Trajectory segregation

In compositional analysis of very small precipitates, or in interface segregation studies, using a probe-hole type atom-probe, one is always faced with the fact that the probe-hole may cover both the matrix and the precipitate phases, or the interface as well as the matrix. Thus any abrupt compositional changes will be smeared out by the size of the probe-hole and also by the effect of ion trajectories. A similar uncertainty seems to exist in the compositional analysis of nitride platelets formed in nitrided Fe-3 at.% Mo alloy, aged between 450 and 600°C, where Wagner ... 

Trajectory segregation When a powder cloud is in flight, fine particles can travel farther than single large particles. For coarse particles, larger particles tend to travel the farthest. 

The segregated-flow model described by (P2) forms a basis to generate an AR. We now develop conditions for the closure of this space with respect to the operations of mixing and reaction by means of a PFR, a CSTR, or a recycle PFR (RR). Consider the region depicted by the constraints of (P2). Our aim is to develop conditions that can be checked easily for the reaction system in question so that, if these conditions are satisfied, we need to solve only (P2) for the reactor targeting problem. We will analyze these conditions based on PFR trajectories projected into two dimensions. Here, a PFR, which is an n-dimen-sional trajectory in concentration space and parametric in time, is generated by the solution of the initial value differential equation system in (PI). Figure 3 illustrates a PFR trajectory and its projections in three-dimensional space, where the solid line represents the actual PFR trajectory and the dotted lines represent the projected trajectories. 

Thus, in a commonly used procedure [16, 92, 120, 145, 165, 167, 170, 175], each point of the segregation isotherm data z, , ) is analyzed with Eq. (32) to find out the surface concentration ((J) ) assigned by the mean field approach (analogous procedure exists in a self-consistent mean field model [166, 174]). Then, for each such pair (c, c )s) the trajectory 2(icAf)1/2 vs ([) is plotted (for the value (IO and its value is read out at surface concentration s (=c )se or (j)sd in Fig. 15). This value is equal to the surface energy derivative (-dfs/dc ))s at concentration < )s. Such a procedure, repeated for each z ((j)00) data point, yields the concentration dependence of the composition derivative of the short-ranged bare surface energy (-dfs/dc ))s vs < )s (see Fig. 16). 

Fig. 20.a Results of the Cahn construction performed for the segregation data [16] of Fig. 19. Composition derivatives of bare surface free energy (-dfs/d( ))s calculated for different temperatures (symbols A, , O, and for T=99,142,165, and 184 °C, respectively) are fitted well by dashed lines, generated by the function (pf+g /ll+Y s). The hatched area marks the surface energy difference -Afs. b Surface energy derivatives (—dfs/d( >)s (dashed lines) and trajectories -2kV< ) (solid lines) plotted for T=99 °C and 184 °C. For T= 184 °C the surface boundary condition (Eq. 26) is met at point at ( >s>( >2, indicating complete wetting regime. If (—dfs/d([ )s was independent of temperature (and equal to that found at 184 °C) then the boundary condition (O) at 99 °C would correspond to partial wetting (c >s<( >2). In practice, however, (—dfs/d([ )s varies with temperature and the real boundary condition at 99 °C ( ) indicates complete wetting again...

If K oo, equilibrium is instantaneously reached and the system evolves along the binodal curve (trajectory a). The segregated phase composition follows the other branch of the binodal curve (trajectory a ). 

Trajectory segregation. If a small particle of diameter x and density Pp, whose drag is governed by Stokes law, is projected horizontally with a velocity U into a fluid of viscosity p and density pf, the limiting distance that it can travel horizontally is Up x /lSp. 

Explain how trajectory segregation occurs. Give examples of two practical situations that might give rise to trajectory segregation of powders in the process industries. 

Trajectory segregation has been identified (Bridgwater et al., 1985) as the main cause of axial segregation or "banding" whereby particles of different sizes are selectively collected into bands occurring over the kiln length. This axial segregation is not considered in the present work and therefore not critically reviewed rather, attention... 

---