Adiabatic crystallization

For the same vacuum level, a crystallizing slurry will have a higher temperature than predicted for the pure solvent because the vapor pressure of the solvent is reduced by the presence of the solute (boiling point elevation). For adiabatic crystallization with the contents temperature as the input to the master control loop, the same temperature profile appropriate for crystallization by jacket cooling would apply here. However, the capability of the vacuum source and the line pressure drop should be considered in conjunction with the boiling point elevation to ensure that the desired final temperature can be met. If this is not satisfied, the desired yield may be achieved by removing some of the distillate, provided the saturation of an impurity is not reached. For most... 

Another highly suitable crystallization technique is adiabatic crystallization where the driving force for crystallization is the of super-saturation in the concentrated lactic acid solution brought about by heat neither being removed nor supplied. This involves lowering the temperature of the concentrated solution (solvent evaporates) and increasing the concentration of LA (two effects (a) solvent evaporates and (b) the temperature of the concentrated LA solution drops, as a result of which the solubility decreases and super-saturation may be resulted). 

Since quantum field many body techniques are not directly transferable into quantum chemistry dealing with small molecular systems, they are not fully transferable into the solid-state physics dealing with great systems (crystals) either. As it was explained in detail in this work, only the COM many-body formulation is applicable in non-adiabatic cases. For non-adiabatic crystals the state of conductivity and superconductivity are two possible solutions of the extended Born-Handy formula. This is a quite different view from that using only the classical many body (without COM). The non-adiabatic treatment of crystals leads always to the splitting into two subsystems. In the case of conductors the first subsystem is the adiabatic core consisting of nuclei and all valence bands, and the second subsystem is the fluid of quasi-free conducting electrons. The explanation of conductors on the basis of a COM true many-body treatment is not so simple as in the case of the... 

Solution crystalli tion (adiabatic evaporation (vacuum cooling))... 

Calculated from single-crystal adiabatic moduH by the Voight method. 

The specific enthalpies ia equation 9 can be determined as described earUer, provided the temperatures of the product streams are known. Evaporative cooling crystallizers operate at reduced pressure and may be considered adiabatic (Q = 0). As with of many problems involving equiUbrium relationships and mass and energy balances, trial-and-error computations are often iavolved ia solving equations 7 through 9. 

If the crystallizer is not of the evaporative type but rehes only on adiabatic evaporative cooling to achieve the yield, the heating element is omitted. The feed is admitted into the circulating hue after withdrawal of the slurry, at a point sufficiently below the free-hquid surface to prevent flashing during the mixing process. 

The exchange reactions (6.20) and (6.21) have been among the basic objects of chemical-reaction theory for half a century. Clearly further investigation is needed, incorporating real crystal dynamics. It is worth noting that the adiabatic model, upon which the cited results are based, can prove to be insufficient because of the low frequency of the promoting vibrations. 

In the Kobe process (Japan) the feed liquor is adiabatically compressed to a point just below the eutectic, where crystallization occurs. Then the mother liquor is removed and the pressure is gradually reduced to atmospheric pressure. It appears that for this process cycle times are short, in the order of 5 minutes. 

The heat of decomposition (238.4 kJ/mol, 3.92 kJ/g) has been calculated to give an adiabatic product temperature of 2150°C accompanied by a 24-fold pressure increase in a closed vessel [9], Dining research into the Friedel-Crafts acylation reaction of aromatic compounds (components unspecified) in nitrobenzene as solvent, it was decided to use nitromethane in place of nitrobenzene because of the lower toxicity of the former. However, because of the lower boiling point of nitromethane (101°C, against 210°C for nitrobenzene), the reactions were run in an autoclave so that the same maximum reaction temperature of 155°C could be used, but at a maximum pressure of 10 bar. The reaction mixture was heated to 150°C and maintained there for 10 minutes, when a rapidly accelerating increase in temperature was noticed, and at 160°C the lid of the autoclave was blown off as decomposition accelerated to explosion [10], Impurities present in the commercial solvent are listed, and a recommended purification procedure is described [11]. The thermal decomposition of nitromethane under supercritical conditions has been studied [12], The effects of very high pressure and of temperature on the physical properties, chemical reactivity and thermal decomposition of nitromethane have been studied, and a mechanism for the bimolecular decomposition (to ammonium formate and water) identified [13], Solid nitromethane apparently has different susceptibility to detonation according to the orientation of the crystal, a theoretical model is advanced [14], Nitromethane actually finds employment as an explosive [15],... 

Here V is the crystal volume, k-p and ks are the isothermal and adiabatic compressibility (i.e., the contraction under pressure), P is the expansivity (expansion/contraction with temperature), Cp and Cv are heat capacities, and 0e,d are the Einstein or Debye Temperatures. Because P is only weakly temperature dependent,... 

Many hypotheses for initiation of liquid expls have been proposed, of which Bowden et al (Refs 13, 14a 27) suggested adiabatic compression of gas bubbles Johansson et al (Ref 28) - vapor or droplet burning Andreev (Ref 29) - droplet formation or suspension behind a burning front is capable of causing a transition to detonation Bolkhovitinov (Ref 33a) - crystallization of the material under pressure Cook et al (Ref 34b) - initiation occurs with the development of a pressure-generated metallic state accompanied by a plasma that provides the postulated requirement of high heat conductivity... 

The spots may be formed in two main ways 1) By friction on the confining surfaces of expls, on grit particles, or on crystals of the explosive itself and 2) By the adiabatic compression of small occluded gas bubbles the presence even of a small bubble can render most expls very sensitive to impact (Ref 19)... 

Ref 22, pp 161-62. Under the title "Thermal Effect of Impact is discussed initiation of liquid expls, such as NG, NGc, etc. It differs from initiation of solid expls (discussed on p 153 of Ref 22) in that there is no friction between crystals as in solids, but everything depends on rise of temperature created by adiabatic compression of gas or vapor in minute bubbles.. For example, with NG contg a bubble as small as 0.1 mm in diam 100% explns can be obtd with impact energy of 400 gram-cm, while 10 to 10 g-cm are required when no gas bubble is present. The temp T2 reached in a bubble due to adiabaric compression of the gas depends, in the case of ideal gas, on the... 

Cook (Ref 3) summarizes the adiabatic decomposition of explosives. Still more recently Bowden (Ref 7) reviewed energy localization effects in single crystals. (See Voi 4, pp D563-69). All these reviews as well as more studies (to be discussed below) emphasize the thermal nature of explosive initiation. Two simple examples will reveal that the thermal energy to produce initiation must be highly localized, ie unless the input energy, known to produce explosions, is concentrated into hot spots no explosions can occur... 

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