Growth constant

The specific growth constant for exponential growth, )J., is defined a.s x dt = dM/M where M is the yeast mass and / is time. Growth is also... 

Thus, the exponential growth constant of the pressure oscillation is directly related to the acoustic admittance of the propellant. Hence, the acoustic admittance can be evaluated directly from the growth rate of the pressure amplitude. Ryan (R5) has also desired this espression on the basis of acoustic-energy considerations. 

Here rx is the rate of cell growth (kg cell m 3 s 1), X is the cell concentration (kg cell m 3) and k is a kinetic growth constant (s 1). For a batch system, this is equivalent to... 

Besides the two growth constants there are four other parameters defined by Eq. (48) which are not specified as combinations of physical properties of the system. For class A systems there are the four algebraic expressions in Eqs. (49) to (53), so that two other quantities, such as the concentrations at infinity, must be specified. For class B problems, where Eq. (53) is not applicable, three parameters must be specified. 

Absorption by a liquid of a single component from a mixture of gases. Let the unprimed phase be a mixture of a soluble gas A and an insoluble gas, the initial mole fraction of A being Yo. Similarly the concentration in the primed phase in volumes of dissolved gas per unit volume of liquid is initially equal to Co. At the interface a Henry s law expression is satisfied, so that, by Eq. (38), C (X, t) = K Y(X, t), where Ki is the solubility of A in the liquid, expressed as volumes of gaseous A per unit volume of liquid per unit mole fraction of A in the gas. The growth constant is then obtained by means of the result... 

As noted previously, the growth constant in the exact solution is given by... 

It is not surprising that the approximate bounds give the correct time dependence for the free boundary motion, since X is identical, except for constant factors, with the Boltzmann similarity variable. For a block of ice whose surface temperature is subjected to a step increase of 5°C. the upper and lower bounds are within 3% of each other, and the approximate growth constant calculated from Eq. (238) is about 0.5% from the exact value. 

Finally, it should be stressed that, in contradistinction to high-molecular weight polymers, the equilibrium growth constants of low-molecular weight oligomers depend on the mechanism of the reaction and on the nature of the reactive end groups. This point was recognized and stressed by Dainton and Ivin (2). 

Blaurock and Carothers (1990) and Blaurock and Wan (1990) described a simple way, valid for butteroil, of analyzing isothermal DSC data to characterize the kinetics of early crystallization in a supercooled oil. This approach yielded a single crystallization-temperature dependent combined nucleation/crystal growth constant (which they called NG). The temperature dependence of NG could be modeled with the Arrhenius equation. 

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