Growth rate empirical

Size-dependent Crystal Growth. A number of empirical expressions correlate the apparent effect of crystal size on growth rate (30). The most commonly used correlation uses three empirical parameters to correlate growth rate with crystal size ... 

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

Kc,K t Empirical pellet growth rate T Thickness of snowballed layer... 

Empirical pellet growth rate con- t Agglomeration time... 

The growth rate of cells is taken proportional to the cell concentration, x, and to an empirical form of the dependence on the concentration, p, of the nutrient. That empirical form was assumed by Monod (1942) to be the same as in the Michaelis-Mewnten model for enzyme kinetics. This makes the rate of cell growth,... 

This approach is not without its shortcomings, the greatest of which is that costs and benefits have proved to be exceedingly difficult to measure. There is far from a consensus on what constitutes an appropriate demonstration of costs of chemical defense (57, 61, 62). In many theoretical discussions of costs of defense, particularly in plants, costs are measured in terms of growth rates (44, 59, 63), rather than in terms of reproductive success. In many empirical estimates of costs, the chemical nature of the defense is not defined (64) or secondary metabolites are measured in bulk (65), without any regard to their individual activities. 

From the above statements it follows that it should be possible to derive the growth kinetics and calculate the growth rate of uncontaminated electrolyte crystals when the following parameters are known molecular weight, density, solubility, cation dehydration frequency, ion pair stability coefficient, and the bulk concentration of the solution (or the saturation ratio). If the growth rate is transport controlled, one shall also need the particle size. In table I we have made these calculations for 14 electrolytes of common interest. For the saturation ratio and particle size we have chosen values typical for the range where kinetic experiments have been performed (29,30). The empirical rates are given for comparison. 

In contrast to the micro- and mesoporous regimes, for which only a few empirical laws for the growth rate and porosity are available, the detailed pore geometry for macropore arrays in n-type silicon can be pre-calculated by a set of equations. This is possible because every pore tip is in a steady-state condition characterized by = JPS [Le9]. This condition enables us to draw conclusions about the porosi-... 

As with nucleation, classical theories of crystal growth 3 20 2135 40-421 have not led to working relationships, and rates of crystallisation are usually expressed in terms of the supersaturation by empirical relationships. In essence, overall mass deposition rates, which can be measured in laboratory fluidised beds or agitated vessels, are needed for crystalliser design, and growth rates of individual crystal faces under different conditions are required for the specification of operating conditions. 

A number of investigators developed empirical growth rate expressions that included a size dependence. These models were siunmarized by Randolph Q2> 341 who showed that they all produced a concave upward semi-log population density plot thus are useful for empirical fits of non-linear MSMPR CSD data, lliese models however, supply no information on what is actually happening to cause the non-linear CSD. 

T. harzianum IMI 275950 isolated from wheat straw grew better on lignocellulose (Table I). Despite these differences, the enzyme yields of the cellulase/xylanase complexes did not correlate with growth rate. These observations from this empirical study indicate that strains isolated or derived for growth on extracted substances may not necessarily be the most useful strains to exploit natural substrates. 

The rate of cell growth is influenced by temperature, pH, composition of medium, rate of air supply, and other factors. In the case that all other conditions are kept constant, the specific growth rate may be affected by the concentration of a certain specific substrate (the limiting substrate). The simplest empirical expression for the effect ofthe substrate concentration on the specific growth rate is the following Monod equation, which is similar in form to the Michaelis-Menten equation for enzyme reactions ... 

If results are obtained as a function of ozone concentration, in theory it should be possible to make extrapolations to ambient conditions by empirically fitting a relation to the concentration against time to cracking/crack growth rate. For natural rubber, there has been evidence that that the relation is broadly linear. 

Since many biochemical reactions and their stoichiometry are not well understood, we often find a more empirical approach to the quantitative assessment of the kinetics. Mass concentration units (e.g., g/L) are often used along with yield coefficients to calculate the distribution of products formed and the amount of substrate consumed. In the absence of any inhibition effects and in the presence of an infinite supply of substrate, the rate of cell growth rx is autocatalytic, that is, it depends only on the concentration of cells (Cx), and the more cells we have, the higher the growth rate. The cell biomass is typically represented by X ... 

An empirical approach also can be used to relate growth kinetics to supersaturation by simply fitting growth-rate data with a power-law function of the form ... 

Several special terms are used to describe traditional reaction engineering concepts. Examples include yield coefficients for the generally fermentation environment-dependent stoichiometric coefficients, metabolic network for reaction network, substrate for feed, metabolite for secreted bioreaction products, biomass for cells, broth for the fermenter medium, aeration rate for the rate of air addition, vvm for volumetric airflow rate per broth volume, OUR for 02 uptake rate per broth volume, and CER for C02 evolution rate per broth volume. For continuous fermentation, dilution rate stands for feed or effluent rate (equal at steady state), washout for a condition where the feed rate exceeds the cell growth rate, resulting in washout of cells from the reactor. Section 7 discusses a simple model of a CSTR reactor (called a chemostat) using empirical kinetics. 

---