Particles Stokes diameter

Stokes diameter Diameter of a sphere of the same density as the particle in question having the same settling velocity as that particle. Stokes diameter and aerodynamic diameter differ only in that Stokes diameter includes the particle density whereas the aerodynamic diameter does not. 

In particle-size measurement, gravity sedimentation at low soHds concentrations (<0.5% by vol) is used to determine particle-size distributions of equivalent Stokes diameters ia the range from 2 to 80 pm. Particle size is deduced from the height and time of fall usiag Stokes law, whereas the corresponding fractions are measured gravimetrically, by light, or by x-rays. Some commercial instmments measure particles coarser than 80 pm by sedimentation when Stokes law cannot be appHed. 

The terminal velocity in the case of fine particles is approached so quickly that in practical engineering calculations the settling is taken as a constant velocity motion and the acceleration period is neglected. Equation 7 can also be appHed to nonspherical particles if the particle size x is the equivalent Stokes diameter as deterrnined by sedimentation or elutriation methods of particle-size measurement. 

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. 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

Free-falling diameter Also known as sedimentation or Stokes diameter, the diameter of a sphere with the same terminal settling velocity and density as a nonspherical or irregular particle. 

Stokes diameter The equivalent spherical diameter of the particle being considered. 

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. 

In general, it appears that the Micromerograph, provided that frequent calibration checks are performed, is a good, reproducible instrument for size measurement. The operator time involved is less than with most other methods, and the calcns are not complicated. As in all sedimentation methods, only when the sample particles are spherical does the Stokes diameter that is measured become a measure of absolute particle size. Microscopic examination should be used to check on particle shape and the effect of deagglomeration... 

Many particle-measuring methods use STORE S LAW to determine particle distributions. By suitable mcUiipulation(see below), we obtain an equation relating the Stokes diameter, M, with the particle density, Pj, and the liquid... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Ghrist, B.F., Stadalius, M.A., Snyder, L.R. (1987). Predicting bandwidth in the high-performance liquid chromatographic separation of large biomolecules. I. Size-exclusion studies and the role of solute stokes diameter versus particle pore diameter. J. Chromatogr. 387,1-19. 

Many particles are not spherical and so will not have the same drag properties as spherical particles. The effective diameter for such particles is often characterized by the equivalent Stokes diameter, which is the diameter of the sphere that has the same terminal velocity as the particle. This can be determined from a direct measurement of the settling rate of the... 

As we just suggested, particle size and shape are important physical properties influencing powder flow and compaction. Particle size is a simple concept and yet a difficult one to quantitate. Feret s diameter, Martin s diameter, projected area diameter, specific surface diameter, Stokes diameter, and volume diameter are but several of the measurements that have been used to quantify particle size using a variety of methods. 

According to Stokes Law, the resistance force F acting on a particle of diameter d, settling at a velocity u in a fluid of viscosity p is given by ... 

Consider a spherical particle of diameter dp and density pp falling from rest in a stationary fluid of density p and dynamic viscosity p.. The particle will accelerate until it reaches its terminal velocity a,. At any time t, let a be the particle s velocity. Recalling that the drag force acting on a sphere in the Stokes regime is of magnitude iirdppu, application of Newton s second law of motion can be written as... 

Da (Dl IDA)m is the Stokes diameter, equal to the diameter of sphere, which in a laminar region (low Reynolds number Re < 0.2), sediments with the same velocity as the considered particle. 

Fig. 7.1 gives a size spectrum of water-borne particles. Particles with diameters less than 10 pm have been called colloids. In soils, the clay-sized and fine silt-sized particles are classified as colloids. Colloids do not dissolve, but instead remain as a solid phase in suspension. Colloids usually remain suspended because their gravitational settling is less than 10 2 cm s 1. Under simplifying conditions (spherical particles, low Reynolds numbers), Stokes law gives for the settling velocity, vs... 

Dpo Initial diameter of drop, meter DpS/a Apparent Stokes settling diameter of floe, meters (18 ft u,J[kc g (pP - p)] 1/2 B Diffusion coefficient, meters2/sec Bp Diffusion coefficient for particles, of diameter Dp, meters2/sec Dpi Diffusion coefficient for particles of diameter >pl, meters2/sec Bp2 Diffusion coefficient for particles of diameter Dp2, meters2/sec e Natural logarithmic base, 2.718 E Potential or potential difference, V Ex Ionization potential, V... 

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

Another type of diameter commonly used is the Stokes diameter, If. This is defined as the diameter of a sphere that has the same density and settling velocity as the particle. Thus Stokes diameters are all based on settling velocities, whereas the aerodynamic diameter (Da) also includes a standardized density of unity. 

The expression given in Eq. (O) for the terminal settling velocity only applies to particles with diameters >1.5 p,m because its derivation is based on the assumption that the relative speed of the air at the surface of the particle is zero. However, as the particle becomes smaller, the air molecules appear less as a continuous fluid and more as discrete molecules separated by space through which the particles can slip. The net effect is that the particles can move faster than predicted by Eq. (O) due to this slipping between gas molecules. To correct for this effect, a correction factor must be applied to the resistance force predicted by Stokes law, Eq. (M). The correction factor, C, is a number greater than 1. Thus Eq. (M) is modified to... 

Clay is a good example of a colloidal dispersion, where divalent ions are of great importance. Clay particles are composed of finely divided crystalline material with an equivalent Stokes diameter less than 2 fim. The particles... 

Given a particle made up of a two-sphere cluster, each sphere having a density of 2 g/cm3 and a diameter of 1 pm, find the aerodynamic and Stokes diameter of the cluster. 

A commonly used size dependent property is the equivalent spherical diameter. The equivalent spherical diameter is the diameter of a sphere with the same volume as the particle. For a cube this sphere would have a diameter 1.24 times the edge length of the cube. Another common equivalent spherical diameter is the Stokes diameter. The Stokes diameter is the diameter of a sphere that has the same terminal settling velocity as an irregular particle. (Note Settling has to be under laminar flow [i.e., Re3molds number less than 0.2] in both cases and the density of both the particle and the sphere are assumed to be the same). 

At a low Re3uiolds number, the drag diameter equals the surface diameter of convex particles. For this case, the Stokes diameter, defined as the free-fall diameter in the laminar flow region, is related to sphericity as follows ... 

If the particle-size distribution of a powder composed of hard, smooth s eres is measured by any of the techniques, the measured values should be identical. However, there are many different size distributions that can be defined for any powder made up of nonspheri-cal particles. For example, if a rod-shaped particle is placed on a sieve, its diameter, not its length, determines the size of aperture through which it will pass. If, however, the particle is allowed to settle in a viscous fluid, the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. 

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