Advancing rate

Figure 2. Transient pressure drop across the porous-medium micromodel of Figure 1 for foam pregenerated in an identical upstream medium. The foam frontal advance rate is 186 m/d. In the wet case, foam advanced into the downstream micromodel which was completely saturated with aqueous surfactant solution. In the dry case, the downstream micromodel contained only air.

We solved the problem by measuring the advancement rate along the b axis of the twin and the single crystal, respectively. The R(p ) value is calculated by means of the equation shown in Figure 1, whereas the R(p) value is given by the following equation ... 

These three features correspond to the two-dimensional morphology of a crystal, and are directly related to the problems of the three-dimensional morphology of polyhedral crystals. Habitus and Tracht. This is because the normal growth rate R which determines Habitus and Tracht is related in the following way to the height of a step, h, the advancing rate of the step, v, and the step separation, A. ... 

Figure 5.4. Relationship between normal growth rate R of a crystal lace and the step height h, the advancing rate v, and the step separation A, of a growth spiral.

Elemental growth spiral layers originating from an isolated dislocation can advance, keeping the step separation constant, unless factors which affect the advancing rate of the spiral steps, such as a local fluctuation in driving force or impurity adsorption, takes place. The step separation of a spiral, A, is related to the critical radius of two-dimensional nuclei, r, in the following manner (see ref. [11], Chapter 3) ... 

Figure 5.11. Various step patterns appear because the advancing rate and the curvature of the spiral layers are affected by the strain field at dislocation cores.

When we observe the process of advancement of elemental spiral steps in situ, it is often noticed that two steps bunch together to form a step with the height of two layers as they advance. The advancing rate of the bunched layer is retarded... 

Since the edge free energies, y, are different for the vapor and solution phases, and particularly for solute-solvent interaction energies, the same crystal species will exhibit different Tracht and Habitus in different ambient phases and different solvents. If impurities are present in the system, this affects y and the advancing rates of steps. There are two opposite cases in impurity effects, and, depending on the interface state, some will promote growth, whereas others will suppress growth. 

The driving force, Ap,/ cT, affects the advancement rate of steps, as well as the state of the interface. Growth temperature (and pressure) may modify the morphology of growth spiral layers and may affect Tracht and Habitus through the modification of the interface state, but the effect will appear through A/ajkT. 

The ratio is up to ten times higher in NaCl solution than the ratios seen in NaOH or KOH solutions. From this, it is deduced that the striations are due to the remarkable anisotropy involved in the step advancing rate of the growth spirals developing on the m faces The main reason why this anisotropy occurs is understood to be due to the NaCl, which is added as a mineralizer in H O. The hydrothermal solution in which natural rock-crystal grows is, in general, NaCl aqueous solution. 

From this equation, we see that the advancement rate of each nt is determined by the stoichiometric coefficient vt ... 

In the case of an isotropic advancement rate of the step, a growth spiral with circular symmetry" is formed. Due to the character of its origin the spiral step can never disappear and the crystal face grows perpetually even at relatively lov supersaturations without the need of a two-dimensional nucleation. 

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