Boundary plane

The liquid-liquid interface is not only a boundary plane dividing two immiscible liquid phases, but also a nanoscaled, very thin liquid layer where properties such as cohesive energy, density, electrical potential, dielectric constant, and viscosity are drastically changed along with the axis from one phase to another. The interfacial region was anticipated to cause various specific chemical phenomena not found in bulk liquid phases. The chemical reactions at liquid-liquid interfaces have traditionally been less understood than those at liquid-solid or gas-liquid interfaces, much less than the bulk phases. These circumstances were mainly due to the lack of experimental methods which could measure the amount of adsorbed chemical species and the rate of chemical reaction at the interface [1,2]. Several experimental methods have recently been invented in the field of solvent extraction [3], which have made a significant breakthrough in the study of interfacial reactions. 

As an example of such applications, consider the dynamics of a hexible polymer under a shear how [88]. A shear how may be imposed by using Lees-Edwards boundary conditions to produce a steady shear how y = u/Ly, where Ly is the length of the system along v and u is the magnitude of the velocities of the boundary planes along the x-direction. An important parameter in these studies is the Weissenberg number, Wi = Ti y, the product of the longest... 

Suzuki et al. studied phosphorus segregation in iron by AES using a similar technique to that described above. Additionally, the orientation of each grain relative to the specimen axis was determined by means of selected area channelling patterns (SACP), and the crystallographic orientation of the boundary plane was... 

Figure 5.34(a) shows the relation between the amount of segregated P and the crystallographic orientation hkl of the grain boundary planes. 

Instead of Je Lodge (46) derived another quantity called constrained shear recovery sIn this case a shear recovery is considered, where the liquid is constrained by boundary planes which are rigid and do not change their mutual distance during recovery of the liquid. Subscript oo means that the recovery is measured after an infinite time, reckoned from the moment that the shear stress is made zero. According to Lodge, a quite different type of recovery occurs, when the mentioned restrictions are released. This fact has already been noted in the first paragraph of this section. In the definition of Je, however, the mentioned restrictions are tacitly made. 

Self-diffusion along the boundary in Exercise 9.6 is highly anisotropic because diffusion along the tilt axis (parallel to the dislocations) is much greater than diffusion transverse to it (i.e., perpendicular to the dislocations but still in the boundary plane). Find an expression for the anisotropy factor,... 

Only x > 0 is considered, since the solution will have mirror symmetry about the grain boundary plane x = 0. 

Finally, the total force across the boundary plane must be zero ... 

The nucleus has cylindrical symmetry around an axis normal to the boundary and mirror symmetry across the grain-boundary plane. Figure 19.27 shows a cross section of the nucleus centered in a patch of boundary of constant circular area, Ac. The area of the nucleus projected on the boundary is indicated by A. The total interfacial energy of this configuration is then... 

Thus the number of counterions far exceeds the number of co-ions. In the boundary membrane-solution a potential jumb occurs due to the difference in concentration on both sides of this boundary plane. It is assumed that a state of equilibrium applies here, so ... 

In the case of an enhanced charge carrier concentration in the space charge (cf. Fig. 4b), mainly the current parallel to the grain boundary plane is important. The corresponding parallel excess grain boundary conductance... 

Hence, in simple cases each bulk layer, each grain boundary plane, and both electrodes of the brick layer model sample, can be represented by separate RC elements (Fig. 7b). The RC elements of the n bulk layers can be combined to a single RC element with the -fold resistance and the 1 / -fold capacitance of a single layer. The n — 1 grain boundary impedances can also be summed, as can the two electrode impedances, and hence the model sample corresponds to a series connection of three RC elements (Fig. 7c) with... 

Fig. 14. Hypothetical bi-grain with microelectrodes (a), and square electrodes on the sides (b). (d) Current density distribution in the grain boundary plane of the 24-grain model sample, and sketch of the grain boundaries for which the current density distribution is plotted (c). Parameters used in the finite element calculations dms = 1/5 Lg, wgb = 10 3 Lg, and p b = 105 phvSk for all grain boundaries. The spikes are due to numerical errors. Owing to computational reasons, the considered plane is not the grain boundary plane itself, but a plane in a distance of 0.052., to the grain boundaries.

---