Checker

Further details of the BB, sometimes referred to as Ladyzhenskaya-Babuska-Brezi (LBB) condition and its importance in the numerical solution of incompressible flow equations can be found in textbooks dealing with the theoretical aspects of the finite element method (e.g. see Reddy, 1986), In practice, the instability (or checker-boarding) of pressure in the U-V-P method can be avoided using a variety of strategies. 

Fig. 10. (a) Wulff furnace design, (b) Checker detail of Wulff furnace refractory. 

Forsterite Refractories. Refractories made from forsterite, Mg2Si04, resist alkah attack and have good volume stabiUty, high temperature strength, and fak resistance to basic slags. Uses include nonferrous metal furnace roofs and glass-tank refractories not in contact with the melt, ie, checkers, ports, and uptakes. 

Other burners are used for low capacity operations. A cascade or checker burner, ia which molten sulfur flows down through brick checkerwork countercurrent to a flow of air, is used ia small units with a sulfur trioxide converter to condition gases entering electrostatic precipitators at boiler plants operating on low sulfur coal. A small pan burner, which is fed with soHd, low carbon sulfur, is used to produce sulfur dioxide for solution ia irrigation water to control the pH and maintain porosity ia the soil. The same type of burner is used to disiafect wastewater ia this case sulfur dioxide is used iastead of chlorine. 

Refractories. Its low coefficient of expansion, high thermal conductivity, and general chemical and physical stabihty make sihcon carbide a valuable material for refractory use. Suitable apphcations for sihcon carbide refractory shapes include boiler furnace walls, checker bricks, mufflers, kiln furniture, furnace skid rails, trays for zinc purification plants, etc (see Refractories). 

Heat is transferred by direct contact with solids that have been preheated by combustion gases. The process is a cycle of alternate heating and reactingperiods. The Wulf process for acetylene by pyrolysis of natural gas utilizes a heated brick checker work on a 4-min cycle of heating and reacting. The temperature play is 15°C (59°F), peak temperature is 1,200°C (2,192°F), residence time is 0.1 s of wmich 0.03 s is near the peak (Faith, Keyes, and Clark, Industrial Chemicals, vol. 27, Wiley, 1975). 

The technique used here has been described previously by the checkers. Instead, the submitters used a dry 500-mL, three-necked flask equipped with a variable speed mechanical stirrer, a IQQ-mL pressureequalizing dropping funnel topped by a gas inlet and a Claisen head containing a low temperature thermometer (-70 C to +35°C), and a bubbler. A stream of nitrogen followed from the gas inlet. 

Dimethyl carbonate is available from Aldrich Chemical Company, Inc. The checkers dried the tetrahydrofuran Immediately before use by distillation from the sodium ketyl of benzophenone under a nitrogen atmosphere. The submitters purchased sodium hydride (50% oil dispersion) from Alfa Products, Morton/Thiokol, Inc. The checkers used 12.24 g of a 50% dispersion of sodium hydride in mineral oil obtained from the same supplier. The dispersion was washed with three portions of pentane to remove the mineral oil and the remaining sodium hydride was allowed to dry under nitrogen. 

The submitters used a 35% dispersion of potassium hydride in mineral oil supplied by Alfa Products, Morton/Thiokol, Inc. the mineral oil was separated by washing the dispersion with five portions of dry hexane. The checkers used a 25% dispersion of potassium hydride in mineral oil obtained from the same source but without removing the mineral oil. The oil remained in the distillation pot when the product was distilled. 

Diethyl ether was dried by the submitters by refluxing over lithium aluminum hydride and was distilled immediately before use. The checkers distilled diethyl ether from the sodium ketyl of benzophenone before use. 

No gas evolution was observed by the checkers in some runs in which an older lot of sodium hydride was used. In this case, the cooling bath was removed and the mixture was allowed to stir at room temperature until the bubbling ceased. 

Diethyl chlorophosphate, supplied by Aldrich Chemical Company, Inc., was used by the submitters without purification and was handled in a glove bag under an atmosphere of dry nitrogen in a well-ventilated hood. The reagent was distilled and stored under nitrogen by the checkers. Aliquots were withdrawn with a syringe as needed. 

Ethereal methyl1ithiurn (as the lithium bromide complex) was obtained by the submitters from Aldrich Chemical Company Inc. The checkers used 1.19 M methyl1ithiurn-lithium bromide complex in ether supplied by Alfa Products, Morton/Thiokol, Inc. The concentration of the methyllithium was determined by titration with 1.0 M tert-butyl alcohol in benzene using 1,10-phenanthroline as indicator. The submitters report that ethereal methyllithium of low halide content purchased from Alfa Products, Morton/Thiokol, Inc., gave similar results. 

The purity of the product was determined by the checkers by GLC analysis using the following column and conditions 3-nm by 1.8-m column, 5% free fatty acid phase (FFAP) on acid-washed chromosorb W (60-80 mesh) treated with dimethyldichlorosilane, 90 C (1 min) then 90 to 200 C (15°C per rain). The chromatogram showed a major peak for methyl 2-methyl-l-cyclohexene-l-carboxylate preceded by two minor peaks for methyl 1-cyclohexene-l-carboxylate and l-acetyl-2-methylcyclohexene. The areas of the two impurity peaks were 5-6% and 0.5-2% that of the major peak. The purity of the product seems to depend upon careful temperature control during the reaction. The total amount of the two impurities was 14-21% in runs conducted at about -15 to -20°C or at temperatures below -23°C. 

The submitters report that after approximately 1 hr some lead(Il) acetate is deposited as an orange-red gum which may temporarily restrict the motion of the stirring bar this was not observed by the checkers. The material generally crystallizes after a short period as a white solid. 

A solution of methyl ithium in ether is prepared from lithium wire and methyl bromide according to the literature procedure, and titrated by the same method as Note 6. The checkers used 1.1 M methyl ithium from Aldrich. 

Cyclopentene oxide is purchased from Arapahoe Chemicals, Boulder, CO, and used without purification. The checkers bought cyclopentene oxide from Lancaster Synthesis. 

Since the efficiency of this washing is dependent upon the degree of settling, the checkers recommend that washing with 50-mL batches of ether be continued until the smell of the alcohol is no longer detectable on a sample of the dry salts. 

The checkers also carried out the entire sequence on three times the scale with slightly better yields. 

The function of the trap is to condense the hexane from the n-butyl-lithium solution. The checkers used a 1-L three-necked flask fitted with a short delivery tube (a quick fit air bleed tube was used), stopper, and rubber tubing connection. The submitters used a water aspirator and a 1-L filter flask with a drying tower between. 

One should try to remove as much hexane as possible from the n-butyl-llthium solution (i.e. greater than 90%) because the purity of the product depends on the polarity of the reaction medium. A warm water bath was used to facilitate solvent removal. The checkers used a variable pressure oil pump with the vacuum adjusted to ca. 10-20 imi. 

Methyl-2-propen-l-ol, purchased from Aldrich Chemical Company, was distilled from anhydrous potassium carbonate. It was added directly to the n-butyllithium solution using a long needle. The checkers quickly replaced the pressure-equalizing dropping funnel with a serum cap to carry out this addition. The funnel was fitted to a small dry flask to prevent the introduction of moisture during the addition period and replaced on the reaction flask immediately afterwards. 

The checkers renewed the ice bath when additions were complete and allowed the flask to remain in the ice bath without addition of fresh ice. 

An extremely violent reaction is observed if the dianion is quenched above 0°C, with ether boiling off at an uncontrollable rate. The submitters observed that if the chiorotrimethyl si lane addition is performed at a lower temperature, the reaction temperature will remain below that of the boiling point of ether. A dry-ice bath made up of 80 20 (v/v) ethanol-water was used the checkers measured a bath temperature of -55 C and kept the reaction in the bath for 16 min before adding chlorotnmethylsilane. 

The submitters observed the appearance of a brown color at this point. The checkers obtained a brown color only after the reaction mixture was added to ether. In a run at half scale the reaction mixture remained milky white for 35 min and turned brown only when ether (500 mL) was added to It. 

The submitters distilled most of the solvent using a bath temperature increasing up to 100°C. The checkers used a rotary evaporator with a hot water bath. 

The checkers observed small MMR peaks assigned to mineral oil at 6 0.9 and 1.28 and peaks assigned to 2-methyl-l-trimethylsi1oxy-3-trimethy1sily1-2-propene at 6 1.87 and 4.1. When the reaction was carried out at half scale the quantity of the latter Impurity was not measurable from the NMR integral however, a run at full scale gave about 10% of the Impurity as estimated from the MMR integral. The product from the run at half scale had bp 56-57 C (2 nm), submitters bp 65 0 (5.5 am). 

The checkers used a dropping funnel with temperature-control Jacket (Normag N 8055, Otto Fritz GmbH, Normschliff-Aufbaugerate (Norraag), D-6238 Hofheim am Taunus). 

The checkers used a home-made, glass-jacketed funnel sealed with a rubber septum. The submitters cut one side and part of the bottom of a styrofoam cup and with tape held this in place around the lower part of the addition funnel. 

Caution tevt-Butyllithium ie pyvophovia in air exaeee quantities of the reagent in the syringe should be discarded oery carefully- The checkers used the reagent available from Aldrich Chemical Company Ltd., England and standardized it by double titration with ethylene dibromide and hydrochloric acid. ... 

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