Heat transfer crystal growth

The cooling liquid passes between the pipes, this annulus being dimensioned to permit reasonable shell-side velocities. The scrapers prevent the buildup of solids and maintain a good film coefficient of heat transfer. Crystal growth is in the bulk of the liquid. The equipment can be operated in a continuous or in a recirculating batch manner. 

Scale. Scale deposits are formed by precipitation and crystal growth at a surface in contact with water. Precipitation occurs when solubiUties are exceeded either in the bulk water or at the surface. The most common scale-forming salts that deposit on heat transfer surfaces are those that exhibit retrograde solubiUty with temperature. 

Flow of mother Hquor through the cooled tubes is initiated, and crystals are grown on the tube surfaces. The heat transfer rate should be controUed so as to moderate crystal growth, thereby producing a relatively uniform layer of high purity soHds. 

S. G. Mueller, R. Eckstein, D. Hofmann, L. Kadinski, P. Kaufmann, M. Koelbl, E. Schmitt. Modelling of the PVT-SiC bulk growth process taking into account global heat transfer, mass transport and heat of crystal-Uzation and results on its experimental verification. Mater Sci Eorum 0 51, 1998. 

K. Kakimoto, H. Ozoe. Heat and mass transfer during crystal growth. Corn-put Mater Sci 10 21, 1998. 

Condensation is generally a transient operation in which, as discussed by Ueda and Takashima(106), simultaneous heat and mass transfer are further complicated by the effects of spontaneous condensation in the bulk gaseous phase. After the creation of supersaturation in the vapour phase, nucleation normally occurs which may be homogeneous in special circumstances, but more usually heterogeneous. This process is followed by both crystal growth and agglomeration which lead to the formation of the final crystal product. As a rate process, the condensation of solids from vapours is less well understood than vaporisation(98). Strickland-Constable(107) has described a simple laboratory technique... 

In this case, the linear growth rate is usually a function of the mass and heat transfer conditions at the surface of the crystal. The linear growth rate may... 

Mochizuki, T. Mori, Y.H. (2006). Clathrate-hydrate film growth along water/hydrate-former phase boundaries - numerical heat-transfer study. J. Crystal Growth, 290 (2), 642-652. 

Mori, Y.H. (2001). Estimating the thickness of hydrate films from their lateral growth rates application of a simplified heat transfer model. J. Crystal Growth, 223, 206-... 

In this section, we focus on diffusive mass transfer. The mathematical description of mass transfer is similar to that of heat transfer. Furthermore, heat transfer may also play a role in heterogeneous reactions such as crystal growth and melting. Heat transfer, therefore, will be discussed together with mass transfer and examples may be taken from either mass transfer or heat transfer. 

Because interface reaction and mass/heat transfer are sequential steps, crystal growth rate is controlled hy the slowest step of interface reactions and mass/heat transfer. For a crystal growing from its own melt, the growth rate may be controlled either by interface reaction or heat transfer because mass transfer is not necessary. For a crystal growing from a melt or an aqueous solution of different composition, the growth rate may be controlled either by interface reaction or mass transfer because heat transfer is much more rapid than mass transfer. Different controls lead to different consequences, including the following cases ... 

In this chapter, the essential aspects of kinetics of heterogeneous reactions (nucleation, interface reaction, and mass/heat transfer) are first presented. Then one class of heterogeneous reactions, the dissolution and growth of crystals, bubbles, and droplets, is elaborated in great detail. Some other heterogeneous reactions are then discussed with examples. Many complex problems in heterogeneous reactions remain to be solved. 

Crystal dissolution/melting/growth may be controlled by interface reaction rate (Figure 1-lla), meaning that mass/heat transfer rate is very high and interface reaction rate is low. Examples include dissolution of minerals with low... 

As can be seen from the expression for the driving force in terms of the chemical potential differences, which are related to the differences in temperature and concentration, the two transporting processes, heat transfer and mass transfer, are coupled in crystal growth. The degree of contribution from the respective transport process is determined by the degree of condensation of the environmental (ambient) phase. To grow crystals in a diluted ambient phase, a condensation process is required, and so mass transfer plays an essential role. The contribution of heat generated by crystallization in this case is small compared with that of the mass transfer. However, for crystallization in a condensed phase, such as a melt phase, heat transfer plays the essential role, and the contribution from the mass transfer will be very small, because the difference in concentration (density) between the solid and liquid phases is very small, smaller, say, than 1 or 2%. It is therefore necessary to classify the types of ambient phases and to be familiar with their respective characteristics from this standpoint. 

In contrast to solid state crystallization, crystallization from vapor, solution, and melt phases, which correspond to ambient phases having random structures, may be further classified into condensed and dilute phases. Vapor and solution phases are dilute phases, in which the condensation process of mass transfer plays an essential role in crystal growth. In the condensed melt phase, however, heat transfer plays the essential role. In addition to heat and mass transfer, an additional factor, solute-solvent interaction, should be taken into account. 

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