Terminal velocity, sedimentation

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. 

A mixture of quartz and galena of densities 3700 and 9800 kg/m3 respectively with a size range of 0.3 to 1 mm is to be separated by a sedimentation process. If Stokes Law is applicable, what is the minimum density required for the liquid if the particles all settle at their terminal velocities ... 

In the sedimenter or gravity settler, the particles in the feed suspension settle due to difference in densities between the particles and the fluid. The settling particle velocity reaches a constant value - the terminal velocity - shortly after the start of sedimentation. The terminal velocity is defined by the following balance of forces acting on the particle ... 

In order to separate the particles in a suspension, the maximum allowable flow rate through the tubular-bowl centrifuge, as shown schematically in Figure 9.3a, can be estimated as follows [1]. A suspension is fed to the bottom of the bowl at a volumetric flow rate of Q (m" s" ) and the clarified liquid is removed from the top. The sedimentation velocity of particles in the radial direction (v = dr/di ) can be given by Equations 9.7 and 9.8 with the use of the terminal velocity under gravitational force v (m s" ) and the gravitational acceleration (m s" ) ... 

When a suspension is allowed to stand, the particles will settle slowly under the influence of gravity due to the density difference between the solid and surrounding fluid, a process known as sedimentation. The velocity of a particle increases as it falls and reaches a constant velocity (known as terminal velocity) at which... 

As is well known, when the gravity and the drag force acting on the particle are numerically the same but in opposite directions, the relative velocity of the particle with respect to the gas flow will be kept constant such a relative velocity is called terminal velocity , denoted as u, = (u - p) and is numerically equal to the sedimentation velocity of the particle in a stationary gas. Setting dupldt = 0 and using Eqs. (2.33) to (2.35) and the data listed in Table 2.1, the terminal velocities for various flow regimes can be directly obtained from Eq. (2.32) as follows ... 

Example. Consider a sample of solid particles for which the average particle size is unknown. The particle density is known (2 g/cm3 at 20 °C) and a sedimentation column (see Figure 2.10) is filled with the solids suspended in water. Measurements indicate a terminal velocity of 0.013 cm/minute. What is the average particle diameter ... 

The time required for a particle to reach its terminal velocity is negligible, but excessively short sedimentation times should be avoided since concentration measurements fluctuate due to the initial agitation, up to a time of about 30 seconds. 

The sedimentation velocity in the centrj uge ( t 16000 rpm) was found to be between 0.4 and 2 x 10 sec or calculated terminal velocity in a gravitation field between 0.1 and 1 cm/year. Circulation of an ink through a magnetic ink jet printer in the presence of a magnetic field did not show agglomeration. 

Inhaled particles vary both in shape and density and these factors affect their capacity to be deposited by sedimentation. The behaviour of such particles can be determined by converting their actual diameter(s) to their aerodynamic diameters). What does this mean Imagine a low-density particle of irregular shape - this will be characterized by a certain terminal velocity as it settles in air. The aerodynamic diameter of the particle is defined as the actual diameter of a spherical particle of unit density with the same terminal velocity. 

PRINCIPLES OF CENTRIFUGAL SEDIMENTATION. In a sedimenting centrifuge a particle of given size is removed from the liquid if sufficient time is available for the particle to reach the wall of the separator bowl. If it is assumed that the particle is at all times moving radially at its terminal velocity, the diameter of the smallest particle that should just be removed can be calculated. 

If the macromolecules are forced by some external agency to flow with a velocity V, light scattering can be used to measure this velocity. There are several possible examples of this (a) macromolecules suspended in a fluid which is in uniform motion with velocity Y, (b) macromolecules falling at their terminal velocities in a viscous solvent under the action of gravity (sedimentation velocity), (c) macroions accelerated to a terminal velocity by an externally imposed electric field (electrophoresis), and (d) macromolecules accelerated to their terminal velocity in an ultracentrifuge (sedimentation velocity). 

In a ccnirifugalfield, a particle sedimenting through a viscous medium also reaches a terminal velocity u. The ccnirilugal acceleration is analytical radius. In this case, the Stokes equation has the form ... 

A solution is developed for the build-up, steady and post-arrest dissipative pore fluid pressure fields that develop around a penetrometer that self-embeds from freefall into the seabed. Arrest from freefall considers deceleration under undrained conditions in a purely cohesive soil, with constant shear strength with depth. Consider a lance falling through the water column that has reached terminal velocity, Uo, and subsequently impacts the soft sediments of the seabed, as illustrated in Figure 5. The non-dimensional pressure, Pd, may be used to define the build-up of pressure following the impact of the penetrometer with the surface of the seabed. The penetrometer impacts the seabed at velocity Uo, represented in dimensionless magnitude as Ud, and decelerates to arrest. Non-dimensional pressures are plotted as the product PdXd, since it is known that the peak pressures, sh-... 

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). 

If there is a narrow distribution of particle sizes then sedimentation is experimentally very simple. A dilute suspension of the particles is shaken in a tall graduated cylinder. After a few seconds the suspension becomes stagnant and the particles start to settle at a constant (terminal) velocity. A clear layer of liquid forms at the top of the cylinder and grows as the particles continue to settle. The velocity of the downward movement of the interface between the clear liquid and suspension is v, which can readily be obtained using a stopwatch and the cylinder graduations. 

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