Terminal velocity small particles

The terminal velocity that particles reach when in free fall is an important particle characteristic. It is also fairly straightforward to measure and was therefore used to check the accuracy and validity of the particle tracking model. The measurement technique is entrainment of a small sample of a particular size class in a narrow tube taking the average of the band within which 90% of the small sample are entrained. In the computational modelling of the particle tracks the upper end of the class size is used as the particle diameter and the particles are started from rest and from a falling velocity greater than their terminal velocity. 

Table 9.13 shows the terminal velocities for particles of a range of diameters from 20 to 0.1 pm, reinforcing the importance of small size in preventing removal of particles before entry into the lower reaches of the respiratory tract. In still air, a cloud of powder of about 20 pm diameter takes a few seconds to settle, whereas powder of around 1 pm diameter takes approximately 60 seconds. 

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... 

For small particles Having a low terminal velocity, V01 Is usually taken aa VQs and v pX taken is ... 

A suspension of a mixture of large particles of terminal falling velocity uol and of small particles of terminal falling velocity uqs may be considered, in which the fractional volumetric concentrations are Cl and Cy, respectively. If the value of n in equation 5.76 is the same for each particle. For each of the spheres settling on its own ... 

Two ores, of densities 3700 and 9800 kg/m3 are to be separated in water by a hydraulic classification method. If the particles are all of approximately the same shape and each is sufficiently large for the drag force to be proportional to the square of its velocity in the fluid, calculate the maximum ratio of sizes which can be separated if the particles attain their terminal falling velocities. Explain why a wider range of sizes can be separated if the time of settling is so small that the particles do not reach their terminal velocities. 

As for other types of fluid particle, the internal circulation of water drops in air depends on the accumulation of surface-active impurities at the interface (H9). Observed internal velocities are of order 1% of the terminal velocity (G4, P5), too small to affect drag detectably. Ryan (R6) examined the effect of surface tension reduction by surface-active agents on falling water drops. 

The approach of representing the fluid and particle motion by their component frequencies is only valid if drag is a linear function of relative velocity and acceleration, i.e., if the particle Reynolds number is low. This is the reason for the restriction on small particles noted earlier. The terminal velocity of the particle relative to the fluid is superimposed on the turbulent fluctuations and is unaffected by turbulence if Re is low (see Chapter 11). 

Viscosity affects the various mechanisms of separation in accordance with the appropriate settling law. Tor instance, viscosity has no effect on terminal velocities in the range where Newton s law applies except as it affects the Reynolds Number which determines which settling law applies. Viscosity does affect the terminal velocity in both the Intermediate law range and Stokes law range as well as help determine the Reynolds Number. As the pressure increases or the temperature decreases the viscosity of the gas increases. Viscosity becomes a large factor in very small particle separation (Intermediate and Stokes law range). 

Consider the collision of particles due to wake attraction, as shown in Fig. E3.1. It is assumed that (a) the motion of the leading particle is not affected by the approach of the trailing particle (b) particles are equal-sized, rigid, and spherical and (c) initially, the particles move nearly at their terminal velocities with a very small velocity difference and are separated by a characteristic distance Zo- An empirical relation can be used to describe the effects of the interparticle distance Z and particle Reynolds number Rep on the drag force of the trailing particle as... 

Transport Reactors The superficial velocity of the gas exceeds the terminal velocity of the solid particles, and the particles are transported along with the gas. Usually, there is some slip between the gas and the solids—the solid velocity is slightly lower than the gas velocity. Transport reactors are typically used when the required residence time is small and the fluid reactant (or the solid reactant) can be substantially converted (consumed). They may also be used when the catalyst is substantially deactivated during its time in the reactor and has to be regenerated. 

If the particles are small, and their terminal velocity can be expressed by Stokes Law, u, = dp(ps — pf)g/p, then the dimensionless number is simplified to... 

Dry deposition is parameterized via a resistance approach in which resistances depend on particle size and density, land-use classification and atmospheric stability (Wesely 1989 Zanetti 1990). Wet deposition is included via below cloud scavenging (washout), using a parameterization based on precipitation rates (Baklanov and Sprensen 2001) and scavenging by snow is parameterized using the scheme by Maryon and Ryall (1996). The terminal settling velocity is considered in both the laminar case, in which Stake s law is used and the mrbulent case in which a iterative procedure is employed (Naslund and Thaning 1991). For very small particles a correction for non-continuum effects is used. 

Small particles accelerate rapidly to a constant or terminal velocity (dw/dr = 0) and the motive force balances the drag force. 

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