Ripening, Ostwald

Ostwald ripening consists of a diffusive transfer of the dispersed phase from smaller to larger droplets. Ostwald ripening is characterized by either a constant volume rate [4,5] (diffusion-controlled ripening) or a constant surface rate 22 [6] (surface-controlled ripening), depending on the origin of the transfer mechanism  

If the ripening is controlled by diffusion across the continuous phase, then the cube of the diameter increases linearly with time (a = 3) and the ripening rate S23 can be derived using the Lifshitz and Slyozov theory [2,3]  

An emulsion that is, for instance, stable over many years at low droplet volume fraction may become unstable and coalesce when compressed above a critical osmotic pressure 11. As an example, when an oil-in-water emulsion stabilized with sodium dodecyl sulfate (SDS) is introduced in a dialysis bag and is stressed by the osmotic pressure imposed by an external polymer solution, coarsening occurs through the growth of a few randomly distributed large droplets [8]. A microscopic image of such a growth is shown in Fig. 5.1. 

At a microscopic scale, a single coalescence event proceeds through the nucleation of a thermally activated hole that reaches a critical size, above which it becomes unstable and grows [29]. We shall term E(r) the energy cost for reaching a hole of size r. A maximum of E occurs at a critical size r, E r ) = Ea being the activation energy of the hole nucleation process (Fig. 5.2). 

Other experiments performed by Bergeron [34] on air foams stabilized with ionic surfactants reveal that the so-called Gibbs or dilatational elasticity e may play an important role in the coalescence process. The Gibbs elasticity measures the variation of surface tension yi t associated to the variation of the surfactant surface concentration F  

Ostwald ripening, referred to as isothermal distillation or molecular diffusion in some texts, is the result of the solubility differences of, say, oil contained within drops of differing sizes. According to the Kelvin equation, the solubility of a substance in the form of spherical particles increases with decreasing size  

The mass transport of oil molecules in emulsions containing aqueous micelles, in which there is a competition between solubilisation of oil into micelles and transfer of oil from small emulsion drops to larger ones, has been studied by McClements et The experiments have involved preparing stock emulsions 

Higuchi and Misra were the first to show that if one of the components of a dispersed phase is completely insoluble in the continuous phase, then even small amounts of such a substance may stop the Ostwald ripening in the system. The reason for this is as follows. In a two-component dispersed phase system, the mass transfer of the more soluble component from small to larger drops caused by the difference in the Laplace pressures changes the composition of the drops. Namely, it increases the concentration of the poorly soluble component in the small drops and decreases it in the larger ones. According to Raoult s law, this results in a compensation of the difference in chemical potentials of the more soluble component caused by the difference in capillary pressures. When the capillary and concentration effects completely compensate, the mass transfer terminates and the drops come to equilibrium . This equilibrium implies the equality of the chemical potentials of the major component in all of the drops of the polydisperse emulsion. Such an equality is unattainable for the second component if its solubility in the continuous phase is truly zero. Kabalnov et have considered two cases as 

Experiments confirm the decrease in the ripening rate on addition of a poorly soluble component to the dispersed phase. Buscall et alP examined emulsions of SDS after adding long chain alkanes. Kabal nov et al showed that eqn. (1.22) was well obeyed for emulsions of SDS and hexane to which small quantities of the alkanes octane to hexadecane were added. Recently, Weers and Arlauskas have provided the first experimental evidence that molecular diffusion in two-component mixtures leads to an increase in the mole fraction of the less soluble component in the smaller drops. Using the technique of sedimentation field-flow fractionation coupled with gas chromatography, the disperse phase composition can be determined for monosized drop fractions. Evidence is also provided for the development of bimodal distributions at low volume fractions of the less soluble component, in excellent agreement with the above predictions. Their system was perfluorooctyl bromide (plus perfluorododecyl bromide) as oil stabilised by egg yolk phospho-lipid.2  

Greenwood (1956) described the behaviour of an assembly of n groups of particles undergoing Ostwald ripening by solution-diffusion controlled transfer between particles according to a general relationship 

In the total particle size distribution, some particles of small diameter decrease in radius, and those in the larger diameter range increase in radius during Ostwald ripening. There will therefore be a radius at which particles neither decrease nor grow in size and if r is this critical radius 

The problem in the solution of Tick s law when applied to dris problem lies in the difficulty in expressing analytically the A jx ratio for each pair of particles in the dispersion. Greenwood provided a limiting case solution to this problem by dealing only with a dilute dispersion in which each particle supplies or receives atoms from the sunounding average concentration solution. In such a dilute dispersion, each particle can be considered to be suiTounded only by 

The graphical representation of this equation showed that the fastest growing radius in the disuibution amax is twice the mean radius, and therefore 

Wagner (1961) examined theoretically the growdr kinetics of a Gaussian particle size distribution, considering two growth mechanisms. When the process is volume diffusion controlled 

As we saw in Chapter 1 of this volume, the solubility of a solid solute in a liquid solution is an equilibrium property of the 

The equilibrium solubility refers to the solubility that would be obtained with very large particles (therefore, small surface areas). As in all thermodynamic calculations, activity coefficients should be used in nonideal solutions. 

If the crystal growth process accompanying the aging phenomenon is diffusion-controlled, it can be shown (Nyvlt et al. 1985) that the size of particle in equilibrium with the solution can be obtained from the relation 

Particles larger than r(c) will grow and particles smaller than r(c) will dissolve. 

Ostwald ripening is often important in proeesses in which crystallization is rapid and crystal sizes are small. This is especially true in a precipitation process and will be diseussed in detail in Chapter 6 of this volume. It is important to remember that the effect of Ostwald ripening is to alter the crystal size distribution with time in a suspension of erystals that is an apparent equilibrium with its saturated solution. Ostwald ripening is an important phenomena if you are concerned with obtaining fine particles or are concerned about changes in the crystal size distribution of your product prior to drying. 

Having prepared an emulsion, foam, suspension or aerosol, changes in the sizes of the dispersed droplets, bubbles or particles may begin immediately due to 

2) In the early literature, the terms atomizer and nebulizer tended to be used interchangeably, but modern practice is to reserve the term nebulizer for collision devices that contain a barrier, and an atomizer for those that do not contain a barrier. 

Several methods can be used to separate specific size fractions of droplets or particles from emulsions, suspensions and aerosols. Some of these, such as filtration, sieving, centrifugation and ultracentrifugation have been introduced in Sections 2.2 and 2.4. 

For aerosok, cascade impactors and mobility sizers can be used, as discussed in Section 2.8.1. 

The difference in chemical potential between different sized droplets was given by Lord Kelvin [35], 

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At equilibrium, crystal growth and dissolving rates become equal, and the process of Ostwald ripening may now appear, in which the larger crystals grow at the expense of the smaller ones. The kinetics of the process has been studied (see Ref. 103). 

In principle, then, small crystals should show a higher solubility in a given solvent than should large ones. A corollary is that a mass of small crystals should eventually recrystallize to a single crystal (see Ostwald ripening. Section IX-4). 

A3.3.4 LATE-STAGE GROWTH KINETICS AND OSTWALD RIPENING... 

A further problem is possible if the reinforcements are very small. Coarsening of the particles or whiskers may occur driven by Ostwald ripening, in which large particles grow through diffusional transport at the expense of smaller ones. This can be minimized by choosing matrices in which the reinforcement elements have very low solid solubilities and diffusion coefficients. Platelets, however, have been shown to be more resistant to coarsening than particles or whiskers. 

There aie a number of major indusuial problems in the operation of the steam reforming of metlrane. These include the formation of carbon on the surface of the catalyst, the sulphidation of the catalyst by the H2S impurity in commercial natural gas, and die decline of catalytic activity due to Ostwald ripening of the supported catalyst particles by migration of catalyst atoms from the smaller to tire larger particles, as the temperamre is increased. A consideration of tire thermodynamics of the principal reaction alone would suggest that the reaction shifts more favourably to the completion of the reaction as the temperature is increased. 

Figure 6.7 The model for atom transfer during Ostwald ripening, showing the flux of atoms from the smaller particle to the larger...

Figure 6.8 The change in particle size distribution which is brought about by Ostwald ripening of an initial Gaussian distribution of particle size...

An illuminating example is the effect of Ostwald ripening on pore size distribution in a sintered body, resulting from vacancy transfer from the smaller to the larger pores, where the decrease in the number and die increase in average diameter of the pores can be clearly seen. The disnibutioii curve for... 

If the pore size distribution is finally the result of Ostwald ripening, it follows that Di oc... 

The elimination of pores comes about by tire combined effects of grain growth and Ostwald ripening in the hnal stages of sintering. 

The interaction among the clusters via the common diffusion held leads in general to a coarsening of the clusters with time t. One denotes this by Ostwald ripening [58,96] (see Sec. HID). According to the Lifshitz-Slyozov theory [58] on this process, the typical cluster radius R increases as... 

S. Olive, U. Grafe, I. Steinbach. The modelling of Ostwald-ripening during non-isothermal heat treatments resulting in temperature dependent matrix solubihty of the precipitate forming elements a further development of the LSW-theory. Comput Mater Sci 7. 94, 1996. 

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