Cunningham Correction Research Articles

Mechanics of removing glass particulates from a solid surface

A series of experiments underscores the importance of the capillary force in the adhesion of a particulate to a surface. The capillary force resulting from a liquid film between a particulate and a surface remains even after the particulate-surface combination is baked above the boiling point of the liquid for 24 h. A mechanical scrubbing force is required to remove the particulate held to a surface by a capillary force. The force on a particulate applied by an air jet is calculated using Stokes's law modified by Cunningham's correction factor. Furthermore, the force required to roll a particulate off a surface is calculated from the theoretical adhesion force between a particulate and a surface and particulate deformation characteristics. The applied force is in good agreement with the theoretical force required to roll off a particulate.

Velocity of solid particles entrained with reduced-pressure air flow in horizontal duct.

The velocity of glass beads entrained with air flow in a horizontal square duct was measured in a range of pressures: 760-1 mmHg, ua: 10, 18 m/sec, dp: 81.5-184 microns, D: 2.45 cm. It is pointed out that with respect to the flow regions in duct and around particle the present experimental conditions are considerably different from those in previous works at atmospheric pressure. Data obtained under reduced pressure are correlated within ±30% by the following equation, which includes the Cunningham correction coefficient Cm. (ua-Up)/ua=1.22Cmdpu0.4aua=air velocity [cm/sec], up=particle velocity [cm/sec], dp=particle diameter [cm].

Brownian Coagulation of Aerosols in the Transition Regime

Earlier experimental studies of Brownian coagulation of aerosols have been extended into the transition regime, i.e. Knudsen number values 0.8–1.6. This was done by working with the same range of particle size as earlier, but at a reduced pressure. A number of modifications were made in the experimental technique, including the use of diethylhexylsebacate instead of dibutylphthalate in order to avoid the possibility of loss to the walls by evaporation. The rate of coagulation at Kn = 0.2 agreed closely with that predicted, using Smoluchowski's coagulation constant for the continuum regime as modified by the Cunningham correction. The rate at higher Knudsen numbers (Kn = 0.8–1.6) was somewhat lower (about 20%) than that predicted by Fuchs' formula for interpolation between the continuum and free molecule regimes.

Brownian coagulation of aerosols at low Knudsen number

Dibutyl phthalate aerosols of narrow size distribution have been prepared in a falling-film generator using nitrogen rather than helium as the carrier gas. The Knudsen number in nitrogen is considerably lower so that the Cunningham correction is much less. A large number of coagulation experiments give average coagulation times in excellent agreement with theory. However, the spread of the values is much greater than obtained earlier in helium. The spread of the results reported here may be due to the lower thermal conductivity of nitrogen.

PARTICLE SIZE CLASSIFICATION BY DEPOSITION ANGLE IN A GAS CENTRIFUGE AT REDUCED PRESSURE

Centrifugal particle size classification by a gas centrifuge which produces a forced vortex was investigated at reduced pressures. In this method, different particle trajectories cause the formation of a continuous gradation of particle size on the rotor wall. Here, particles in the subsieve and submicron ranges were classified with good resolution because the ''Cunningham correction'' increases as pressure decreases. Also, the computed solutions gave excellent agreement with the experimental results. The numerical solutions with and without the integral term for non-uniform motion have been compared, the approximate equation of best fit for the drag coefficient of spherical particles being used in both cases.

On the Aerosol Particle Slip Correction Factor

The slip correction factor for equations of particle motion is an item to which apparently little thought is given these days. The fact that the constants are for the most part empirical and that the values used are specifically for an air/oil droplet system are not usually considered even when very different atmospheres and aerosols are under investigation. Fuchs and Stechkina have developed a completely theoretical expression which requires as a measurement only the percentage of gas molecules reflected diffusely from the particle. This development is presented in simplified form and its use encouraged as a direct replacement for the Cunningham correction factor.

The influence of the particle size of homogeneous insecticidal aerosols on the mortality of mosquitoes in confined atmospheres

Cooperative tests were made between the Bureau of Entomology and Plant Quarantine, and the Central Aerosol Laboratory, Columbia University, to compare the mortalities produced in confined atmospheres by aerosols of different sized particles. Apparatus for the generation of homogeneous aerosols, and instruments and methods of measuring the particle size and concentration, which had been developed by the Central Aerosol Laboratory in previous studies related to screening and other smokes, were utilized. Exposures of 10–30 minutes in aerosol concentrations of around 100 γ/l. were necessary to produce high mortalities when particles of 1 μ or less in diameter were used. Exposure of 0.5–2 minutes in aerosol concentrations of around 25 γ/l. produced high mortality when particles were 5–16 μ in diameter. When Ct (concentration of oil in γ containing 8% DDT multiplied by time of exposure in minutes) values which produced 50% mortality of females (calculated by graphical interpolation) were plotted against particle size, the toxicity was shown to be increased by 250 or more times by increasing the diameter of the particle from 0.33 to 11 μ. This curve corresponds to a curve in which the time necessary for an aerosol to settle out of 1 cc. is plotted against particle size, as calculated according to Stokes' Law and Cunningham's correction. It also shows that the toxicity is proportional to the rate of deposition which, in turn, is proportional to the square of the radius (or diameter) of the aerosol particle for the sizes discussed.