Dust free space

The time of movement of a particle from a given point near the plate to the edge of the dust-free space may be observed experimentally. The temperature of the gas is known and the temperature gradient is easily determined from the gas temperature and the observed thickness of the dust-free space. Cawood found that Eq (10-5) gives results of the correct order of magnitude but somewhat greater than observed experimentally. The difference between the results obtained by Eq (10-5) and those obtained experimentally may be attributed to the fact that the temperature gradient is not constant. 

Experimental—Extensive studies of the nature of the dust-free space about hot bodies were made by Watson (1936) who established the relation between the thickness of the dust-free space and the tempera-... 

The mean value of K for vertical planes is approximately 15.6 X 10 and for horizontal rods is 7.6 X 10-6. Thus, for horizontal rods 8 = 7.6 X 10 6 AT-Hc-°- and for vertical plane surfaces 8 = 15.6 X 10 6 ATwhere 8 is expressed in cm, AT in deg C, and Hc in calories per sq cm per sec. Watson reports that lies extended the work discussed above to a study of the effect of air pressure on the dust-free surface for a vertical-plane surface 3.1 cm high and 3.0 cm wide. Iels found that at any one temperature the thickness of the dust-free space... 

The dust-free space surrounding hot bodies. Trans. Faraday Soc., 32 (Part 8) 1073-1081. 

Early observations on the width of the dust-free space were made by Aitken (1884a, b) and Lodge and Clark (1884). Later Watson (1936) and Miyake (1935) developed an empirical formula which fit experimental observations that the dust-free space increases with increasing temperature of the body and decreasing air pressure, and decreases with increasing molecular weight of the surrounding gas. For example, Watson found an empirical relationship between the width in centimeters of the dust-free space adf and temperature in the form... 

Example 11.1 A vertical heating element is held at a temperature of 100°C higher than the surrounding air. Estimate the width of the dust-free space around the surface of the element. 

Thermophoretic forces produce very obvious effects near areas of significant temperature gradients. For instance, one can often observe a black deposit on the wall just above a hot-water radiator or pipe. Convection currents conduct the warm gas and particles over the radiator, but since the cooler surfaces nearer the radiator are not protected by a dust-free space, deposition takes place. On a ceiling or on walls of rooms heated by convection, one can often see a replica of the construction behind the plaster formed by deposited particles. Again, the dust is deposited on the cooler portions of the surface on spaces between the laths if the laths are poor heat conductors and directly opposite the laths if they are good conductors. In a room that is heated by direct radiation, such as by an open fire, the walls and furniture of the room are warmer than the air, so that particles suspended in the air are not deposited by thermal forces (Lodge, 1883 Gibbs, 1924). 

As mentioned earlier, thermal forces give rise to a dust-free space around bodies that are warmer than their immediate environment. Formulation of an equation which describes the width of this dust-free space appears to be quite difficult, generally involving numerical so-... 

For the heated vertical plate and horizontal cylinder, the flow results from natural convection. The stagnation configuration is a forced flow. In each case the flow is of the boimdai7 Kiyer type. Simple analytical solutions can be obtained when the thickness of the du.st-free space is much smaller than that of the boundary layer. In this case the gas velocity distribution can be approximated by the first term in an expansion in the distance norroal to the surface. Expressions for the thickness of the dust-free space for a heated vertical surface and a plane stagnation flow are derived below. 

The thickness of the dust-free space increases with distance from the bottom edge of the vertical plate. The value of K can be obtained from (2.56),... 

Values of 5df based on the first term of the expansion of the velocity near the surface compare well with numerically computed values based on the complete velocity and temperature distributions. Calculations of iat for alumina and copper particles (0.5 < dp < 2 /im) indicate that for temperature differences as small as 10°C the dust-free space would be thick enough to prevent particle deposition. 

So far, the analysis Has not taken into account the effects of the Brownian motion which allows diffusive leakage through the dust free space to the heated surface. This effect has also been studied in some detail in connection with wafer contamination (Friedlanderet al., 1988 Ye et al. 1991). The equation for simultaneous convection, diffusion, thermophoresis and sedimentation for the nne dimensional stagnation fiow configuration is... 

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