Growth mass transfer

The boiling mechanism can conveniently be divided into macroscopic and microscopic mechanisms. The macroscopic mechanism is associated with the heat transfer affected by the bulk movement of the vapor and Hquid. The microscopic mechanism is that involved in the nucleation, growth, and departure of gas bubbles from the vaporization site. Both of these mechanistic steps are affected by mass transfer. 

The modeling of fluidized beds remains a difficult problem since the usual assumptions made for the heat and mass transfer processes in coal combustion in stagnant air are no longer vaUd. Furthermore, the prediction of bubble behavior, generation, growth, coalescence, stabiUty, and interaction with heat exchange tubes, as well as attrition and elutriation of particles, are not well understood and much more research needs to be done. Good reviews on various aspects of fluidized-bed combustion appear in References 121 and 122 (Table 2). 

Supersaturation has been observed to affect contact nucleation, but the mechanism by which this occurs is not clear. There are data (19) that infer a direct relationship between contact nucleation and crystal growth. This relationship has been explained by showing that the effect of supersaturation on contact nucleation must consider the reduction in interfacial supersaturation due to the resistance to diffusion or convective mass transfer (20). 

The effects of a solvent on growth rates have been attributed to two sets of factors (28) one has to do with the effects of solvent on mass transfer of the solute through adjustments in viscosity, density, and diffusivity the second is concerned with the stmcture of the interface between crystal and solvent. The analysis (28) concludes that a solute-solvent system that has a high solubiUty is likely to produce a rough interface and, concomitandy, large crystal growth rates. 

The data plotted in the figure clearly support the predicted positive dependence of crystal size on agitation rate. Precipitation in the crystal film both enhances mass transfer and depletes bulk solute concentration. Thus, in the clear film model plotted by broken lines, bulk crystal sizes are initially slightly smaller than those predicted by the crystal film model but quickly become much larger due to increased yield. Taken together, these data imply that while the initial mean crystal growth rate and mixing rate dependence of size are... 

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

Flow thins protective film to equilibrium thickness which is a function of both mass transfer rate and growth kinetics. Erosion corrosion rate is controlled by the dissolution rate of the protective film. 

A strain of Azotobacter vinelandii was cultured in a 15 m3 stirred fermenter for the production of alginate. Under current conditions the mass transfer coefficient, kLa, is 0.18 s. Oxygen solubility in the fermentation broth is approximately 8 X 10 3 kgm-3.9 The specific oxygen uptake rate is 12.5 mmol g 1 h. What is the maximum cell density in the broth If copper sulphate is accidentally added to the fermentation broth, which may reduce the oxygen uptake rate to 3 mmol g 1 h 1 and inhibit the microbial cell growth, what would be the maximum cell density in this condition ... 

Table 3.1 shows the kinetic parameters for cell growth, rate models with or without inhibition and mass transfer coefficient calculation at various acetate concentrations in the culture media. The Monod constant value, KM, in the liquid phase depends on some parameters such as temperature, initial concentration of the carbon source, presence of trace metals, vitamin B solution, light intensity and agitation speeds. The initial acetate concentrations in the liquid phase reflected the value of the Monod constants, Kp and Kp. The average value for maximum specific growth rate (/xm) was 0.01 h. The value... 

The well-known aerobic downflow process is a trickled bed filter. Attached growth is used in the biological treatment of wastewater. Air passes through the bed while the liquid is forced to down by gravity. Figure 13.2 shows the liquid gas system for the mass transfer... 

Fig. 13.2. Liquid gas mass transfer process in biological filter, attached growth system.

Cole R, Shulman HL (1966) Bubble growth rates at high Jacob numbers Int J Heat Mass Transfer 9 1377-1390... 

Mei R, Chen W, Klausner JF (1995a) Vapor bubble growth in heterogeneous boiling Int J Heat Mass Transfer 38 909-919... 

ReveUin R, Thome J. (2008) A theoretical model for the prediction of the critical hat flux in heated micro-channel. Int. J. Heat and Mass Transfer 51 1216-1225 Roach GM, Abdel-Khahk SI, Ghiaasiaan SM, Dowling MF, Jeter SM (1999) Low-flow critical heat flux in heated microchannels. Nucl Sd Eng 131 411 25 Robinson AJ, Judd RL (2001) Bubble growth in a uniform and spatially distributed temperature field. Int J Heat Mass Transfer 44 2699-2710... 

Thorncroft GE, Klausner JF, Mei R (1998) An experimental investigation of bubble growth and detachment in vertical upflow and downflow boiling. Int J Heat Mass Transfer 41 3857-3871 Thorncroft GE, Klausner JF, Mei R (2001) Bubble forces and detachment models Multiphase Sci Technol 13 35-76... 

Yuan H, Qguz HN, Prosperreti A (1999) Growth and collapse of a vapor bubble in a small tube. Int J Heat Mass Transfer 42 3643-3657... 

Chemical vapor deposition processes are complex. Chemical thermodynamics, mass transfer, reaction kinetics and crystal growth all play important roles. Equilibrium thermodynamic analysis is the first step in understanding any CVD process. Thermodynamic calculations are useful in predicting limiting deposition rates and condensed phases in the systems which can deposit under the limiting equilibrium state. These calculations are made for CVD of titanium - - and tantalum diborides, but in dynamic CVD systems equilibrium is rarely achieved and kinetic factors often govern the deposition rate behavior. 

Like enzymes, whole cells are sometime immobilized by attachment to a surface or by entrapment within a carrier material. One motivation for this is similar to the motivation for using biomass recycle in a continuous process. The cells are grown under optimal conditions for cell growth but are used at conditions optimized for transformation of substrate. A great variety of reactor types have been proposed including packed beds, fluidized and spouted beds, and air-lift reactors. A semicommercial process for beer used an air-lift reactor to achieve reaction times of 1 day compared with 5-7 days for the normal batch process. Unfortunately, the beer suffered from a mismatched flavour profile that was attributed to mass transfer limitations. 

---