Stage unstable

Fig. 3.17. Molecular dynamic simulation results for the onset of fracture growth instablity in a triangular lattice network with Lennard-Jones potential, having an initial crack at the left-side boundary, (a) Initial stages of growth, and (b) late stage unstable growth with large propagation velocities (Abraham et al 1994).

The preceding conclusion is easily verified experimentally by arranging two bubbles with a common air connection, as illustrated in Fig. II-2. The arrangement is unstable, and the smaller of the two bubbles will shrink while the other enlarges. Note, however, that the smaller bubble does not shrink indefinitely once its radius equals that of the tube, its radius of curvature will increase as it continues to shrink until the final stage, where mechanical equilibrium is satisfied, and the two radii of curvature are equal as shown by the dotted lines. 

For adiabatic reactors one example was presented by Berty et al (1968) on a six-stage adiabatic reactor system that had intercoolers between the stages. Every adiabatic stage is always sensitive or unstable but the full six-stage... 

Conventional stoiehiometrie equations show the reaetants that take part and the produets formed in a ehemieal reaetion. However, there is no indieation about what takes plaee during this ehange. A detailed deseription of a ehemieal reaetion outlining eaeh separate stage is referred to as the meehanism. Meehanisms of reaetions are based on experimental data, whieh are seldom eomplete, eoneerning transition states and unstable intermediates. Therefore, they must to be eon-tinually audited and modified as more information is obtained. 

The released energy might result from the wanted reaction or from the reaction mass if the materials involved are thermodynamically unstable. The accumulation of the starting materials or intermediate products is an initial stage of a runaway reaction. Figure 12-6 illustrates the common causes of reactant accumulation. The energy release with the reactant accumulation can cause the batch temperature to rise to a critical level thereby triggering the secondary (unwanted) reactions. Thermal runaway starts slowly and then accelerates until finally it may lead to an explosion. 

During precipitate ageing, a gradual transformation of an initially precipitated metastable phase into a final crystalline form often occurs. The metastable phase may be an amorphous precipitate, a polymorph of the final material, a hydrated species or some system-contaminated substance (Mullin, 2001). In 1896, Ostwald promulgated his rule of stages which states that an unstable... 

In many cases, addition or removal of water proceeds sufficiently slowly that some of the physical properties of unstable species (such as hydrated neutral quinazoline or anhydrous 2-hydroxypteridine) can be observed. In these cases, reaction kinetics can also be examined. Addition of water to pteridine is of special interest in relation to studies of the formation and hydrolysis of Schiflf bases. The reaction proceeds in two reversible stages, 3 4 5 ... 

On its own, PVC is an extremely unstable polymer, in fact, almost certainly the least naturally stable polymer in commercial use. As Grassie has noted, Had this polymer been discovered at the present stage of development of the plastics industry, it would almost certainly have been eliminated as useless because of its general instability to all common degradative agents [2]. 

The stage is now set for the crucial polycyclization event. Tertiary carbinol 8, derived from the action of methyllithium on enone 9, is a rather unstable substance, and it was submitted to the polycyclization reaction without purification. When intermediate 8 is treated with trifluoroacetic acid (TFA) and the vinyl cation trapping agent ethylene carbonate in 1,2-dichloroethane at 0°C, the desired... 

With the exception of iron(II) and uranium(IV), the reduced solutions are extremely unstable and readily re-oxidise upon exposure to air. They are best stabilised in a five-fold excess of a solution of 150g of ammonium iron(III) sulphate and 150 mL of concentrated sulphuric acid per litre [approximately 0.3M with respect to iron] contained in the filter flask. The iron(II) formed is then titrated with a standard solution of a suitable oxidising agent. Titanium and chromium are completely oxidised and produce an equivalent amount of iron(II) sulphate molybdenum is re-oxidised to the Mo(V) (red) stage, which is fairly stable in air, and complete oxidation is effected by the permanganate, but the net result is the same, viz. Mo(III)- Mo(VI) vanadium is re-oxidised to the V(IV), condition, which is stable in air, and the final oxidation is completed by slow titration with potassium permanganate solution or with cerium(IV) sulphate solution. 

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