Growth heat-transport-limited

Estimating Heat-Transport-Limited Growth Rates... 

FIGURE 6.24 Schematic illustration of heat-transport-limited growth. The rate of growth of a slice of transformed phase of thickness dx is determined by the rate at which the heat absorbed (or released) by this transformed volume can be conducted to (or away from) the interface. 

The heat-transport-limited solidification rate estimated by this approach is almost one order of magnitude slower than the mass-transport-limited growth rate that was calculated in Example 6.7. Thus, it is likely that heat transport will limit the solidification of this ingot under these conditions. 

Ga(CH3)3 + AsH3 —> GaAs 195, 198 Two-dimensional, axisymmetric flow, mass- and heat-transfer analysis, reactor geometry effects, flow transitions, and mass-transport-limited growth. 

We see from this example that heat transport is a key factor influencing stabiUty. In solidification of binary mixtures or alloys both heat and mass transport must be eonsidraed. If the solute is preferentially soluble in the hquid phase, for example, solute must diffuse from the interfaee to the bulk hquid as sohdification proeeeds. Sinee diffusion coefficimts are often mueh smalf than thermal diffu-sivities in liquids, the sohdification rate is often limited primarily by solute diffusion. By an argument similar to that given above for heat transport, we eonclude that solute (hffusion in the hquid is destabilizing and ean lead to dendritic growth. 

Similarly, impervious yttria-stabilized zirconia membranes doped with titania have been prepared by the electrochemical vapor deposition method [Hazbun, 1988]. Zirconium, yttrium and titanium chlorides in vapor form react with oxygen on the heated surface of a porous support tube in a reaction chamber at 1,100 to 1,300 C under controlled conditions. Membranes with a thickness of 2 to 60 pm have been made this way. The dopant, titania, is added to increase electron How of the resultant membrane and can be tailored to achieve the desired balance between ionic and electronic conductivity. Brinkman and Burggraaf [1995] also used electrochemical vapor deposition to grow thin, dense layers of zirconia/yttria/terbia membranes on porous ceramic supports. Depending on the deposition temperature, the growth of the membrane layer is limited by the bulk electrochemical transport or pore diffusion. 

Though most simulators provide a library of standard models for process units, there is only limited support for very specific units such as those typically occurring in polymerization processes. Ecpiation-oriented ]895, 916] and object-oriented [54, 1002[ process modeling environments are suitable for the development of customized models for non-standard units such as for the leacher in the PA6 process. Complex transport problems involving fluid dynamics as well as other kinetic phenomena (i. e. chemical reaction, nucleation and growth of particles, interfacial heat and mass transfer etc.) can be treated... 

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