Segregation solution

C. W. White, Segregation, Solute Trapping, and Supersaturated Alloys... 

Abrupt changes in the concentration of segregating solute were first observed in experimental studies of carbon segregation in interstitial metal-carbon alloys by Hamilton and Blakely . More recently, such transitions have also been observed in substitutional Cu-... 

Segregated solute concentration profile c(x) across boundary as a function of increasing boundary velocity v (the x axis is perpendicular to the boundary). cXL is the solute concentration in the adjoining crystals, (b) Boundary velocity vs. pressure, P, on boundary as a function of increasing cXL. (c) In v vs. 1/T as a function of increasing cXL. (d) In v vs. In cXL as a function of increasing P. From Cahn [10],... 

The finite volume methods have been used to discretised the partial differential equations of the model using the Simple method for pressure-velocity coupling and the second order upwind scheme to interpolate the variables on the surface of the control volume. The segregated solution algorithm was selected. The Reynolds stress turbulence model was used in this model due to the anisotropic nature of the turbulence in cyclones. Standard fluent wall functions were applied and high order discretisation schemes were also used. 

It lends itself to a segregated solution algorithm, thereby offering extremely efficient memory management, since the equations are linearized and sets of equations for each dependent variable are decoupled. 

The moments of the segregating solution with the continuous initial NDF can be computed analytically from Eq. (C.7) ... 

Figure C.l. Examples of moments found for segregating solution in Eq. (C.13) with = 1/2.

To summarize, the effects of micromixing are important in principle, but for thin fluids and not extremely sensitive reactions, are of a lesser order of magnitude effect than the macromixing. Therefore, the simple-to-use segregation solution, Eq. 12.4-1, 2, almost always can be utilized to predict conversions without actually knowing the real details of the micromixing. For those cases, such as combustion, where extremely fast reactions occur, some of the population balance methods to be described later can provide a general method of attack. 

Both of these segregation phenomena can contribute to solute segregation that occurs over a longer distance from the boundary than expected from pure equilibrium considerations. Indeed, many measured segregation solute profiles near boundaries extend into grains at a greater distance than expected from equilibrium vacancy consideration. If such segregation affects corrosion tendencies, then IGC can occur. 

The boundary mobility Mb is determined by the difiusion coefficient Da for the atomic migrates across the grain boundary of the pure material, which is called intrinsic boundary mobility. In ionic solids, because both cations and anions could diffuse, Da is the difiusion coefficient of the species that are rate-limiting or lowest. In real ceramics, various drag forces, such as segregated solutes, inclusions, pores, and second-phase films, can be applied to the grain boundary. As a result, experimental boundary mobility is lower than the Mb given by Eq. (8.30) in most cases. 

This equation indicates that the presence of dopants is the most effective way to reduce the boundary mobUily if the diffusion coefficient of the rate-limiting species Db is low and the segregated solute concentration QCoo is high. 

The drag force exerted by the segregated solutes against the boundary movement, Ff, is expressed as... 

The boundary mobility Mi, depends on the diffusion coefficient Da for the atomic jumps across the boundary of the pure material and is termed the intrinsic boundary mobility. Eor an ionic solid, in which both cations and anions must diffuse. Da represents the diffusion coefficient of the rate-limiting (or slowest) species. In ceramics, the experimentally determined boundary mobility is rarely as high as M , given by Eq. (9.30) because as described later, segregated solutes, inclusions, pores, and second-phase films can also exert a drag force on the boundary. 

McLean (68) showed that the segregated solute concentration at the grain boundary Cgb is related to the solute concentration in the lattice Co by ... 

Liquid film governing equations are solved using the segregated solution procedure, where the two equations are separately solved and coupling is recovered through the iterative procedure. 

The result of the discretization process is a finite set of coupled algebraic equations that need to be solved simultaneously in every cell in the solution domain. Because of the nonlinearity of the equations that govern the fluid flow and related processes, an iterative solution procedure is required. Two methods are commonly used. A segregated solution approach is one where one variable at a time is solved throughout the entire domain. Thus, the x-component of the velocity is solved on the entire domain, then the y-component is solved, and so on. One iteration of the solution is complete only after each variable has been solved in this manner. A coupled solution approach, on the other hand, is one where all variables, or at a minimum, momentum and continuity, are solved simultaneously in a single... 

Freckles are chains of equiaxed grains which appear on the surface of some cast metals (see Fig. 7.10) and are regions enriched in all but the inversely segregated solute,It has been shown that these are the result of fast flowing liquid jets in the partly solidified zone which are driven by density inversions produced Ity thermal and... 

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