Sedimentation terminal settling velocity

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. 

Sedimentation of particles follows the principle outlined above [Eq. (1)] in which particles in the Stokes regime of flow have attained terminal settling velocity. In the airways this phenomenon occurs under the influence of gravity. The angle of inclination, t /, of the tube of radius R, on which particles might impact, must be considered in any theoretical assessment of sedimentation [14,19]. Landahl s expression for the probability, S, of deposition by sedimentation took the form ... 

Sedimentation of airborne particles is caused by gravitational force (Hinds 1998). In a laminar flow, the terminal settling velocity vtiP of a spherical particle of diameter dP and density pP is... 

If the particle concentration in a suspension is high, then the particles do not sediment independently, but are influenced by the motions of surrounding particles (hindered settling). Hindered settling behaviour can be described by applying a correction factor to the Stokes Law terminal settling velocity (dx/dt from Eq. 2.20) to obtain a hindered settling velocity. Several equations have been advanced to describe the correction [69]. The Richardson-Zaki equation for this is ... 

Although with an aerosol each particle will settle at its own terminal settling velocity, settling rarely takes place in absolutely still air since there is always some circulation and mixing. This mixing has the effect of producing a uniform aerosol concentration which decreases with time because of sedimentation. 

As discussed previously, terminal settling velocities of aerosol particles are generally quite small. Under normal circumstances it is unreasonable to expect that simple sedimentation as such will be an effective removal mechanism. 

The velocity of sedimentation is a result of a force balance shown in Figure 11.1 for a sphere of radius R moving at a terminal settling velocity, Vf The force of gravity, TrR p g), is a result of the... 

Sedimentation [22] of the disperse phase usually takes place under the force of gravity. (It may be caused also by an imposed centrifugal force field). A sphere of diameter D and density d under the influence of gravitational force Fg will have a terminal settling velocity Vts in the laminar region governed by Stake s law ... 

The fourth moment is proportional to the total projected area of the material sedimenting from a stationary fluid. For spherical particles larger than 1 the terminal settling velocity... 

The third coagulation mechanism, differential sedimentation, occurs when a particle falling at its terminal settling velocity collides with a slower settling particle. This is represented as a cross-sectional area of collision multiplied by the difference in Stokes settling velocities of the colliding particles... 

For non-flocculated systems Richardson and Zaki [1954] were able to draw an analogy between sedimentation and fluidisation and diowed that the settling rate is linked to the terminal settling velocity of the particles by the voidage or volumetric concentration of the solids, raised to a power that is a function of the particle Reynolds number. These relationships are described by the equation ... 

The so-caUed Sigma concept has been widely used in the field of centrifugal sedimentation ever since its first development by Ambler in 1952. It is a simplified relation between the machine performance in terms of X50, total volumetric flow rate Q and an index of the centrifuge size E. The cut size X50 is represented by its terminal settling velocity Vg in the given liquid under gravity so that from Stokes law (using equation 7.5b for the definition of K)... 

The elutriation method is really a reverse sedimentation process in which the particles are dispersed in an upward flowing stream of fluid. All particles with terminal falling velocities less than the upward velocity of the fluid will be carried away. A complete size analysis can be obtained by using successively higher fluid velocities. Figure 1.4 shows the standard elutriator (BS 893)(6i for particles with settling velocities between 7 and 70 mm/s. 

Although the sedimentation velocity of particles tends to decrease steadily as the concentration of the suspension is increased, it has been shown by Kaye and Boardman11 that particles in very dilute suspensions may settle at velocities up to 1.5 times the normal terminal falling velocities, due to the formation of clusters of particles which settle in well-defined streams. This effect is important when particle size is determined by a method involving the measurement of the settling velocity of particles in dilute concentration, though is not significant with concentrated suspensions. 

Creaming. Droplets in an emulsion will have some tendency to rise or settle according to Stokes law. An uncharged spherical droplet in a fluid will sediment if its density is greater than that of the fluid. The driving force is that of gravity the resisting force is viscous and is approximately proportional to the droplet velocity. After a short period of time the particle reaches terminal (constant) velocity, dx/dt, when the two forces are matched. Thus... 

Sedimentation analysis. The distribution of the powder grains by size is calculated from the terminal velocity with which the grains fall, under the action of gravitation, into a liquid of a definite viscosity (settling velocity). 

Terminal settling vebdty Sedimentation inter ce velocity Filtrate vdodty after cake formation Filtrate velocity before cake formation Particle diameter... 

These forces and drag coefficients have been verified experimentally, mainly from measurements on the terminal velocity of a settling particle. The main factors considered in such studies are terms >1, B, and F in Eq. 3-1. For the terminal velocity determination, >1=0 and Fg = (irDplG) (pp - Pf)g. For the sedimentation system, the velocity of the fluid is zero. Thus, one has... 

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