Size methods sedimentation

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. 

TTiere are several particle sizing methods, all based upon sedimentation and Stokes Law. If a particle is suspended in a fluid (which may be gas, or any liquid), the force of resistance to movement by the particle will be proportional to the particle s velocity, v, and its radius, r, vis-... 

The sizing methods involve both classical and modem instrumentations, based on a broad spectrum of physical principles. The typical measuring systems may be classified according to their operation mechanisms, which include mechanical (sieving), optical and electronic (microscopy, laser Doppler phase shift, Fraunhofer diffraction, transmission electron miscroscopy [TEM], and scanning electron microscopy [SEM]), dynamic (sedimentation), and physical and chemical (gas adsorption) principles. The methods to be introduced later are briefly summarized in Table 1.2. A more complete list of particle sizing methods is given by Svarovsky (1990). 

Temperature control is an important factor in determining particle size by sedimentation methods. During a typical run changes in spin fluid temperature of 2-4°C were common. This temperature change (DELTEMP) was used as the covariate in the analysis of covariance. 

Aerosols composed of solid particles suspended in a gas are commonly referred to as dust or smoke, the exact terminology usually depending on the size and sedimentation rate of the particles, or the method of aerosol formation. In some situations, aerosols formed through dispersion processes are termed dusts while those arising from condensation processes are called smokes. Alternatively, some prefer to label as dusts aerosols of sufficient particle size to have relatively rapid (e.g., noticeable over a short time span) sedimentation rates in air, while smokes would be of smaller, lighter particles. Regardless of the terminology employed, it is clear that solid aerosols constitute a very important, and usually undesirable, component of many modern processes. 

Because of these constraints many particle size methods are not applicable to floes. For example the uncertainty and variability of floe density within the outer envelope volume, the possible irregularity of shape and their fragile nature means, that all types of sedimentation method are inapplicable. 

Measured size distributions depend not only on the physical dimensions of the particles but also on the method of size analysis used. Size distributions by the Coulter Principle will only agree with sedimentation data if the particles are spherical. Indeed the difference is a measure of particle shape. Since classifiers separate particles on the basis of their Stokes sizes a sedimentation method of size analysis should be used to determine their grade efficiency. Sedimentation analyses are also applicable to many other industrial situations. 

We begin with two experimental methods, sedimentation and electrophoresis, that measure the driven motion of polymer chains and colloidal particles. In each method, an external force is applied directly to particular molecules in solution, and particle motion is observed. The forces are buoyancy and the Coulomb force. Light pressure ( optical tweezers ) has also been used to move particles this method appears in Chapter 9. Chapter 2 presents phenomenology associated with sedimentation by polymers and sedimentation of particulates through polymer solutions. The sedimentation rate of polymers in homogeneous solution, and the sedimentation of particulate probes through polymer solutions, both depend on the polymer concentration and molecular weight and the size of the particulates. 

Sedimentation is another classical particle classification and sizing method for liquid-bom particles. Sedimentation methods are based on the rate of settling of particles in a liquid at rest under a gravitational or centrifugal field. The relationship between settling velocity and particle size is reduced to the Stokes equation at low Reynolds numbers ... 

Microscopic observation of aerosol particles permits direct measurement of particle size. This is in contrast to indirect methods such as sedimentation, impaction, mobility analysis, and light scattering, wherein the particle size is estimated from the measurement of a property related to size. Microscopy also provides the opportunity to observe particle shapes, and it requires only an extremely small amount of sample. Linear measurements made with a microscope can be very accurate and, often serve as a primary measurement for the calibration of other aerosol-sizing methods. However, microscopic methods for determining particle size distributions are, in general, tedious and require consistency, skill, and careftd preparation. 

Particle Size. Wet sieve analyses are commonly used in the 20 )J.m (using microsieves) to 150 )J.m size range. Sizes in the 1—10 )J.m range are analyzed by light-transmission Hquid-phase sedimentation, laser beam diffraction, or potentiometric variation methods. Electron microscopy is the only rehable procedure for characterizing submicrometer particles. Scanning electron microscopy is useful for characterizing particle shape, and the relation of particle shape to slurry stabiUty. 

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. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Clays (qv) are aluminosihcate minerals, some of which have definite chemical compositions. In regard to tar sands, however, clay is only a size classification and is usually deterrnined by a sedimentation method. According to the previous definition of fines, the fines fraction equals the sum of the silt and clay fractions. The clay fraction over a wide range of fines contents is a relatively constant 30% of the fines. 

In the United States, a number of physical tests are performed on siUcon carbide using standard AGA-approved methods, including particle size (sieve) analysis, bulk density, capillarity (wettabiUty), friabiUty, and sedimentation. Specifications for particle size depend on the use for example, coated abrasive requirements (134) are different from the requirements for general industrial abrasives. In Europe and Japan, requirements are again set by ISO and JSA, respectively. Standards for industrial grain are approximately the same as in the United States, but sizing standards are different for both coated abrasives and powders. 

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