Smaller Particles

We consider the motion of a large particle in a fluid composed of lighter, smaller particles. We also suppose that the mean free path of the particles in the fluid, X, is much smaller than a characteristic size, R, of the large particle. The analysis of the motion of the large particle is based upon a method due to Langevin. Consider the equation of motion of the large particle. We write it in the fonn... 

Illustration of a dialysis membrane in action. In (a) the sample solution is placed in the dialysis tube and submerged in the solvent, (b) Smaller particles pass through the membrane, but larger particles remain within the dialysis tube. 

A separation method in which a mixture passes through a bed of porous particles, with smaller particles taking longer to pass through the bed due to their ability to move into the porous structure. 

The process of smaller particles of precipitate clumping together to form larger particles. 

The reverse of coagulation in which a coagulated precipitate reverts to smaller particles. 

SI units stands for Systeme International d Unites. These are the internationally agreed on units for measurements, (p. 12) size-exclusion chromatography a separation method in which a mixture passes through a bed of porous particles, with smaller particles taking longer to pass through the bed due to their ability to move into the porous structure, (p. 206)... 

For smaller particles, the theory indicates that efficiency decreases according to the dotted line of Figure 7. Experimental data (134) (sofld line of Eig. 7) for a cyclone of Eig. 9 dimensions show that equation 15 tends to overstate collection efficiency for moderately coarse particles and understate efficiency for the finer fraction. The concept of particle cut-size, defined as the size of particle collected with 50% mass efficiency, determined by equation 16 has been proposed (134). 

Venturi scmbbers can be operated at 2.5 kPa (19 mm Hg) to coUect many particles coarser than 1 p.m efficiently. Smaller particles often require a pressure drop of 7.5—10 kPa (56—75 mm Hg). When most of the particulates are smaller than 0.5 p.m and are hydrophobic, venturis have been operated at pressure drops from 25 to 32.5 kPa (187—244 mm Hg). Water injection rate is typicaUy 0.67—1.4 m of Hquid per 1000 m of gas, although rates as high as 2.7 are used. Increasing water rates improves coUection efficiency. Many venturis contain louvers to vary throat cross section and pressure drop with changes in system gas flow. Venturi scmbbers can be made in various shapes with reasonably similar characteristics. Any device that causes contact of Hquid and gas at high velocity and pressure drop across an accelerating orifice wiU act much like a venturi scmbber. A flooded-disk scmbber in which the annular orifice created by the disc is equivalent to a venturi throat has been described (296). An irrigated packed fiber bed with performance similar to a... 

Solution Filtration. The polymer solution, free of unacetylated ceUulose, rigid particle contaminants, and dirt, must pass through spinnerets with holes of 30—80 ]lni diameter. Multistage filtration, usuaUy through plate-and-frame filter presses with fabric and paper filter media, removes the extraneous matter before extmsion. Undesirable gelatinous particles, such as the hemiceUulose acetates from ceUulose impurities, tend to be sheared into smaller particles rather than removed. The solution is also aUowed to degas in hoi ding tanks after each state of filtration. 

For large amounts of fillers, the maximum theoretical loading with known filler particle size distributions can be estimated. This method (8) assumes efficient packing, ie, the voids between particles are occupied by smaller particles and the voids between the smaller particles are occupied by stiH smaller particles. Thus a very wide filler psd results in a minimum void volume or maximum packing. To get from maximum packing to maximum loading, it is only necessary to express the maximum loading in terms of the minimum amount of binder that fills the interstitial voids and becomes adsorbed on the surface of the filler. 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

Residue Hea.tup. Equations 27—30 can be used to estimate the time for residue heatup, by replacing the Hquid properties, such as density and heat capacity, with residue properties, and considering the now smaller particle in evaluating the expressions for ( ), and T. In the denominator of T, 0is replaced by and is replaced by T the ignition temperature of the residue. 

During Stage II the growing particles maintain a nearly constant monomer concentration. The concentration of monomer is particle-size dependent, with smaller particles having lower concentrations (28). 

Three generations of latices as characterized by the type of surfactant used in manufacture have been defined (53). The first generation includes latices made with conventional (/) anionic surfactants like fatty acid soaps, alkyl carboxylates, alkyl sulfates, and alkyl sulfonates (54) (2) nonionic surfactants like poly(ethylene oxide) or poly(vinyl alcohol) used to improve freeze—thaw and shear stabiUty and (J) cationic surfactants like amines, nitriles, and other nitrogen bases, rarely used because of incompatibiUty problems. Portiand cement latex modifiers are one example where cationic surfactants are used. Anionic surfactants yield smaller particles than nonionic surfactants (55). Often a combination of anionic surfactants or anionic and nonionic surfactants are used to provide improved stabiUty. The stabilizing abiUty of anionic fatty acid soaps diminishes at lower pH as the soaps revert to their acids. First-generation latices also suffer from the presence of soap on the polymer particles at the end of the polymerization. Steam and vacuum stripping methods are often used to remove the soap and unreacted monomer from the final product (56). 

The higher efficiency of fortified rosin sizes is beHeved to result from the semihydrophilic nature of the rosin adduct molecules, which results in a more dispersed system of particles during size precipitation by alum. Consequendy, there is a more uniform distribution of somewhat smaller particles on the sized fibers. This dispersing effect may result from the strong tendency of aluminum to coordinate with organic anions. 

Reactivity is affected by particle size. Smaller particles react faster. However, the dominant factor for reactivity is the soHdification rate. Material that is soHdified quicker reacts faster with alcohol (30). Commercial P4S q is a soHd solution containing P4S2Q, P4SC), P4Sy, free sulfur, etc (33). SoHdification rate... 

A recent trend in particle analysis has been the introduction of personal computer-based automation (3). Sophisticated software packages can be used to automate and speed up the analysis. In some cases these computers can even carry out continuous process control (qv) (see Computer technology). The latest machines also allow the measurements of smaller particles and can detect a wider range of sizes. Machines based on light-scattering principles are being more widely accepted by the industry because of speed. An average analysis takes from 1—2 min, whereas those based on sedimentation principles require from 10—120 min. 

Particle Velocity on a. Surfa.ce. Smaller particles, those that are more irregular in shape and/or those that have a higher surface roughness, typically have a higher frictional drag on a hopper or chute surface. 

On a chute, higher drag results in lower particle velocity which can be accentuated by stratification on the chute surface because of the sifting mechanism. Concentrations of smaller particles close to the chute surface and larger particles at the top of the bed of material, combined with the typically higher frictional drag of finer particles, often result in a concentration of fine particles close to the end of the chute, and coarse particles farther away. This can be particulady detrimental if portions of the pile go to different processing points, as is often the case with multiple outiet bins or bins with vertical partitions. 

In order to obtain a homogenous and stable latex compound, it is necessary that insoluble additives be reduced in particle size to an optimum of ca 5 )Tm and dispersed or emulsified in water. Larger-size chemical particles form a nucleus for agglomeration of smaller particles and cause localized dispersion instabiHty particles <3 fim tend to cluster with similar effect, and over-milled zinc oxide dispersions are particularly prone to this. Water-soluble ingredients, including some accelerators, can be added directly to the latex but should be made at dilute strength and at similar pH value to that of the latex concentrate. 

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