Phase geometrical stability

These fascinating bicontinuous or sponge phases have attracted considerable theoretical interest. Percolation theory [112] is an important component of such models as it can be used to describe conductivity and other physical properties of microemulsions. Topological analysis [113] and geometric models [114] are useful, as are thermodynamic analyses [115-118] balancing curvature elasticity and entropy. Similar elastic modulus considerations enter into models of the properties and stability of droplet phases [119-121] and phase behavior of microemulsions in general [97, 122]. 

For the phase stability analysis we follow the method given by Kanamori and Kakehashi of geometrical inequalities and compute the antiphase boundary energy defined by... 

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

Geometrical shape is by no means the only molecular property which governs phase stability and behaviour and there are numerous examples of cases in which molecules of similar shape form condensed phases with very different properties. These differences are attributed to subtle chemical... 

The importance of the geometrical factor in determining the stability of these phases has been pointed out (Pearson 1972). In a simplified description, Laves phases AM2 of the MgCu2 type may be presented as cubic face-centred packing of large spheres A which form tetrahedral holes that are occupied by tetrahedra of smaller spheres M. The ideal value of the radius ratio rA/rM is 1.225. The values experimentally observed for the various Laves types range from 1.05 to 1.7. 

Some aspects of the mentioned relationships have been presented in previous chapters while discussing special characteristics of the alloying behaviour. The reader is especially directed to Chapter 2 for the role played by some factors in the definition of phase equilibria aspects, such as compound formation capability, solid solution formation and their relationships with the Mendeleev Number and Pettifor and Villars maps. Stability and enthalpy of formation of alloys and Miedema s model and parameters have also been briefly commented on. In Chapter 3, mainly dedicated to the structural characteristics of the intermetallic phases, a number of comments have been reported about the effects of different factors, such as geometrical factor, atomic dimension factor, etc. on these characteristics. 

Viscosity is an important physical property of emulsions in terms of emulsion formation and stability (1, 4). Lissant (1 ) has described several stages of geometrical droplet rearrangement and viscosity changes as emulsions form. As the amount of internal phase introduced into an emulsion system increases, the more closely crowded the droplets become. This crowding of droplets reduces their motion and tendency to settle while imparting a "creamed" appearance to the system. The apparent viscosity continues to increase, and non-Newtonian behavior becomes more marked. Emulsions of high internal-phase ratio are actually in a "super-creamed" state. 

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