Particle sizes Terminal velocity

Thus, in the gravitational-crossflow zone particle separation is a two-dimensional process, where their trajectories are in fact ballistic tracks. Unlike the counterflow zone, the cut size depends not only on the particle s terminal velocity, but mainly on the chamber length and height. These parameters are chosen in such a way that particles with the cut size land at the farthest point A of the bottom (Fig. lb). 

Thus, a particle of terminal velocity v can ascend if it is in a coaxial circle of radius r. Assuming a homogeneous distribution of particles, the fraction of this size contained in a cylinder of radius r is ... 

Batch, semibatch, or continuous-flow operation can be simulated. The continuous phase is assumed well mixed. Particle movement was either random or followed the flow direction of the sum of the local average fluid velocity and the particle gross terminal velocity. The probability of droplet breakup is assigned based on droplet size. Binary breakage was assumed to form two randomly sized particles whose masses equal the parent drop. The probability of coalescence exists when two drops enter the same grid location. Particles are added and removed to simulate flow. 

Up to this point we have considered spherical particles of a known diameter Dp and density pp. Atmospheric particles are sometimes nonspherical and we seldom have information about their density. Also a number of techniques used for atomospheric aerosol size measurement actually measure the particle s terminal velocity or its electrical mobility. In these cases we need to define an equivalent diameter for the nonspherical particles or even for the spherical particles of unknown density or charge. These equivalent diameters are defined as the diameter of a sphere, which, for a given instrument, would yield the same size measurement as the particle under consideration. A series of diameters have been defined and are used for such particles. 

Different sizes of particle settle at different terminal velocities, and this property can be used in several ways to determine the size distribution of a sample. In the Andreasen Pipette a sample of the material is dispersed in a liquid and allowed to settle from time zero. At intervals a sample of fluid is extract from a depth H below the surface. These samples are evaporated to dryness and weighed to give concentrations. This produces a set of concentrations Cj and the known initial concentration Cq. At any time t the sample withdrawn will contain particles with terminal velocities equal to or less than H/t, at their original concentration, larger particles will have settled below the level of the pipette tip. The objective of the experiment is to determine the particle size distribution of dolomite powder, and compare... 

When a suspension is introduced into the inclined lamella settler, the feed suspension may be characterized by means of its solids volume fraction and its particle size density function fjO p)- The corresponding quantities for the overflow and underflow streams are ji,/i(rp) (rp). Often such problems are analyzed instead using the solids volume fraction and the particle settling (terminal) velocity density function /[t/pzt), where the particle settling velocity Upzt in the Stokes law range is related to the particle radius tp by relation (6.3.1) ... 

Flue particles ia a fluidized bed are analogous to volatile molecules ia a Foiling solution. Therefore, the concentration of particles ia the gas above a fluidized bed is a function of the saturation capacity of the gas. To calculate the entrainment rate, it is first necessary to determine what particle sizes ia the bed can be entrained. These particles are the ones which have a terminal velocity less than the superficial gas velocity, assuming that iaterparticle forces ia a dilute zone of the freeboard are negligible. An average particle size of the entrainable particles is then calculated. If all particles ia the bed are entrainable, the entrained material has the same size distribution as the bed material. 

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. 

As shown by Fig. 14-90, entrainment droplet sizes span a broad range. The reason for the much larger drop sizes of the upper curve is the short disengaging space. For this cui ve, over 99 percent of the entrainment has a terminal velocity greater than the vapor velocity. For contrast, in the lower cui ve the terminal velocity of the largest particle reported is the same as the vapor velocity. For the settling velocity to limit the maximum drop size entrained, at least 0.8 m (30 in) disengaging space is usually required. Note that even for the lower cui ve, less than 10 percent of the entrainment is in drops of less than... 

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

Table 4.4 Terminal velocities of particles of different sizes...

It is found that the major factor which determines the behaviour of the solid particles is their terminal falling velocity in the liquid. This property gives a convenient way of taking account of particle size, shape and density. 

In a recent study of the transport of coarse solids in a horizontal pipeline of 38 mrrt diameter, pressure drop, as a function not only of mixture velocity (determined by an electromagnetic flowmeter) but also of in-line concentration of solids and liquid velocity. The solids concentration was determined using a y-ray absorption technique, which depends on the difference in the attenuation of y-rays by solid and liquid. The liquid velocity was determined by a sail injection method,1"1 in which a pulse of salt solution was injected into the flowing mixture, and the time taken for the pulse to travel between two electrode pairs a fixed distance apart was measured, It was then possible, using equation 5.17, to calculate the relative velocity of the liquid to the solids. This relative velocity was found to increase with particle size and to be of the same order as the terminal falling velocity of the particles in the liquid. 

As can be seen, two factors are particularly critical (a) the density of the particle, since heavier particles are more difficult to fluidize, and (b) particle size, since the necessary gas velocity varies as the square of the particle diameter. The design of the reactor is also important since gas velocity at the top must be less than the terminal velocity of the particles, otherwise they would be blown out of the bed.P l... 

A particle falling freely in vacuum is subjected to a constant acceleration, and its velocity increases continuously. The velocity at any point depends only on the distance from the starting point, and is independent of the size and the density of the particle. Thus a heavy stone and a feather fall at exactly the same rate in an evacuated system. However, in the event of a particle falling in a fluid medium, there is resistance to this fall or movement. The resistance increases as the velocity of the particle increases, and this continues until the forces tending to accelerate the particle and the fluid resistance forces become equal. The particle is then said to have attained its terminal velocity it continues to fall, but with a uniform velocity. 

This expression shows that, unlike the terminal velocity of the particle, its initial acceleration is independent of the particle size and depends only on the densities of the solid particle and the fluid. This type of acceleration, known as differential acceleration, may be exploited by designing equipment which provides frequent opportunities for accelerating the particles from rest. If a particle is allowed to accelerate from rest for a brief period of time and then arrested and subsequently allowed to fall once more, the total distance travelled by it will be influenced more by the differential acceleration and, therefore, by the specific gravities of the particle and of the liquid, than by its terminal velocity, or in other words, by its size. In this way, as the preferential movement of dense particles to the bottom of a bed... 

For very small particles or low density solids, the terminal velocity may be too low to enable separation by gravity settling in a reasonably sized tank. However, the separation can possibly be carried out in a centrifuge, which operates on the same principle as the gravity settler but employs the (radial) acceleration in a rotating system (o r) in place of the vertical gravitational... 

Here, Vt is the terminal velocity of the particle in a gravitational field and is the cross-sectional area of the gravity settling tank that would be required to remove the same size particles as the centrifuge. This can be extremely large if the centrifuge operates at a speed corresponding to many g s. 

---