W/O/W EMULSION STABILITY 343 tracer m external phase 8 / / / / / / / / 5 0 i i 0 10 20 30 i i 40 50 60 time (clays) Figure 1. Appearance kinetic of the tracer in the external phase at two temperatures (25 and 40øC). zine at the end of the fabrication process (t = 0) A is the maximal value ofdihydralazine (in percent) liberated in the aqueous external phase for an infinite time k is the rate of the phenomenon, which thus characterizes the speed of the instability process and t is the time (in days) from the fabrication of the W/O/W emulsion. The percentages Pt and Po are calculated according to the following equation: where Qw is the amount of dihydralazine introduced in the primary emulsion, which thus corresponds to the maximum amount of tracer that can be entrapped, and Qt is the amount of tracer released in the external aqueous phase at time t. The preceding equations are based on the amount of tracer rather than its concentration. Indeed, amounts do not depend on changes in volumes of the inner and external phases that may appear during the monitoring of the emulsion stability. The A and k values are summarized in Table III. The stability of the studied emulsion was shown during three months at ambient temperature: parameter A values were similar through the different methods and less than 2.5%. The spectrophotometric A values compared with the chromatographic one, and confirmed that the sample treat- ment did not lead to an additional breakdown. The difference between k determined by UV or visible spectrophotometry was attributed to the delay for the in situ derivatiza- tion.

344 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS Table III Parameters of Eq. 2 Calculated for Two Temperatures of Storage (Average Values of Three Measures on Two Batches: n = 6) Standard UV Visible Temperature Parameter deviation spectrometry spectrometry HPLC 25øC A 2.19 2.34 2.18 tr^ 0.05 0.08 0.02 k 0.084 0.067 0.082 trk 0.005 0.007 0.002 40øC A 7.72 7.82 7.79 or^ O. 08 O. 08 O. 01 k 0.229 0.217 0.220 O' k O. 007 O. 007 O. O01 Both A and k values increase with temperature. The breakdown of the emulsion was both amplified (increase in A value) and accelerated (increase in k value). Thus, accel- erated stability study at 40øC can be considered as a valuable means to predict the long-dated behavior of the emulsion. However, to be valid, the accelerated study must proceed from the same phenomenon of instability as the ambient temperature stability. Consequently, the experimenter must perform a careful search of which temperature should lead to the more valuable results. In our example, the total oil film disruption was not observed at 40øC, due to the greater stability of the primary emulsion. The increase of the multiple emulsion breakdown between ambient temperature and 40øC can be attributed to the weakening of the oil barrier with temperature. Due to temperature, the oil film loosens and becomes more subject to disruption. This explains the simultaneous amplification and acceleration of the instability phenomenon. At higher temperatures, the breakdown may proceed from the stability of the oil film itself. Visual inspection of multiple emulsion stored a few weeks at 70øC shows a total breakdown. However, the phase, corresponding to the primary emulsion, appears to be solidified, which prevents the total disruption of the internal aqueous droplets. Conse- quently, even if higher values of parameters A and k can be observed at those temper- atures (70øC), the instability phenomenon is not the same as at 25 or 40øC and cannot be used for predictive means. CONCLUSION Dihydralazine was proven to be a convenient indicator for W/O/W multiple-emulsion breakdown studies. It met the well-accepted criteria of non-diffusibility, stability, and detectability. Also, the low amount of dihydralazine included in the internal phase ensures that the tracer does not compromise the emulsion stability. Indeed, it is possible to include it as tracer, jointly with active substances in the early development steps of a new formulation. Dihydralazine can be used whatever the emulsion formula is if the preliminary determination of partitioning coefficient is measured in liquid media con- taining lipophilic or hydrophilic surfactant as concentration in the emulsion formula. (A forthcoming study on this subject is in progress in our laboratory.) The consistency of