Growth-rate

Particle growth refers to an increase in particle size due to separation of material from solution. The growth rate is often mass transfer controlled and is given by  

The literatme on crystallization kinetics [95, 96, 97] have discussed several mathematical expressions depending upon the process complexity for each of the mentioned mechanisms. For example, growth can be size-independent or size-dependent, it can have a constant value, or it may be a function of thermodynamic parameter like solubility. Thus, the selection of proper kinetics specific to the batch crystallization process is a very essential part in process modeling. 

One of the first models for crystal growth is McCabe AL law and is given by the following size independent rate. 

More importantly, the crystallization kinetics of all samples of different molar mass displays the characteristic discontinuity due to the different radial growth rates of a - and a-spherulites. Independent of the molar mass, the transition from growth of a -crystals to growth of a-crystals occurs at 100-120 C [28]. 

This means that, to calculate the relative crystallinity, we have to calculate only the fictive volume fraction q . But to obtain p, we need to consider the growth rate and the nuclei number density. 

The increasing number of activated nuclei is the first noticeable effect induced by flow. The effect of flow on growth rate was also observed (Monasse 1995), but it is usually less important and can be neglected (Koscher and Fulchiron 2002), while the effect of flow on nucleation must be considered. 

For a spherulite, the radial growth rate G can be calculated by applying the Hofifman-Lauritzen theory (Lauritzen and Hoffman 1960) 

The equilibrium melting temperature may depend on pressure. Fulchiron et al. (2001) express the pressure dependence as a polynomial function 

To determine the parameters Go and Kg, one needs to measure the growth rate G(7). For materials with slow crystallization kinetics, one can easily measure the spherulite growth rate as a function of temperature from micrographs (Fig. 4.2). Then Gq and Kg are determined by plotting In G + W/Rg T - T ) against T + T ) jlT AT. 

When inoculating a fresh medium, the cells encounter an environmental shock, which results in a lag phase. The length of this phase depends upon the type of organism, the age and size of the inoculum, any changes in nutrient composition, pH and temperature. When presented with a new nutrient the cell adapts itself to its new environment and normally produces the required enzyme. 

The Monod equation is frequently used to describe the stimulation of growth by the concentration of nutrients as given by  

The saturation constant for Saccharomyces cerevisiae on glucose is 25 mg/L, for Escherichia on lactose 20 mg/L, and for Pseudomonas on methanol 0,7 mg/L. Here, is the maximum growth rate achievable when 

S and the concentration of all other essential nutrients is unchanged. The saturation constant is the approximate division between the lower concentration range where p is essentially linearly related to S and the higher rate where p becomes independent of 5.1 1 

The effect of excessive nutrient or product concentrations on growth is often expressed empirically as  

In heavily infected fish, the cestodes were so closely packed that individuals were (remarkably ) reported as being partially or totally fused together These zones of fusion gave strong histochemical reactions for -SH groups and appeared to be areas of intense metabolic activity. This suggested (750) that, in heavy infections, parasites which fail to find room for attachment on the host mucosa may derive their nutriment from another individual worm. This unusual observation clearly requires confirmation. 

Although, in many species, the adult scolex does little damage to the mucosa, some species (e.g. D. latum, H. microstoma, Multiceps sp.) can produce marked pathogenetic effects. Consideration of these is beyond the scope of this book. The literature in this field has been reviewed by Arme et al. (25). 

Species Host Pre-patent period (days) Reference 

Some relevant studies on growth and/or maturation in the two major orders, Pseudophyllidea and Cyclophyllidea are as follows. 

It is well recognised that the growth rate can be affected by numerous intrinsic and extrinsic factors related to the host, such as host species or strain (733), host nutrition, endocrine status or environmental conditions (e.g. temperature), as well as the worm burden present. 

---

Mobility of this second kind is illustrated in Fig. XVIII-14, which shows NO molecules diffusing around on terraces with intervals of being trapped at steps. Surface diffusion can be seen in field emission microscopy (FEM) and can be measured by observing the growth rate of patches or fluctuations in emission from a small area [136,138] (see Section V111-2C), field ion microscopy [138], Auger and work function measurements, and laser-induced desorption... 

Figure C2.8.7. Principal oxide growth rate laws for low- and high-temperature oxidation inverse logarithmic, linear, paralinear and parabolic.

Alonso C, Salvarezza R C, Vara J M and Arvia A J 1990 The meohanism of silver (I) oxide formation on polyorystalline silver in alkaline solution. Determination of nuoleation and growth rates Electrochim. Acta 35 489-96... 

Growth rate dispersion Growth regulator, plant Growth regulators... 

The apphcations of high purity gases are primary in the semiconductor industries. From 1991 to 1995, the North American semiconductor bulk gas sales increased from U.S. 214 to 252 million (aimual growth rate of 4.2%) and specialty gas sales increased from U.S. 78 million to 169 million (aimual growth rate of 21.4%). 

One drawback of static crystallization is that crystal layer growth rates are very slow. In the Sulzer MWB process, growth rates are gready improved by allowing a film to dow down vertical tubes (83). 

Performance in Colter. The modified monomer should perform well ia commercial deposition equipment. Performance considerations iaclude the growth rate of the coating, the uniformity of thickness of the coating over the chamber volume, and the efficiency with which the dimer is converted to useful coatings on the substrates. 

Acetic acid has a place in organic processes comparable to sulfuric acid in the mineral chemical industries and its movements mirror the industry. Growth of synthetic acetic acid production in the United States was gready affected by the dislocations in fuel resources of the 1970s. The growth rate for 1988 was 1.5%. 

Acetic anhydtide is a mature commodity chemical ia the United States and its growth rate in the 1970s and 1980s was negative until 1988 when foreign demand neatly doubled the exports of 1986. This increase in exports was almost certainly attributable to the decline in the value of the U.S. doUar. Over four-fifths of all anhydtide production is utilized in cellulose acetate [9004-35-7] manufacture (see Cellulose esters). Many anhydtide plants are integrated with cellulose acetate production and thus employ the acetic acid pyrolysis route. About 1.25 kg acetic acid is pyrolyzed to produce 1.0 kg anhydtide. 

Adipic acid is a very large volume organic chemical. Worldwide production in 1986 reached 1.6 x 10 t (3.5 x 10 lb) (158) and in 1989 was estimated at more than 1.9 x 10 t (Table 7). It is one of the top fifty (159) chemicals produced in the United States in terms of volume, with 1989 production estimated at 745,000 t (160). Growth rate in demand in the United States for the period 1988—1993 is estimated at 2.5% per year based on 1987—1989 (160). Table 7 provides individual capacities for U.S. manufacturers. Western European capacity is essentially equivalent to that in the United States at 800,000 t/yr. Demand is highly cycHc (161), reflecting the automotive and housing markets especially. Prices usually foUow the variabiUty in cmde oil prices. Adipic acid for nylon takes about 60% of U.S. cyclohexane production the remainder goes to caprolactam for nylon-6, export, and miscellaneous uses (162). In 1989 about 88% of U.S. adipic acid production was used in nylon-6,6 (77% fiber and 11% resin), 3% in polyurethanes, 2.5% in plasticizers, 2.7% miscellaneous, and 4.5% exported (160). 

Usage Actual 1982 1987 Forecast, 1992 Average aimual growth rate, 1987-1992,%... 

Some of the chemical derivatives, especially those tied to agricultural uses, tend to experience some cycHcal demand. However, because of the speciali2ed nature of many of the fluorinated chemicals, these products are positioned in strong, high performance market areas having above average growth rates. 

The growth rate of U.S. formaldehyde uses has declined since the 1960s as shown (116) ... 

---