Nanoemulsion stability: experimental evaluation of the flocculation rate from turbidity measurements

The coalescence of liquid drops induces a higher level of complexity compared to the classical studies about the aggregation of solid spheres. Yet, it is commonly believed that most findings on solid dispersions are directly applicable to liquid mixtures. Here, the state of the art in the evaluation of the flocculation rate of these two systems is reviewed. Special emphasis is made on the differences between suspensions and emulsions. In the case of suspensions, the stability ratio is commonly evaluated from the initial slope of the absorbance as a function of time under diffusive and reactive conditions. Puertas and de las Nieves (1997) developed a theoretical approach that allows the determination of the flocculation rate from the variation of the turbidity of a sample as a function of time. Here, suitable modifications of the experimental procedure and the referred theoretical approach are implemented in order to calculate the values of the stability ratio and the flocculation rate corresponding to a dodecane-in-water nanoemulsion stabilized with sodium dodecyl sulfate. Four analytical expressions of the turbidity are tested, basically differing in the optical cross section of the aggregates formed. The first two models consider the processes of: a) aggregation (as described by Smoluchowski) and b) the instantaneous coalescence upon flocculation. The other two models account for the simultaneous occurrence of flocculation and coalescence. The latter reproduce the temporal variation of the turbidity in all cases studied (380≤[NaCl]≤600 mM), providing a method of appraisal of the flocculation rate in nanoemulsions.

Scattering by two rayleigh-debye spheres

The Rayleigh-Gans approximation theory is applied to the problem of scattering by two neighboring spherical particles. For simplicity, we have examined in detail the case of two identical uniform spheres. Differential intensities for any arbitrary location of the particle pair relative to the incident wave, mean intensities, and mean scattering cross sections for randomly oriented particles are considered. The results show good agreement with the exact theory. Some numerical results are presented for the particular case of touching spheres (dumbbells), which are either at random, or are at specific, orientation relative to the direction of polarization of the incident wave. It is observed that for small spheres at random orientation, the scattering cross section is four times the value for that of a single sphere. This factor is two for large particles. We also observe that both the intensity and dissymmetry patterns for two spheres are totally different from the single particle ones.