Fluid-solid interfaces melts

The above remarks point out the interest of direct measurements of the boundary condition (BC) for the fluid velocity at a fluid solid interface. To obtain reliable information on the flow velocity BC of a fluid, with a spatial resolution from the wall down to molecular sizes, is a particularly difficult challenge. Conventional velocimetry techniques (even laser velocimetry) are far from such a resolution. We have developed a near field laser velocimetry technique which allows to increase significantly the spatial resolution compared to more conventional velocimetry techniques. This technique has been used to characterize the friction between a polymer melt and a solid wall and to understand how surface modifications weakening the interactions between a solid and a given simple fluid affected the fluid -- wall friction. 

A second example of convective dissolution is the dissolution of a solid floor or roof. Forced convection means that the fluid is moving relative to the solid floor or roof such as magma convection in a magma chamber, or bottom current over ocean sediment. Free convection means that there is no bulk flow or convection, but the interface melt may be gravitationally unstable, leading to its rise or fall. 

A generalization of the condition (2-112) is required if there is an active phase transformation occurring at S, i.e., if the liquid is vaporizing or the solid is melting. In this case, we must distinguish between the bulk fluid velocities in the limit as we approach the interface, and the velocity of the interface itself, u1 n (where the interface is specified still by the criteria of zero excess mass discussed earlier). The condition of conservation of mass then requires that... 

Consider a mushy layer that lies above a static solid region and below a semiinfinite fluid region in a binary solution of concentration Coo, and temperature Too, and unidirectional solidification from below. Both the melt/mushy and mushy/solid interfaces move upwards with a constant velocity V. The mushy layer extends form z = 0 to z = h x, y. t). The boundary conditions at the Z -> oo are. 

Convection in Melt Growth. Convection in the melt is pervasive in all terrestrial melt growth systems. Sources for flows include buoyancy-driven convection caused by the solute and temperature dependence of the density surface tension gradients along melt-fluid menisci forced convection introduced by the motion of solid surfaces, such as crucible and crystal rotation in the CZ and FZ systems and the motion of the melt induced by the solidification of material. These flows are important causes of the convection of heat and species and can have a dominant influence on the temperature field in the system and on solute incorporation into the crystal. Moreover, flow transitions from steady laminar, to time-periodic, chaotic, and turbulent motions cause temporal nonuniformities at the growth interface. These fluctuations in temperature and concentration can cause the melt-crystal interface to melt and resolidify and can lead to solute striations (25) and to the formation of microdefects, which will be described later. 

Returning to our pellet, we note the point where it reaches the end of the delay zone when the solid bed has acquired a small upward velocity toward the barrel surface. At some point in the extruder, our pellet will reach the melt film-solid bed interface, experiencing toward the end of this approach a quick (exponential) rise in temperature up to the melting point. After being converted into melt, our fluid particle is quickly swept... 

Indeed, the shear stress at the solid surface is txz=T (S 8z)z=q (where T (, is the melt viscosity and (8USz)z=0 the shear rate at the interface). If there is a finite slip velocity Vs at the interface, the shear stress at the solid surface can also be evaluated as txz=P Fs, where 3 is the friction coefficient between the fluid molecules in contact with the surface and the solid surface [139]. Introducing the extrapolation length b of the velocity profile to zero (b=Vs/(8vy8z)z=0, see Fig. 18), one obtains (3=r bA). Thus, any determination of b will yield (3, the friction coefficient between the surface and the fluid. This friction coefficient is a crucial characteristics of the interface it is obviously directly related to the molecular interactions between the fluid and the solid surface, and it connects these interactions at the molecular level to the rheological properties of the system. 

Let us denote the bulk-phase densities on the two sides of the interface as p and p and the fluid velocities as u and u. The orientation of surface S is specified in terms of a unit normal n. In general, the surface S is not a material surface. For example, if there is a phase transition occurring between the two bulk phases (e.g., a solid phase is melting or a liquid phase is evaporating), mass will be transferred across S. However, the surface S is not a source or sink for mass, and thus mass conservation requires that the net flux of mass to (or from) the surface must be zero. 

It is generally accepted, based on empirical evidence, that the no-slip condition applies under almost all circumstances for small-molecule (Newtonian) fluids at either solid surfaces or at a fluid-fluid interface and also applies under many circumstances for complex liquids, such as polymer solutions or melts. This assertion is based primarily on comparisons of predictions from solutions of the equations of motion, which incorporate the no-slip condition, and experimental data - we shall discuss one example of a problem for which this kind of comparison has been done in the next chapter. Here, we simply note that these comparisons with experiments are often between macroscopic quantities - such as overall... 

In spite of this, it is perhaps useful to briefly consider the conditions at solid boundaries and fluid interfaces for complex/non-Newtonian fluids. One reason for doing this is that it provides additional emphasis to the idea from the proceeding paragraphs that there will be conditions when the commonly applied no-slip condition breaks down. It should be stated, at the outset, that the question of slip or no-slip is still a matter of current research interest for complex fluids. Nevertheless, the occurrence of sbp is generally accepted to be much more common for complex/non-Newtonian fluids than for Newtonian/small molecule liquids. In the latter case, we have seen that slip generally involves either extreme shear stresses or solid walls that exhibit extremely weak attractive interactions with the hquids, and the issue is primarily one of basic scientific interest. Polymer melts, on the other hand, commonly exhibit apparent manifestations of slip that play a critical role in the success or failure of certain types of commercial processing applications.43... 

The flow of a viscous fluid generates heat throughout the fluid. This should not be confused with frictional heating, which occurs at the interface between two solids in relative motion. The power dissipated in a small cube of melt in a shear flow, is the product of the shear force on the top and bottom surfaces and the velocity difference between these surfaces. When this quantity is divided by the volume of the cube, the power dissipated per unit volume W is found to be... 

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