Factor, Stokes

STORE S LAW. (1) The rate at which a spherical particle will rise or fall when suspended in a liquid medium varies as the square of its radius the density of the particle and the density and viscosity of the liquid are essential factors, Stoke s lav/ is used in determining sedimentation of solids, creaming rale of fat particles in milk, etc. (2) In atomic processes, the wavelength of fluorescent radiation is always longer than that of the exciting radiation,... 

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

It is well known that the intensity of scattered light varies as the fourth power of the frequency, and based on this alone one would predict the Stokes lines to be less intense than the anti-Stokes by a factor of... 

The upper sign is for anti-Stokes scattering, the lower for Stokes scattering. The factor in the parentheses is... 

For spherical particles of radius R moving through a medium of viscosity 17, Stokes showed that the friction factor is given by... 

The spherical geometry assumed in the Stokes and Einstein derivations gives the highly symmetrical boundary conditions favored by theoreticians. For ellipsoids of revolution having an axial ratio a/b, friction factors have been derived by F. Perrin, and the coefficient of the first-order term in Eq. (9.9) has been derived by Simha. In both cases the calculated quantities increase as the axial ratio increases above unity. For spheres, a/b = 1. 

Since f is a measurable quantity for, say, a protein, and since the latter can be considered to fail into category (3) in general, the friction factor provides some information regarding the eilipticity and/or solvation of the molecule. In the following discussion we attach the subscript 0 to both the friction factor and the associated radius of a nonsolvated spherical particle and use f and R without subscripts to signify these quantities in the general case. Because of Stokes law, we write... 

Cunningham-Stokes correction factor for small particles when fluid does not behave as continuum in air, for = 1 fim, = 117 for = 0.1 //m, = 2.7... 

Fig. 4. Terminal velocities in air of spherical particles of different densities settling at 21°C under the action of gravity. Numbers on curves represent tme (not bulk or apparent) specific gravity of particles relative to water at 4°C. Stokes-Cunningham correction factor is included for settling of fine particles.

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

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

Wilke-Chang This correlation for D°b is one of the most widely used, and it is an empirical modification of the Stokes-Einstein equation. It is not very accurate, however, for water as the solute. Otherwise, it apphes to diffusion of very dilute A in B. The average absolute error for 251 different systems is about 10 percent. ( )b is an association factor of solvent B that accounts for hydrogen bonding. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

Wall Effects When the diameter of a setthng particle is significant compared to the diameter of the container, the settling velocity is reduced. For rigid spherical particles settling with Re < 1, the correction given in Table 6-9 may be used. The factor k is multiplied by the settling velocity obtained from Stokes law to obtain the corrected set-... 

TABLE 6-9 Wall Correction Factor for Rigid Spheres in Stokes Law Region... 

FIG. 14-115 Experimental collection efficiencies of rectangular impactors. C is the Stokes-Ciinningbam correction factor Pp, particle density, g/ond U, superficial gas velocity, approaching the impactor openings, cm/s and ig, gas viscosity, P. Calveri, Yung, and Leung, NTIS Puhl. PB-24S050 based on Mercer and Chow, J. Coll. Interface Sci., 27, 75 (1.96S).]... 

K. Stokes-Cunningham correction factor Dimensionless Dimensionless Dimensionless... 

For single-stage precipitators, and may be considered as essentially equal. It is apparent from Eq. (17-31) that the mobihty in an elecdric field will be almost the same for all particles smaller than about l- Im diameter, and hence, in the absence of reentrainment, collection efficiency should be almost independent of particle size in this range. Very small particles will actually have a greater mobihty because of the Stokes-Cunningham correction factor. Values of are listed in Table 17-14 for 70°F, = 2, and % = %i = % = 10 statV/cm. 

Since the Stokes diameter for the rod-shaped particle will obviously differ from the rod diameter, this difference represents added information concerning particle shape. The ratio or the diameters measured by two different techniques is called a shape factor. 

Cunningham correction factor A factor used as a refinement to the Stokes equation for falling particles of small diameter. These tend to slip between the air molecules and, as a result, fall faster. Cup anemometer A device used by meteorologists for the measurement of wind speed. 

Stokes law This relates to the factors that control the passage of a spherical particle through a fluid. The Stokes diameter of a particle is the diameter of a sphere of unit density, which would move in a fluid in a similar manner to the particle in question, which may not be spherical. 

Kcr = Proportionality Foctor, Dimensionless Km = Stokes-Cunningham Correction Factor, Dimensionless... 

Enter capacity at 125 GPM, follow vertically to 86 feet of head, then to right to viscosity of 27.8 centi-stokes, and up to correction factors ... 

Kfne = Proportionality factor in Stokes-Cunningham correction factor, dimensionless k = Constant for wire mesh separators 1 = Wire mesh thickness, ft L = Length of vessel from hydrocarbon inlet to hydrocarbon outlet, or length of decanter, ft L[ = Liquid entering Webre separator, lbs pel- minute per square foot of inlet pipe cross-section L, = EnLrainment from Webre unit, lb liquid per minute per square foot of inlet pipe cross section... 

Elutriation differs from sedimentation in that fluid moves vertically upwards and thereby carries with it all particles whose settling velocity by gravity is less than the fluid velocity. In practice, complications are introduced by such factors as the non-uniformity of the fluid velocity across a section of an elutriating tube, the influence of the walls of the tube, and the effect of eddies in the flow. In consequence, any assumption that the separated particle size corresponds to the mean velocity of fluid flow is only approximately true it also requires an infinite time to effect complete separation. This method is predicated on the assumption that Stokes law relating the free-falling velocity of a spherical particle to its density and diameter, and to the density and viscosity of the medium is valid... 

For example, for equal volumes of gas and liquid ( =0.5), Eq. (266) predicts that the Stokes velocity (which is already very small for relatively fine dispersions) should be reduced further by a factor of 38 due to hindering effects of its neighbor bubbles in the ensemble. Hence in the domain of high values and relatively fine dispersions, one can assume that the particles are completely entrained by the continuous-phase eddies, resulting in a negligible convective transfer, although this does not preclude the existence of finite relative velocities between the eddies themselves. 

In this equation, % is a proportionality factor known as the bead-solvent friction coefficient which purports to account in some kind of average way for the complex molecular interactions as the polymer segments (schematized by the bead) move about in the solvent. Following Stokes law of drag resistance, this friction coefficient is usually given as = 67trisa, with a equal to the bead radius. 

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