 2.43E+07
1 42.71 2.43E+07
1.5 42.70 2.30E+07
2 43.26 2.33E+07
2.5 44.94 2.23E+07
3 45.16 2.23E+07
4 44.92 2.20E+07
4.5 46.27 2.10E+07
Neither carbomer nor agglomerate:
• Carbomer control particle concentration at
50x was around 200 particles/mL, a
negligible contribution when extrapolated to
75kx
• Agglomerates ruled out by DLVO Theory (top
right) after experiencing similar results in
ionic media
Dilution of
Nanoemulsion vs
Equilibrium % of
XX in Water
Calculated from
two trials at 36
hours
0
20
40
60
80
100
1 10 100 1000 10000 100000 1000000
% XX in Water at Equilibrium
Log P 4.62 ± .03
Log P1 4.64
Log P2 4.60