Cunningham’s Correction

Cunningham s Correction—In addition to the upper limit of particle size, Stokes equation also has a lower limit. When the particles are small compared with the mean free path of the molecules, the particles may slip between the molecules. Thus, less resistance is encountered and the particles develop a higher velocity. For diameters of O.l/i and less we must apply a correction to the velocity determined by Stokes equation, Eq (2-9), which is due to Cunningham (1910)... 

Calculate the settling rates for particles having diameters of 0.01, 0.03, and 0.05 m with and without Cunningham s correction. Assume settling in air at 20 deg C and a specific gravity relative to air of 8.3... 

For small particles where particle diameter is similar to the mean free path of gas molecules (A.), Cunningham s correction factor Cc must be applied ... 

For droplets in air less than about 5 pm in diameter, the actual drag force is even lower, since the surrounding air is not a continuum at these scales. Millikan s resistance factor (or Cunningham s correction) multiplies the terms on the right-hand side of Eq. 9 to form the corrected drag force ... 

The Cunningham s correction factor has to be applied since the particle size is less than 5 j,m. The mean free path, A, equals... 

Cunningham slip correction Millikan s resistance factor... 

Millikan s resistance factor Cunningham slip correction Definition... 

Stokes-Cunningham correction factor sphericity correction constant Coulomb s law constant, 8.987 x 10 ... 

When water undergoes self-ionization, a range of cationic species are formed, the simplest of which is the hydronium ion, HjO (Clever, 1963). This ion has been detected experimentally by a range of techniques including mass spectrometry (Cunningham, Payzant Kebarle, 1972), as have ions of the type H+ (HaO) with values of n up to 8. Monte-Carlo calculations show that HjO ions exist in hydrated clusters surrounded by three or four water molecules in the hydration shell (Kochanski, 1985). These ions have only a short lifetime, since the proton is highly mobile and may be readily transferred from one water molecule to another. The time taken for such a transfer is typically of the order of 10 s provided that the receiving molecule of water is correctly oriented. 

FIG. 14-115 Experimental collection efficiencies of rectangular impactors. C is the Stokes-Cunningham correction factor pp, particle density, g/cm3 Ug, superficial gas velocity, approaching the impactor openings, cm/s and g, gas viscosity, P. [Calvert, Yung, and Leung, NTIS Publ. PB-248050 based on Mercer and Chow, J. Coll. Interface Sci., 27, 75 (1968).]... 

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