Mixing induction time

As shown in Fig. 6-2, at low values of this ratio—fast mixing and long induction time— mixing would have a minimal effect on nuclei size, whereas at high ratios—slow mixing and short induction time—mixing effects would be critical to nuclei size. Local supersaturation could be visualized as a parameter as shown. 

Calculation of the induction time is crucial, since gaining a stable and continuous process requires residence times in the mixer < precipitation induction times in order to prevent incrustation in the mixing device. The induction... 

Adiabatic calorimetry. Dewar tests are carried out at atmospheric and elevated pressure. Sealed ampoules, Dewars with mixing, isothermal calorimeters, etc. can be used. Temperature and pressure are measured as a function of time. From these data rates of temperature and pressure rises as well as the adiabatic temperature ri.se may be determined. If the log p versus UT graph is a straight line, this is likely to be the vapour pressure. If the graph is curved, decomposition reactions should be considered. Typical temperature-time curves obtained from Dewar flask experiments are shown in Fig. 5.4-60. The adiabatic induction time can be evaluated as a function of the initial temperature and as a function of the temperature at which the induction time, tmi, exceeds a specified value. 

Unless carried out very carefully, data from flow reactors may be influenced by experimental uncertainties. Potential problems with the flow reactor technique include imperfect mixing of reactants, radial gradients of concentration and temperature, and catalytic effects on reactor walls. Uncertainties in induction times, introduced by finite rate mixing of reactants, presence of impurities, or catalytic effects, may require interpretation of the data in terms of concentration gradients, rather than just exhaust composition [442]. 

Fig. 22. Selective hydrogen mixing between C2H4 and C2D4 during induction time Tor the isomerization of m-2-butene-d0, and superimposed hydrogen scrambling between C2D4 and cis-2-butene-dQ after the induction time on cut single crystal catalyst of MoS2 at 100°C (8,14).

A strong pilot ensures a minimal induction time (At ), but owing to the effect that scale has on the flow, the relative importance of the mixing time Atm sometimes needs to be evaluated [11], thus, the ignition delay time could be presented as... 

Hoffman and Friedman [106] proposed a mechanism for the induction time in development based on heterogeneous electrochemical theories of corrosion. The model explains the empirical relation derived by Pontius and Willis. In this case the two half-cell reactions of silver and developer give rise to a mixed or corrosion potential, Ecorr, which if electron transfer is rate-limiting can be described by Eq. (74),... 

There are two conditions under which the particles of active metal placed on the surface of a macroelectrode can represent microelectrodes. The first condition is that the substrate is conducting but inert relative to the process under consideration. The second one is that the grains are sufficiently small to permit activation control of the electrochemical process on them, making thus, mixed overall control, as in the case of the tips of growing dendrites,11,12,31 or during the induction time of the formation of spongy deposits.32-34... 

An adaptation of the Damkochicr number (Da) is a useful concept for evaluation of mixing effects in crystallization. It is the ratio of the characteristic mixing time to its corresponding process time (nucleation induction time, crystal growth/supersaturation release time, or reaction time). Studies of these times and the resulting predicted Damkoehler number in a laboratory setting can provide evidence of possible scale-up problems. 

In a mixed solution without crystals present and at constant supersaturation, increased mixing intensity can reduce the induction time—the time elapsed after mixing to create supersaturation to the time crystals first appear. Induction time decreases up to a critical speed, after which it remains unchanged (Myerson 2001, p. 145). Additional discussion may be found in Chapter 4. 

By analogy, a Da number for nucleation could be visualized as a ratio between mixing time and induction time ... 

Mixing time and induction time can be the time required from the initial state to 95 % or other percentages of the final state. 

For pharmaceuticals, most of the reactive crystallization processes are salt formation from an acid and base. In this situation, the reaction rate is generally much faster than the mixing or crystallization rate, and the mixing sensitivity depends primarily upon the magnitude of the induction time, or Da for nucleation. 

Figure 6-2 Particle size as a function of a crystallization Da number (the ratio of mixing time/nucleation induction time).

The critical mixing factors in a stirred tank at e impeller speed and type, as well as their influence on local turbulence and overall circulation. Since all aspects of these factors cannot be maintained constant on scale-up either locally or globally, the extent to which changes in the crystallizing environment will affect nucleation is extremely difficult to predict. To the mixing issue must be added the uncertainties caused by soluble and insoluble impurities that may be present in sufficiently different concentrations from batch to batch to cause variation in induction time, nucleation rate, and particle size. 

For crystallization, the objective of an in-line mixing device would be to mix the product solution and antisolvent to the molecular level in less than the induction time for nucleation. The impinging jet and vortex mixer designs can achieve these high degrees of micromixing at significant scale in an economical manner. 

Ideally, the mixing is sufficiently intense locally to achieve reagent blending to the molecular level before reaction, and the reaction is complete in less than the induction time so that nuclei can form from the expected molecular composition. In this case,... 

Mixing time can be varied as discussed above, but reaction and induction time are both system specific. Reaction time and induction time are both concentration dependent, and induction time also is a function of supersaturation (t, j decreases with increasing 5). 

Mostly, particles are larger when synthesized from higher concentrations of TES, although the increase in radius is quite small, and sometimes the opposite trend is described (2). After the reactants are mixed, the turbidity of the solution suddenly rises after a certain induction time and then slowly increases to its final value. The induction time is closely related to the total time of the particle growth. If the particles reach their final radius in a short time, the induction period is also short. 

By using micro-scale equipment, the inventory can be greatly reduced, leading to an intrinsically safe operation. In addition, the gases can be mixed in a characteristic time lower than the induction time of the reaction. For example, in a first approximation, safe mixing of hydrogen and oxygen will occur at characteristic distances below 100 pm [22],... 

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