Ostwald ripening theory

Kabalnov, A.S. Shchukin, E.D. Ostwald ripening theory applications to fluorocarbon emulsion stability. Adv. Colloid Interf. Sci. 1992, 38, 69-97. 

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. 

Kabalnov, A. S. and Shchukin, E. D. 1992. Ostwald ripening theory Applications to fluorocarbon emulsion stabihty. Adv. Colloid Interface Sci. 38 69—97. 

Vengrenovitch RD (1982) On the Ostwald ripening theory. Acta Metall 30 1079-1086... 

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. 

An analogy may be drawn between the phase behavior of weakly attractive monodisperse dispersions and that of conventional molecular systems provided coalescence and Ostwald ripening do not occur. The similarity arises from the common form of the pair potential, whose dominant feature in both cases is the presence of a shallow minimum. The equilibrium statistical mechanics of such systems have been extensively explored. As previously explained, the primary difficulty in predicting equilibrium phase behavior lies in the many-body interactions intrinsic to any condensed phase. Fortunately, the synthesis of several methods (integral equation approaches, perturbation theories, virial expansions, and computer simulations) now provides accurate predictions of thermodynamic properties and phase behavior of dense molecular fluids or colloidal fluids [1]. 

C. Wagner Theory for the Coarsening of Solid Precipitates Caused hy Ostwald Ripening. Z. Elektrochem. 65, 581 (1961). 

Although the above derivation is for crystals, the theory is also applicable to bubble size distribution. In addition to the above four assumptions, the other conditions for its application include (v) no Ostwald ripening, which would modify CSD, and (vi) no coalescence of bubbles. 

P.W. Voorhees and M.E. Glicksman. Solution to the multi-particle diffusion problem with application to Ostwald ripening—I. Theory. Acta Metall., 32(11) 2001—2011, 1984. 

V.A. Snyder, J. Alkemper, and P.W. Voorhees. The development of spatial correlations during Ostwald ripening A test of theory. Acta Materialia, 48(10) 2689-2701, 2000. 

Classical theories of emulsion stability focus on the manner in which the adsorbed emulsifier film influences the processes of flocculation and coalescence by modifying the forces between dispersed emulsion droplets. They do not consider the possibility of Ostwald ripening or creaming nor the influence that the emulsifier may have on continuous phase rheology. As two droplets approach one another, they experience strong van der Waals forces of attraction, which tend to pull them even closer together. The adsorbed emulsifier stabilizes the system by the introduction of additional repulsive forces (e.g., electrostatic or steric) that counteract the attractive van der Waals forces and prevent the close approach of droplets. Electrostatic effects are particularly important with ionic emulsifiers whereas steric effects dominate with non-ionic polymers and surfactants, and in w/o emulsions. The applications of colloid theory to emulsions stabilized by ionic and non-ionic surfactants have been reviewed as have more general aspects of the polymeric stabilization of dispersions. ... 

This process was first recognized by Ostwald and is known as Ostwald ripening. The mathematical details were worked out independently by Lifshitz and Slyozov and by Wagner ° and is known as the LSW theory. However, this theory is based on a mean field approximation and is restricted to low volume fraction systems. Voorhees and coworkers extended the LSW theory to finite volume fraction systems and conducted a series of flight experiments designed to test this and similar theories. ... 

Ratke, L. Uffelmann, D. Bender, W. Voorhees, P.W. Theory of Ostwald ripening due to second-order reaction. Scripta Metall. et Mater. 1995, 33, 363. 

The quantity (2 y V / RT) is termed the characteristic length, and has an order of 1 nm or less, indicating that the difference in solubihty of a 1 pm droplet is of the order of 0.1%, or less. In theory, Ostwald ripening should lead to the condensation of all droplets into a single drop however, this does not occur in practice as the rate of growth decreases with increases in droplet size. 

Ostwald ripening can be quantitatively assessed from plots of the cube of the radius versus time t (the Lifshitz-Slesov-Wagner LSW) theory [18,19],... 

Ostwald ripening is observed when the substance of the emulsion droplets (we will call it component 1) exhibits at least minimal solubility in the continuous phase, p. As discussed above, the chemical potential of this substance in the larger droplets is lower than in the smaller droplets see Equation 5.115. Then a diffusion transport of component 1 from the smaller toward the larger droplets will take place. Consequently, the size distribution of the droplets in the emulsion will change with time. The kinetic theory of Ostwald ripening was developed by Lifshitz and Slyozov, Wagner, and further extended and applied by other authors. " The basic equations of this theory are the following. 

The LSW theory dealing with Ostwald ripening [50,51] is, strictly speaking, valid for the case of immobile oil droplets when the molecular diffusion is the only mechanism of mass transfer. Under these circumstances, the contributions of molecular and convective diffusion are related by the Peclet number (Npe) ... 

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