Free-molecular

The maximum acceptable concentration for free (molecular) bromine is 0.1 mg/L for ionic bromate, 100 mg/L. 

Partial Concentration. The sum of the partial concentrations (pressures) in a free molecular gas is equal to the total concentration (pressure). However, all gaseous components, at the same partial pressure or absolute pressure or ratios thereof, are not likely to have the same significance to any or all vacuum appHcations. The significance of the condensed-phase concentrations must therefore be considered. 

In general, the test object caimot be heated above its operating temperature in space. As free molecular conditions are obtained around the object, it outgases and, if solar-spectmm photons impinge on the object, increases the release of gas. Because the object is in a vessel and the area of the hole lea ding to the gas pump is small compared with the projected interior area of the vessel, molecules originating from the test object can return to the test object provided that they do not interact in some manner with the vessel walls and the other components of the molecular environment. The object inside the vessel estabhshes an entirely different system than the clean, dry, and empty vacuum vessel. The new system no longer has the capabiUty to reach the clean, dry, and empty base pressure within a reasonable time. 

In free molecular flow, if gaseous conductance were not independent of the flow direction, a perpetual-motion machine could be constmcted by connecting two large volumes by a pair of identical ducts having a turbine in front of one of the ducts. A duct that has asymmetricaUy shaped grooves on its waU surface could alter the probabUity of molecular passage in such a way that for a tube of equal entrance and exit areas, the probabUity of passage would be made directional. 

Kn = 0.1-10 Transition flow between slip flow and free molecular flow, treated statistically, e.g., by the Boltzmann equation... 

Kn> 10 Free molecular flow motion of individual molecules, that must be modeled and then treated statistically... 

The much lower amount of formic acid formation during methanol oxidation compared with formaldehyde oxidation agrees with expectations if we assume that formic acid is predominantly formed by further oxidation of (free) molecular formaldehyde produced in a first step of methanol oxidation. Under the present reaction conditions, only a very small fraction, about 1 part per thousand, of the total reactant passing through the cell reacts to give formaldehyde, formic acid, or CO2. The rest... 

Figure 14 Free molecular flow through an orifice Knudsen effusion.

Knudsen effusion will be involved later as we discuss free molecular flow in channels and tubes. Knudsen effusion also finds application in the measurement of the vapor pressure of materials of low vapor pressure, typically in the... 

As the pressure is lowered, slip occurs, and the flow mechanism is referred to as transition flow. At pressures so low that collisions between gas molecules are rare compared to the collisions between the gas and the tube wall, the flow is said to be Knudsen flow or free molecular flow. Free molecular flow prevails when Lla > 1. For air at 25°C, this condition means that we have free molecular flow when aPm on < 5. We now consider an intuitive derivation of the result for Fc in the free molecular flow region. 

Figure 20 Mass transfer and momentum exchange during free molecular flow in a long tube.

The conductance for free molecular flow in an orifice of nonzero thickness may be written... 

Knudsen s result for free molecular flow in a tube is given by Eq. (73). With/ = 1, Knudsen s result and the second term in Eq. (84) differ only by a numerical factor. In Knudsen s result, the numerical factor is 2/3 in Eq. (84), the corresponding factor is n/8. Thus, except for a modest difference in the numerical factor, the slip term in Eq. (84) is the Knudsen free molecular flow term, and transition flow in a tube appears as a mixture of free molecular flow and viscous flow. That is, the total flow behaves approximately as a sum of two parallel flow mechanisms. 

Knudsen writes the conductivity coefficient as a linear combination of the viscous flow coefficient, Fv, and the free molecular flow coefficient denoted Fm,... 

Figure 22 The pressure dependence of conductance A plot of the ratio of the total conductance to the free molecular flow conductance as a function of the ratio of tube radius to mean free path.

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