Rate of settling particles

Darby R. Determine settling rates of particles in non-Newtonian fluids. Chem Eng 103(12) 107-112, 1996. 

The main reasons for the modification of the settling rate of particles in a concentrated suspension are as follows ... 

In studying these problems the author applied the fundamental information available, such as Stokes law for the settling rate of particles and Sell s work (5) on the efficiency of deposit of particles in a moving air stream. However, this fundamental work is based on ideal conditions never found in practical problems, so that the job was to correlate the fundamental information with actual conditions. 

R. Darby, Determining settling rates of particles, Chem. Eng., 109-112 (December 1996). 

The results here presented are valid for particles falling freely in air. The settling rate of particles smaller than 10 m in diameter is insignificant (order of a few cm/ sec). Such particles cannot fall vertically they are only able to come into contact with the surface as a result of inertial, diffusion, and Brownian motion. In this case, not only vertical surfaces, but also plates inclined at ce > 90° may become dusty. 

Both particle size and the liquid viscosity affect the rate of particle settling. The rate of settling due to gravitational force decreases with decreasing particle size and increasing viscosity. The process mechanisms are sensitive to the relative rates of filtration and gravity sedimentation. 

The settling rates of various size particles at 50 F (10 C) is illustrated in Table 1. 

Design basis. Particles in suspension will settle when the upward flow velocity of the fluid, Mli, is less than the settling rate of the particles, R. i.e. 

Classifiers that depend on the difference in the settling rates of different size particles in water are frequently used for separating fine particles, in the 50 to 300 /im range. Various designs are used. The principal ones used in the chemical process industries are described below. 

Thickeners, thickeners are primarily used for liquid-solid separation (see Section 10.4). When used for classification, the feed rate is such that the overflow rate is greater than the settling rate of the slurry, and the finer particles remain in the overflow stream. 

Stokes law is rigorously applicable only for the ideal situation in which uniform and perfectly spherical particles in a very dilute suspension settle without turbulence, interparticle collisions, and without che-mical/physical attraction or affinity for the dispersion medium [79]. Obviously, the equation does not apply precisely to common pharmaceutical suspensions in which the above-mentioned assumptions are most often not completely fulfilled. However, the basic concept of the equation does provide a valid indication of the many important factors controlling the rate of particle sedimentation and, therefore, a guideline for possible adjustments that can be made to a suspension formulation. 

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... 

Carder KI, Steward RG, Betzer BR (1982) In situ holographic of the size and settling rates of oceanic particles. Journal of Geophysical Research 87 5681-5685 Cherry RD, Higgo JJW, Fowler SW (1978) Zooplankton fecal pellets and element residence times in the ocean. Nature 274 246-248... 

Hindered settling results from collisions between particles and also between particles and the wall. In addition high particle concentrations reduce the flow area and increase the velocity of the fluid with a consequent decrease in settling rate. Furthermore particle concentrations increase the apparent density and dynamic viscosity of the fluid. 

Pettyjohn, E.S. and Christiansen, E.B., Effect of particle shape on free-settling rates of isomeric particles, Chemical Engineering Progress, 44, pp. 157-72 (1948). 

The settling rate of the dispersions in cyclohexane initially increases with AOT adsorption but later decreases. The initial increase is attributed to the formation of interparticle surfactant aggregates (Fig. 39A). At higher concentrations, the adsorbed molecules aggregate with excess of surfactant in solution rather than with molecules on the particle, so that flocculation ceases to occur and the dispersion is restabilized. The schematic representation of the surfactant assemblies at the interface is as shown in Fig. 39B. 

In this type of bioreactor the substrate solution passes through a settled bed of particles held in a column and product emerges continuously at the far end. The degree of conversion is determined by the time the fluid remains in the bed and this contact time is determined by the free volume in the reactor bed divided by the flow rate through the column V/Fj. 

Since the finer particles in the dispersion remained dispersed for long times, and the settling rate of only the coarser particles was measured by the settling test, the recorded total settling times represent the minimum of attainable stability of a given dispersion because the test measures the worst performers in the system. 

Because of their small size, individual coccoliths should sink slowly (Lerman et al., 1974) and, consequently, spend long periods of time (on the order of 100 years) in the water column. This long residence time should lead to dissolution of the coccoliths in the undersaturated part of the water column. The origin of coccolith ooze on portions of the seafloor overlain by undersaturated waters, therefore, is difficult to explain by arguments based on settling rates of individual particles (e.g., Bramlette, 1958, 1961 Honjo, 1975, 1976 Roth et al., 1975). Schneidermann (1977) has summarized the major factors considered to be important in accumulation of coccoliths in sediments overlain by undersaturated waters. They are ... 

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