Melt solid interface shape

Connection between Transport Processes and Solid Microstructure. The formation of cellular and dendritic patterns in the microstructure of binary crystals grown by directional solidification results from interactions of the temperature and concentration fields with the shape of the melt-crystal interface. Tiller et al. (21) first described the mechanism for constitutional supercooling or the microscale instability of a planar melt-crystal interface toward the formation of cells and dendrites. They described a simple system with a constant-temperature gradient G (in Kelvins per centimeter) and a melt that moves only to account for the solidification rate Vg. If the bulk composition of solute is c0 and the solidification is at steady state, then the exponential diffusion layer forms in front of the interface. The elevated concentration (assuming k < 1) in this layer corresponds to the melt that solidifies at a lower temperature, which is given by the phase diagram (Figure 5) as... 

Results from a quasi steady-state model (QSSM) valid for long crystals and a constant melt level (if some form of automatic replenishment of melt to the crucible exists) verified the correlation (equation 39) for the dependence of the radius on the growth rate (144) and predicted changes in the radius, the shape of the melt-crystal interface (which is a measure of radial temperature gradients in the crystal), and the axial temperature field with important control parameters like the heater temperature and the level of melt in the crucible. Processing strategies for holding the radius and solid-... 

Thermoporometry. Thermoporometry is the calorimetric study of the liquid-solid transformation of a capillary condensate that saturates a porous material such as a membrane. The basic principle involved is the freezing (or melting) point depression as a result of the strong curvature of the liquid-solid interface present in small pores. The thermodynamic basis of this phenomenon has been described by Brun et al. [1973] who introduced thermoporometry as a new pore structure analysis technique. It is capable of characterizing the pore size and shape. Unlike many other methods, this technique gives the actual size of the cavities instead of the size of the openings [Eyraud. 1984]. 

These estimates of solid-liquid interface shape and position are based on u and v which satisfy all boundary conditions except the no slip condition at the solid-liquid (melting-freezing) interfaces. Therefore, to determine their accuracy, they must be compared with other solutions based on velocity fields which do satisfy these conditions. 

We noted in Section VII-2B that, given the set of surface tension values for various crystal planes, the Wulff theorem allowed the construction of fhe equilibrium or minimum firee energy shape. This concept may be applied in reverse small crystals will gradually take on their equilibrium shape upon annealing near their melting point and likewise, small air pockets in a crystal will form equilibrium-shaped voids. The latter phenomenon offers the possible advantage that adventitious contamination of the solid-air interface is less likely. 

Tenets (i) and (ii). These are applicable only where the reactant undergoes no melting and no systematic change of composition (e.g. by the diffusive removal of a constituent) and any residual solid product phase offers no significant barrier to contact between reactants or the escape of volatile products [33,34]. When all these conditions are obeyed, the shape of the fraction decomposed (a) against time (f) curve for an isothermal reaction can, in principle, be related to the geometry of formation and advance of the reaction interface. The general solution of this problem involves intractable mathematical difficulties but simplifications have been made for many specific applications [1,28—31,35]. 

Figures 5 and 6 show the effect of temperature on the removal of solid C20 (melting point = 37 °C) by C E04. These plots of normalized intensity of the v CH2 band versus time were obtained from two series of experiments, in which the initial layer thickness was varied somewhat. As discussed above, these plots must be regarded as qualitative descriptors of the removal process, due to the optical complexity of the interface. The removal process may involve not only solubilization, but also a surfactant - induced displacement of C q crystallites from the IRE surface, which cannot be treated as a gradual thinning of the C20 layer. Repeated experiments on the effect of temperature on removal rate indicate that if the conditions of layer preparation (hydrocarbon concentration in hexane, speed of withdrawal from the solution) are held constant, then reproducible band intensities of the initial layers are obtained. The shape of the removed plots (Figures 5 and 6) are affected by the initial layer thicknesses. More rapid removal was usually observed for thinner layers of smaller initial Qq band intensity.

In the presence of catalysts, heterogeneous catalytic cracking occms on the surface interface of the melted polymer and solid catalysts. The main steps of reactions are as follows diffusion on the surface of catalyst, adsorption on the catalyst, chemical reaction, desorption from the catalyst, diffusion to the liquid phase. The reaction rate of catalytic reactions is always determined by the slowest elementary reaction. The dominant rate controller elementary reactions are the linking of the polymer to the active site of catalyst. But the selectivity of catalysts on raw materials and products might be important. The selectivity is affected by molecular size and shape of raw materials, intermediates and products [36]. 

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