Diameter Stokes

This calculation requires knowledge about the shape of the particle and its density. 9.7.2 Stokes Diameter 

The diameter of a sphere having the same terminal settling velocity and density as the particle is defined as its Stokes diameter ), . For irregularly shaped particles Dst is the diameter of a sphere that would have the same terminal velocity. The Stokes diameter for Re 0.1 can then be calculated using (9.42) as 

Stokes Diameter What is the relationship connecting the volume equivalent diameter and the Stokes diameter of a nonspherical particle with dynamic shape factor X for Re 0.1  

Calculate the Stokes diameter of the NaCl particle of the previous example. The two approaches (dynamic shape factor combined with the volume equivalent diameter and the Stokes diameter) are different ways to describe the drag force and terminal settling velocity of a nonspherical particle. The terminal velocity of a nonspherical particle with a volume equivalent diameter Dve is given by (9.104), 

By definition this settling velocity can be also written as a function of its Stokes diameter as 

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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. 

Stokes diameter by centrifugal sedimentation from various sources. 

Fig. 5. Tinting strength versus median Stokes diameters for a range of reinforcing tread blacks.

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. 

Thus the Stokes diameter of any partiele is that of an equivalent sphere having same terminal settling veloeity and is a useful additional partiele eharaeteristie for partieulate systems involving fluid motion. 

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. 

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. 

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. 

Stockbarger process Stokes diameters Stokes Einstein equation Stoke s law... 

Thus, electrophoresis commonly measures size/charge ratios of migrating molecules (or, better, charge/size ratios (z/dft). The Stokes diameter of a protein [nm] is related to the molar mass Mr [g moh1] by Eq. (9.17). 

The diameter of a sedimenting species determined from Stokes law assuming a spherical shape. Also referred to as the Stokes diameter or (divided by a factor of 2) the settling radius . 

Because the radius of a nonspherical molecule cannot be defined precisely, molecular friction coefficients and diffusion coefficients are often related to the Stokes radius (or Stokes diameter). This is defined as the radius (or diameter) of a sphere having / and D values identical to those of the molecule under consideration. 

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... 

Of course, the observed behavior could result from some combination of these effects. The first possibility given above cannot be expected to explain the observed effect alone unless the BBB chain behaves in a far different way than other linear polymers for which v does not exceed ca. 0.80 6,7). Calculation of the Stokes diameter D8 from the data for [77], and M in Table I yields values of the order 5 A., which seems too low to be meaningful. Calculation of < from the Fox-Flory relation (13)... 

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. 

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. 

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