Ostwald ripening calculation

Figure 13.14 Differences in equilibrium melting temperature for ice crystals based on Ostwald ripening calculations for an ice-sucrose solution. (From Hartel 1998a with permission.)...

In this case, d (nm) is the diameter of spherical particles. Both sets of equations are only approximations, particularly for goethite, the particles of which are often acicular. However, they do enable an estimate of the rise in solubility, as particle size drops, to be obtained (see Fig. 8.3). There is little difference between the results calculated using the two sets of equations for particles >100 nm, but for 10 nm particles there is more than an order of magnitude difference between the two equations. The higher solubility of smaller particles may lead to their transformation to larger ones via solution, a process called Ostwald ripening. 

Surface Dilational Properties. The calculations just given suggest that all foam will rapidly disappear, but several foams can be fairly persistent, and some can hardly be destroyed. Stabilization to Ostwald ripening (or to disproportionation as foam researchers usually call it) is thus possible. 

Although this system was somewhat idealized, relative to the hiPP, it is still a multicomponent system, due to the broad molecular weight distribution of the HDPE. Using some approximations (described in Reference 29), the theoretical rate constant for Ostwald ripening was calculated from Equation 12.4 and was OR = 3.6 X 10 cm s . The experimentally determined rate constant (K in Equation 12.3) was = 4.8 x 10 cm s. The agreement between the experimentally measured and the theoretically calculated rate constants is quite good. The ratio of these two rate constants is =1.3. This was taken as an indication... 

Table 12.4 Parameters for Calculation of Theoretical Rate Constants for Coarsening by Ostwald Ripening (Evaporation/Condensation) and Coalescence for HDPE (Fraction)/HPB Blend .

The frequency distribution of diameters is the most widely used way of presenting population size data. It contains useful information which aids the prediction of emulsion kinetic behavior e.g., sedimentation and diffusion are functions of droplet size. Also, one can follow flie evolution of the DSD as a function of time, the shift towards fewer/larger droplets being evidence of droplet-depletion mechanisms, such as coalescence and Ostwald ripening. From the distribution, the kinetic coefficients can be calculated, allowing prediction of how the DSD will develop (e.g., 48, 55). This is described in detail by Dukhin et al.. Chapter 4, this volume. Figure 11 shows how the addition of a demulsifier can destabilize an emulsion and bring about emulsion resolution. The example is a water-in-crude oil emulsion, the demulsifier a phenolic resin alkoxy-late. 

One of the processes by which an emulsion, like a foam, destroys itself is by Ostwald ripening the diffusion of liquid from small to large droplets. Calculate the time required for a benzene droplet to disappear when it is positioned near much larger droplets at a distance comparable to its radius. Assume droplet radii of 100 and 1000 nm. The solubility of benzene in water may be taken as 0.2% (vol/vol) the diffusion constant of benzene in water D = 10 cm s the interfacial tension of water-benzene s = 25 mN m" and the molar volume of benzene Vm = 100 cm. ... 

The DFT results for the previous addressed 16 selected processes were used to train a reactive force field (RFF) [17], from which the rates of all 544 relevant processes were calculated for the self-diffusion of gold on bare Au(lOO) surface. In order to investigate the effect of chlorine on Ostwald ripening, the explicit influence of chlorine atom on top of a gold adatom was tackled by means of DFT results for the same 16 selected processes as before. The results will be presented in Section 3.6. 

In summary, the combination of large-scale KMC simulations with DFT calculations and analytically solvable thermodynamic models yield a good agreement with experiments on two-dimensional Ostwald ripening on Ag and Au metals in a bare fcc(lOO) surface or in chlorine containing electrolytes. 

Examples of atomistic models addressing PEMFC materials s stability and aging, a) DFT modeling of surface oxide formation b) atomistic description of nanoparticle (Ostwald) ripening c) calculation of surface and bulk composition of alloyed catalyst d) change of potential as function of alloy composition. 

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. 

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

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