Rate of Ostwald ripening

The rate of Ostwald ripening depends on the size, the polydispersity, and the solubility of the dispersed phase in the continuous phase. This means that a hydrophobic oil dispersed as small droplets with a low polydispersity already shows slow net mass exchange, but by adding an ultrahydrophobe , the stability can still be increased by additionally building up a counteracting osmotic pressure. This was shown for fluorocarbon emulsions, which were based on perfluo-rodecaline droplets stabilized by lecithin. By adding a still less soluble species, e.g., perfluorodimorphinopropane, the droplets stability was increased and could be introduced as stable blood substitutes [6,7]. 

Here, is the molar volume of the solute, y is the interfacial tension, (oo) is the solubility of the solute in the continuous phase for a droplet with infinite cur-vamre (a planar interface), and S r) is the solubility of the solute above a curved interface of radius r. Hence, there is a higher concentration of dissolved lipid molecules around a small droplet than around a larger one. Solubilized lipid molecules will move from the smaller droplets to the larger droplets because of this concentration gradient. Once steady state has been achieved, the rate of Ostwald ripening oa is given by (88). 

Equation (10.63) shows that the larger the difference between Tj and tj, the higher the rate of Ostwald ripening. 

All nanoemulsions showed an increase in droplet size with time, as a result of Ostwald ripening. Figure 14.11 shows plots of versus time for all the nanoemulsions studied. The slope of the Hnes gives the rate of Ostwald ripening CO (in m s ), and this showed an increase from 2 to 39.7x 10 m s as the surfactant concentration was increased from 4% to 8 wl%. This increase may have been due to a number of factors ... 

As expected from the Ostwald ripening theory [LSW theory, Eq. (14.16)], the rate of Ostwald ripening decreases as the oil solubihty decreases. Isohexadecane has a rate of Ostwald ripening similar to that of dodecane. 

In contrast to the electrostatic stabilization provided by SDS [40,41 ], the nonionic surfactant NP-40 imparts a steric repulsion force between two interactive hairy particles [42, 43]. Stable St mini-emulsions with NP-40 in combination with various coemulsifiers (CA, HD, DMA or SMA) were prepared and characterized [ 13]. The rate of Ostwald ripening for these mini-emulsions decreases in the series CA>DMA>HDsSMA. 

For a polydisperse emulsion with some solubility for the oil phase, the smaller droplets disappear by oil diffusion and become deposited on the larger ones. This process may be significantly reduced by proper choice of the interfacial layer. The lower the interfacial tension, then the lower the rate of Ostwald ripening. More important is the Gibbs elasticity e, which arises from interfacial tension gradients ... 

As mentioned above, the best procedure to follow Ostwald ripening is to plot versus time, following Eq. (6.68). This gives a straight line, from which the rate of Ostwald ripening can be calculated. In this way one can assess the effect of the various additives that may reduce Ostwald ripening, e.g. addition of highly insoluble oil and/or an oil-soluble polymeric surfactant. 

Theoretically, Ostwald ripening should lead to condensation of all particles into a single one. However, this does not occur in practice since the rate of Ostwald ripening decreases with time. For two particles with radii ri and t2 (ri < 72),... 

Eigure 1.29 shows the variation of r with time t for 20 80 0/W nanoemulsions at two C12EO4 concentrations prepared by the PIT method. It can be seen from Fig. 1.28 that the emulsion containing the higher surfactant concentration gives a higher rate of Ostwald ripening. This may be due to solubilization of the oil by the surfactant micelles. 

Further evidence for Ostwald ripening was obtained by using a more soluble oil, namely a branched hexadecane (Arlamol HD). The results are shown in Fig. 1.31 for nanoemulsions prepared using 4% surfactant. It can be seen that the more soluble oil (Arlamol HD) give a higher rate of Ostwald ripening when compared with a less soluble oil such as hexadecane. 

The rate of Ostwald ripening is 1.1 x 10 and 2.4 x 10 °m s at 1.6 and 2.4 /o 1NUTEC SP1 respectively. These rates are 3 orders of magnitude lower than those obtained using a nonionic surfactant. Addition of 5 % glycerol was found to decrease the rate of Ostwald ripening in some nanoemulsions. 

Equation (3.52) shows that the larger the difference between r and tj, the higher the rate of Ostwald ripening. The latter can be quantitatively assessed from plots of the cube of the radius versus time t [99,101,102],... 

According to the Lifshitz-Slezov-Wagner (LSW) theory [15-18], the rate of Ostwald ripening (Ro) can be expressed as... 

Figure 5.1. Rate of Ostwald ripening for emulsions as a funotion of the solubility of the constituent in water. The constituents of the oil phase include />alkanes (n = 9-16) [19] and some common monomers. St, BA, and MMA represent styrene, n-butyl acrylate, and methyl methacrylate, respectively. The data of the solubility of monomers in water were used to estimate the Ostwald ripening rate of the homogenized monomer droplets via the extrapolation method.

Based on the extended LSW theory, the rate of Ostwald ripening for the costabilizer containing miniemulsion can be calculated by the following equation [15] ... 

Neglecting the effects of molar volume and interfacial tension, the following empirical equation can be used to reasonably predict the overall rate of Ostwald ripening for the monomer emulsion in the presence of costabiUzer [18] ... 

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