S TOKES' law forms the basis of most methods used to obtain the particle size distribution of soils in the particle size range below 50 microns. Stokes' law states that the resistance (F R) offered a perfect sphere moving through a fluid under a condition of streamline (viscous) flow is (a)

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Many industrial processes, including waste treatment and fermentation to produce alcohol and acids, require oxygen in substantial quantities to promote biological growth. Oxygen is only a very slightly soluble gas of the order of 10 parts per million in water from air. Even the use of pure oxygen will increase the solubility to only about five times this value. Thus, the amount of oxygen transferred in a single pass through an aeration device can only be very small. An ordinary waste treatment process may require an amount of oxygen equivalent to saturation of the liquid from 100 to 200 times. The low solubility leads to relatively high energy requirements to provide the oxygen needed. An ideal aeration device would be one in which the gas was not compressed and liquid turbulence was minimized.It was observed that saturation of water by air was approached in an ordinary laboratory aspirator (8). This nozzle type of device, as well as an orifice or Venturi, operate on the Bernoulli principle of the conservation of energy; that is an increase of velocity (kinetic energy) at a point in the flow stream results in a decrease of pressure (pressure energy). The velocity can be increased such that the pressure at the restriction falls below that of the atmosphere and air is forced into the liquid stream through a suitable opening.Preliminary work (10) indicated that there was at least some evidence that devices of this type could be used as economical mass transfer equipment, and that even though residence times were small, transfer rates were relatively large. There was also an indication that the energy consumption expended in flow of the liquid through the device might be less than that for other methods of aeration. The air-water system afforded observation of mass transfer phenomena. The effects of dissolved substances and simulated industrial wastes on the transfer process were also investigated. THEORETICAL CONSIDERATIONSIt has been reported (6, 14) that the bulk of the mass transfer from a gas to a liquid (bubbles) occurs when interfacial area is first formed. This observation results from unsteady state transfer to liquid elements which predominates during the initial period of contact of the phases (17). This behavior is significant for transfer in Bernoulli types of devices in which the residence time in the high velocity section is quite small and flow is highly turbulent. In these devices the gas is brought into contact with the liquid at the point of low pressure. Subsequent movement of the two-phase stream through the expansion section, a region of decreasing velocity (increasing pressure), results in a reduction of bubble size and a smaller interfacial area of transfer. Because of high turbulence, the liquid elements of the interface are rapidly replaced and a new transfer area is formed.The partial pressure of oxygen on the gas side increases with increasing Venturi pressure, and the liquid concentration increases downstream from the throat; the driving forces involved for mass transfer are thus somewha...

Greek Letters cz / 3 bo so = electrostatic permittivity @ = circumferential angle I.C = gas viscosity pro pee, etc. = components of eddy viscosity tensor p p d s p o ps urn, coo, etc. = components of Reynolds stress tensor Subscripts c = characteristic value f n = nozzle r = radial component s = solid particle z = axialcomponent 8 = circumferential component Superscripts and Symbols * = dimensionless value o = jet angle with radius in a horizontal plane = jet angle with wall in a vertical plane = temperature coefficient of volume expansion at To = density of suspending gas = density of dispersed solids = characteristic average gas density = density of solid particle = relative to the gas velocity = temporal or ensemble average = order of magnitude given in parentheses LITERATURE CITED

Steady and unsteady transfer of oxygen from air to liquid was observed using a 3-in. diameter column. Oxygen transfer efficiencies obtained were roughly 1% per foot from 14 to 53 ft for sulfite solutions. Air input through single orifices of V4-and Vg-in. diameters showed similar column performance with the larger diameter favored. Average values of the transfer factor, (KLa), were 14 hM for steady-state transfer to sulfite and 13 hr-1 for unsteady-state transfer to water at the same air rate. This provides validity for the experimental and interpretative methods employed. Possible advantages from use of tall tanks are lower energy requirements for air compression by at least a factor of 4, smaller land area needs, and simplified construction and piping requirements. A disadvantage is increased liquid pumping costs. Design implications for biological reactors are reduced tank volumes, less tendency for upset resulting from high oxygen availability, and a sludge mass which is more reactive and easily suspended.