Free melt surface

Boundary conditions are mainly the usual ones such as the no-slip condition for the velocity at the melt/crucible boundary or the continuity of the temperature and the heat flux. At the free melt surface the normal melt velocity is set equal to zero, while the tangential velocities of the melt and gas are subjected to the following conditions ... 

A detailed comparison of computed and experimental [75] temperature variation in time in a few reference points and corresponding power spectral density is presented in Fig. 6.6. The maximal melt depth under the crystal is about 10 cm, tref = 3 cm for all points. The underestimation of the temperature of about 10 K is seen, in contrast to the distribution along the melt/crucible boundaries probably, this systematic discrepancy is related to the difficulties of the high-temperature measurement. The reproduction of the spectral characteristics is good at the free melt surface and becomes poorer with the lowering of the reference point position deeper into the melt, probably, due to a weakening of the regularizing action of the crystal rotation on the flow. 

Fig. 6.6 Left the temperature distribution in time right the spectral power density. Reference points (from top down) the free melt surface 2 cm lower 4 cm lower.

The radiation problem has been solved using a new approach already mentioned above. The following assumptions have been made the melt is opaque, the absorption coefficient of the crystal is wavelength dependent, the crystallization front is black, the crucible waU is diffusely reflective, while the crystal side surface and the free melt surface can be either diffusely or specularly reflective. Scattering, as a rule, was neglected. 

Coupling of Subproblems Both subproblems were matched along the free melt surface and the crystal/melt interface where the following boundary conditions were set ... 

S correspond to liquid and solid phases, respectively, El is the melt emissivity, is the density of radiative flux incident on the free melt surface, is the density of radiative flux at the crystal/melt interface in the range of semitransparency of the crystal and h is the current coordinate of the crystallization front along the pulling direction. Since a triple point is stationary, the pulling rate can be determined from Eq. (8.2b) as follows... 

Simulation of heat transfer was performed for an experimental setup [14] that allows growing crystals up to 80 mm in diameter. A schematic diagram of the setup is presented in Fig. 8.1. The temperature distribution along the cmcible wall was given and the meniscus shape near the triple point was neglected, the crystal cone angle was equal to 45. The crystal side surface and free melt surface could be either diffusely or specularly reflective. 

As one can gather from Eq. (14.17), during crystal pulling from the variable cross section crucible, several possibilities emerge to control the volatile activator in crystal. The direct path is variation of C(q. Besides, C(S) depends on the crystal pulling rate and the relation of the values of crystal transverse cross section vs. free melt surface ds l(d — ds ). In the variable cross section crucible, the value of this relation can be easily varied, the volatile activator concentration for ingots of various diameters being kept constant and made the same. 

AB diblock copolymers in the presence of a selective surface can form an adsorbed layer, which is a planar form of aggregation or self-assembly. This is very useful in the manipulation of the surface properties of solid surfaces, especially those that are employed in liquid media. Several situations have been studied both theoretically and experimentally, among them the case of a selective surface but a nonselective solvent [75] which results in swelling of both the anchor and the buoy layers. However, we concentrate on the situation most closely related to the micelle conditions just discussed, namely, adsorption from a selective solvent. Our theoretical discussion is adapted and abbreviated from that of Marques et al. [76], who considered many features not discussed here. They began their analysis from the grand canonical free energy of a block copolymer layer in equilibrium with a reservoir containing soluble block copolymer at chemical potential peK. They also considered the possible effects of micellization in solution on the adsorption process [61]. We assume in this presentation that the anchor layer is in a solvent-free, melt state above Tg. The anchor layer is assumed to be thin and smooth, with a sharp interface between it and the solvent swollen buoy layer. 

Improved compositions useful for the production of foamed rotomoulded articles are provided. The compositions of the invention are comprised of a first thermoplastic resin component which is an ethylene polymer in pellet form containing a foaming agent and a second thermoplastic resin component which is a powder consisting of a mixture of different particle size and melt index ethylene polymers. An improved process for producing foamed rotomoulded articles having uniformly foamed interiors and smooth exterior skins which are snbstantially free of surface defects is also provided. 

The sorbitol solution produced from hydrogenation is purified in two steps [4]. The first involves passing the solution through an ion-exchange resin bed to remove gluconate and other ions. In the second step, the solution is treated with activated carbon to remove trace organic impurities. The commercial 70% sorbitol solution is obtained by evaporation of the water under vacuum. The solid is prepared by dehydration until a water-free melt is obtained which is cooled and seeded. The crystals are removed continuously from the surface (melt crystallization). The solid is sold as flakes, granules, pellet, and powder forms in a variety of particle size distributions. 

This review has discussed the phase behavior of polymer blends and symmetric block copolymer melts in thin film geometry, considering mostly films confined between two symmetrical hard walls. Occasionally, also an antisymmetric boundary condition (i.e. one wall prefers component A while the other wall prefers component B) is studied. These boundary conditions sometimes approximate the physically most relevant case, namely a polymeric film on a solid substrate exposed to air or vacuum with a free, fiat surface (Fig. 1). The case where the film as a whole breaks up into droplets (Fig. 2) due to dewetting phenomena is not considered, however, nor did we deal with the formation of islands or holes or terraces in the case of ordered block copolymer films (Fig. 4b-d). 

The comparison of the hysteresis behavior in simulation and experiment, shows that the hysteresis is mainly due to the existence of metastable states rather than due to kinetic effects. The asymmetry in the freezing and melting branches of the adsorption curve is explained based on the Landau free energy surfaces. The Landau free energy approach is a powerful tool in determining the freezing temperature, nature of the phase transition, structure of the confined phases, existence of metastable states and origin of the hysteresis behavior. 

Classical homogeneous nucleation theory gives a nucleation rate that depends essentially on the crystal-melt surface free energy a. In order to make predic-... 

This study is consistent with the idea that crystal surfaces at temperatures close to melting have some kind of disordered layer or layers, often called liquid-like . Due to the different equilibrium volumes of the liquid and solid phases, this region makes the surface either contract (as in the case of the ice surface) or expand (as it is for Lennard-Jones systems). The positive interfacial excess stress of the ice/water interface therefore makes it similar to liq-uid/vapor interfaces, and the water/vapor interface in particular, for which the excess stress is equal to the interfacial free energy (surface tension). 

Fig. 7. — Schematic Free-energy Surface for the Melting and Setting of Carrageenan and Agar Gels. [The system follows the path shown by the arrows. Axes are labeled G (relative Gibbs free-energy), S (entropy), and T (temperature). Note that it is not suggested that the absolute free-energy of any species increases with the temperature, nor that the entropy of the transition state is constant with changing temperature (see the text). The model was constructed by Mr. F. B. Williamson.7 ]...

Classical thermod5mamics regarded melting as the outcome of the intersection of free-energy surfaces of a solid (subscript S) or a liquid (subscript L)... 

The common feature of these processes is that two flat, or slightly convex, melt surfaces come together under pressure, with some outwards flow. The orientation produced is at right angles to the original flow direction. In the welding of extrusions, there is a layer of soft semisolid polymer behind the melt layer. When the melt flows outwards to form a bead at the free surfaces, this semisolid material undergoes shear deformation. 

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