Mean free path for air

The average diameter of a gaseous particle is about 3 x 10 cm, which is, as will be shown, very small compared with the mean free path. Table 5 gives the mean free path for air at some pressures. 

The mean free path for dry air at other temperatures and pressures can be determined from the relationship... 

Jennings (1988) reviewed the literature on viscosity with regard to compiling exact measurements for the mean free path of air molecules. He considered both dry air and moist air. At 20°C Jennings gives a value of 1.8193 x 10-4 cP for the viscosity of dry air, 1.815 x 10-4 cP for air at 50 percent relative humidity, and 1.8127 X 10-4 cP for air at 100 percent relative humidify. These figures indicate that for most aerosol work, a value for viscosity at 20°C of 1.82 x 10 4 cP is reasonably accurate regardless of the humidity. 

At room temperature, a simple expression is used for the calculation of the mean free path of air [3] ... 

Before we discuss the role of the Knudsen number, we need to consider the calculation of the mean free path for a vapor. It will soon be necessary to calculate the mean free path both for a pure gas and for gases composed of mixtures of several components. Note that even though air consists of molecules of N2 and O2, it is customary to talk about the mean free path of air, X.ajr, as if air were a single chemical species. 

The mean free path of air varies with height above the Garth s surface as a result of pressure and temperature changes (Chapter 1). This change for standard atmospheric... 

FIGURE 9.3 Mean free path of air as a function of altitude for the standard U.S. atmosphere (Hinds 1999). 

The mean free path of air varies with height above the Earth s surface due to pressure and temperature changes (Section 1.3.1). This change for standard atmospheric conditions (see Table A.7) is shown in Figure 8.3. The net result is an increase of the air mean free path with altitude, to roughly 0.2 m at 10 km. 

Nanoaerosol particles interact with the carrier gas molecules and consequently affect their dynamics. Nanoaerosol particles are small enough to approach the mean free path of air, which is about 67 nm under standard conditions. For nanoaerosol the continuum assumption is no longer valid and can attain free molecular flow there is a noncontinuum interaction between the particles and the carrier gas. The corresponding slipping effect is quantified by the Cunningham coefficient in terms of gas mean free path (A) and particle diameter ... 

Since an additional ellipsometric measurement would be needed to determine the carbon-overcoat thickness, the ellipsometric measurement of PFOM thickness directly on non-carbon-overcoated silicon is more straightforward. Silicon strips and wafers were dip coated with PFOM. The PFOM thickness measnred by ellipsometry and the dIX from XPS are listed in table 4.8. The thickness measured by ellipsometry was divided by the dIX from XPS for each sample (last two columns in table 4.8). The experimentally determined average electron mean free path for PFOM film is X = 2.66 nm. Sliders were dip coated with PFOM at the same conditions as the silicon wafers and strips, and dIX was measured on the air bearing surface of each slider by XPS. These dIX were multiplied by A, = 2.66 nm, as determined above, to estimate the PFOM thickness on the air bearing surface. These results are listed in table 4.9. The concentration of the PFOM solution was 650 ppm, and the withdrawal rate was 1.6 mm/s. 

At low temperatures, the "knee" of the curve, where conductivity drops off from the high-pressure "plateau," occurs at lower pressures. This shift is explained by considering that the mean free path of air is shorter for low temperatures. Thus, it is necessary to reach a lower pressure before the mean free path lengthens to a point where it becomes equal to insulation pore size, and gas conductivity is reduced. 

Space away from Earth surface is the closest natural approximation of perfect vacuum. In this condition, force of friction is almost negligible. However, even in the deep vacuum of intergalactic space, there are merely few hydrogen atoms per cubic meter (Borowitz and Beiser 1971). In comparison, the air at Earth surface contains about 10 molecules per cubic meter (Davies 1977). The sparse density of matter in outer space means that electromagnetic radiation can travel great distances without being scattered the mean free path for a photon in intergalactic space is about 10 km (Chapmann 1991). 

To evaluate the heat transfer by molecular conduction, we will first need to determine the mean free path for the remaining gas in the evacuated space from Eq. (7.5). Assume that the gas in the evacuated space is air. The viscosity of air at 300K is 18.47 //Pas. 

---