Cooling rate effects scale

Fig. 6.17 The generalized spin auto-correlation function (t) for temperatures T = 0.40,0.30,0.25,0.23, and 0.22 are plotted versus t/tsc (in logarithmic scale) where tsc = 130,400,1160,2260 and 3700 for the respective temperatures. All the curves collapse onto a single curve at late times. This result stems from a simulation of the 2d version of model A with N = 10, P = 200, and = 0.8 after eliminating all cooling rate effects.

In Figure 1, we present the luminosity functions obtained with the assumptions of total miscibility (full line) and total separation (dashed line) for an age of the Galactic disk of 15 10 years. These luminosity functions take into account the increase of the vertical scale height over the plane of the disk with the age of the objects. This geometrical effect [2] nearly suppress the bump at L 10-4 Lq which would have been produced by the strong decrease of the cooling rate in the case of total separation [3]. 

This criterion, as in (5.12), uses a comprehensive kinetic description of the reaction. In fact, this ratio allows comparison of the characteristic time of the reaction rate with the cooling rate. It is strongly affected by a change in the reactor size, as explained in Section 2.4.1.2. Moreover, it varies non-linearly with reactor size. Hence it is especially important to consider its effect during scale-up. 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

Parameters that affect crystallization may influence either the thermodynamic behavior or the crystallization kinetics (or both). Parameters that influence lipid crystallization include chemical composition, subcooling, cooling rate, agitation, minor components of fats (mono- and diacylglycerols, polar lipids, etc.), and scale of operation. The effects of these parameters on lipid crystallization will be reviewed briefly in this section. More detailed information about the effects of these parameters on lipid nucleation and crystal growth may be found elsewhere (4, 24, 28, 54). 

One effect that sustained exposure to elevated temperature has is to stabilize the structure of the material. The processing of polymer materials frequently leaves residual stresses of various types in the material. In addition, the cooling rate on a polymer with a crystalline structure may be such that the equilibrium is not reached during processing. Sustained exposure to heat will result in relaxation of the residual frozen-in stresses and/or the recrystallization of the material. Both of these effects involve movement of the material on a molecular or micro scale with a consequent distortion of the overall shape of the object. In the case of a quenched polyethylene film which has a high degree of clarity, the effect of the recrystallization would be to increase the haze level so that the material becomes opalescent or even opaque. 

From this it can be seen that as the temperature of a supercooled liquid is being reduced, the time it takes for structural relaxations to occur increases very rapidly. If the cooling rate is kept constant, then at a certain temperature there will no longer be sufficient time for the liquid to return to equilibrium before the temperature is reduced. At this temperature the liquid undergoes a kinetic transition to the glassy phase and the structure is effectively fixed on an experimental time-scale. This is often defined [25, 44] as 100 s, which corresponds to a viscosity of -lO Pa s. It is also apparent from this definition of the glass transition that it is dependent on the rate at which the liquid is cooled a slower cooling rate will... 

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