Apparent leak rate

The apparent leak rate data are given in units of liter-millimeter of mercury per second and as cubic centimeters of gas at N.T.P. per second. In experiments where the permeability is to be calculated the data will be given in the units of cubic centimeter (N.T.P.) per second per square centimeter per millimeter per centimeter of mercury. 

Tests at900°C. The long period or equilibrium apparent leak rates of both the mullite and zircon double-walled furnace units are of the order of the limit of error of the author s measuring method, i.e., 1.7 to 3.4 X 10-9 l.-mm. of mercury per second, or 2 to 4 X 10-9 cc. at N.T.P. per second. These values were observed after 15 to 24 hours of pumping and after exposure to a dry gas atmosphere with the zirconium specimen removed. Control experiments were made without the furnace tube present. 

Tests at 1000°C. After 1 hour of pumping the apparent leak rate of a mullite double-walled vessel is 1.7 X 10 8 l.-mm. of mercury per second or 2 X 10-8 cc. (N.T.P.) per second. In terms of permeability rates this value is equivalent to 3 X 10-10 cc./sq. cm./second/mm./cm. of mercury. Roeser (28) has studied a number of refractory procelain tubes from several manufacturers. His permeability values vary from 8.3 X 10 10 to 5 X 10-8 cc./sq. cm./second/mm./cm. of mercury. We have studied two double-walled vessels. These two tubes give nearly identical apparent leak rates although one is constructed of mullite and the other from zircon. It may be possible that more sensitive tests would show up differences in apparent leak rates. 

The comparison with Roeser s (28) data is only valid if we interpret our data in terms of permeation of gas through the walls of the furnace tubes. This type of permeation does not apply to the author s study in which a protective vacuum was used. However, regardless of the source of the gas, the performance of the tubes studied here is superior to the tubes studied by Roeser. The difficulties inherent in measuring and interpreting apparent leak rate data will be discussed in the next several sections. 

Table IV shows a summary of the experiments. The gases were admitted to the vacuum system in turn and, after evacuation, the apparent leak rate was measured at definite intervals. If helium was added for 2 hours at 900°C. at a pressure of 7.6 cm. the vacuum system did not completely recover after 1402 minutes. Hydrogen behaves in a similar manner.

Effect of gas pressure on adsorption and surface permeation processes. In order to understand the nature of this gas evolution following a previous charge of the furnace tube with gases, it is necessary to study the extent of adsorption and permeation of the gases into the tube material as a function of the pressure with the intermediate chamber evacuated. The extent of these processes is measured by apparent leak rate measurement 10 minutes after evacuation of the gas. 

Table V shows the results for oxygen. The adsorption or permeation process is apparently very strongly affected by the pressure used in pretreating the tube with oxygen. The apparent leak rate is roughly proportional to the square root of the pressure. One explanation of this law may be that the adsorption or surface diffusion of the gas is atomic in nature.

Effect of Time of Reaction on Apparent Leak Rate (900°C. mullite double-walled tube, 30-minute test)... 

A Tian-Calvet microcalorimeter (model BT 2.15, Setaram, France) was used to measure the enthalpies of adsorption of propane and propylene at room temperature. The samples (0.1 g) were treated under different conditions (i) vacuum at 523 K, (ii) vacuum at 773 K, (iii) He at 1073 K and (iv) H2 at 1073 K, all for 4h. Then, thqr were s ed into a Pyrex RMN tube in pure He and placed into the microcalorimetric celL A conventional manometric system coupled to the microcalorimet was used to m isare the amount adsorbed employing a (type 660) manometer witii a pr xsion of 0.001 Torr. The maximum apparent leak rate of the manometric system (including tire calorimetric cells) was 10 Torrmiri in a volume of about 60 cm. ... 

The influence of the D2 pressure during the exchange reaction on both the apparent rate constant (k) and the leak rate (R) is shown in Figure 3B. 

Figure 8. A. Arrhenius plot of the first-order rate constants on LaY % 8580cm x band, Flfi/70 0 3650cm l LaY O 3640cm l band, FJfi/70 % 3550cm l. B. Langmuir plot of the apparent rate constants (k) and the leak rate (R) for sample F55/70 at 850° C...

Noise present in the detector signal may have two components, long-term noise and short-term noise. The former causes a slow baseline wander measured over a 1 h period and may be attributed to fluctuations in temperature, column stationary phase bleed, flow rate variation, or pneumatic leaks. Short-term noise is observed as small, sharp spikes of shorter duration than component peaks and usually arises in the detector. Most integrators smooth the signal so that noise is not apparent unless a direct plot mode is selected. It is important to establish the mean noise level, the baseline, in order to determine the limit of detection. The time period of a peak is most conveniently described by the peak width at half height and the noise, N, is measured as the variation between maxima and minima of the noise peaks over the time period. The contribution of noise to the total component signal should be less than 1% (Figure 5.17). 

The existence of Arnold diffusion is irrelevant to the properties of separatrix manifolds, which still mediate the transport of chaotic trajectories within the regions of phase space they control. However, if Arnold diffusion is present in a given multidimensional system, the possibility exists for chaotic motion initially trapped between two nonreactive (trapped) KAM layers to eventually become reactive. This would presumably manifest itself as an apparent bottleneck to the rate of population decay, as chaotic trajectories slowly leak out from the region occupied by regular KAM surfaces into the portion of phase space more directly accessible to the hypercylinders. However, transport via the Arnold diffusion mechanism typically manifests itself on time scales much larger than those that we observe in numerical simulations (Arnold diffusion usually occurs on the order of thousands of mappings, or vibrational periods), and so it seems improbable that this effect would be observed in a typical reaction dynamics simulation. It would be interesting to characterize the effect of Arnold diffusion in realistic molecular models. 

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