Falling speed

Elutriation The separation of particles in a fluid by gravity, which allows those with the greater falling speed settle as the fluid flows through an elutriator. 

Following growth by condensation, droplets grow further by collision coalescence (colliding mainly due to different fall speeds). Some small... 

Because the particles in the accumulation mode are very small (most of them have diameters less than 1 pm when dry), they have very small fall speeds (a 1 /im sphere of unit density has a fall speed of about 10 cm/s). Thus, they are only removed in any quantity by the formation of clouds with subsequent precipitation. 

Single particles will tend to be carried out of the bed if the fluid velocity exceeds the terminal falling speed u, of the particles given by equation 9.5. Thus the normal range of fluidization velocity is from umf to a,. However, it may be found that the fluid velocity required to bring about fast fluidization is significantly higher than u, because particles tend to form clusters. 

There are several different types of effective diameters. One of the most commonly used is the aerodynamic diameter, Da, which is defined as the diameter of a sphere of unit density (1 g cm 3) that has the same terminal falling speed in air as the particle under consideration. This effective diameter is particularly useful because it determines the residence time in the air and it reflects the various regions of the respiratory system in which particles of different sizes become deposited. D, is given by Eq. (A) ... 

Falling speed of the canister hardly affects cloud dimensions, but the mass ratio of HE/fuel, canister volume and ambient temp control cloud dimensions... 

As the bound moisture is removed and the material is heated to a temperature of 58 to 62 °C in the falling-speed drying section, the content of methylol groups in batches Nos. 1,2, and 3 slightly increases, which may be due to the effect of agglomerating additives. 

There are several definitions of respirable dust (Lippmann, 1970). In 1952 the British Medical Research Council (BMRC) defined the respirable fraction in terms of the terminal settling velocity (free-falling speed) by the equation... 

If the particle-size distribution of a powder composed of hard, smooth s eres is measured by any of the techniques, the measured values should be identical. However, there are many different size distributions that can be defined for any powder made up of nonspheri-cal particles. For example, if a rod-shaped particle is placed on a sieve, its diameter, not its length, determines the size of aperture through which it will pass. If, however, the particle is allowed to settle in a viscous fluid, the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. 

The diameter of a sphere with same drag resistance (or free-falling speed) as the particle... 

Problem 9-21. Nonlinear Microrheology. A common way to measure the viscosity of a liquid is to drop a heavy spherical ball into a large tank of the fluid and measure the steady speed with which the ball descends. When the ball is only slightly more dense than the liquid, the Reynolds number based on the ball s fall speed will be small, and the viscosity can be determined from the Stokes settling velocity Ustokes = [(2/9)Apa2g//r], where Ap is the density difference between the ball and the fluid, a is the ball radius, g is the acceleration of gravity, and /i is the fluid viscosity. 

Note that g(r) is a function of the constant fall speed U from the Smoluchowski equation (1), and that at small Pe the 0(Pe) problem must be solved to get the correction to the fall speed.]... 

The efficiency of wet removal of gases and particles is due to the fact that the falling speed of precipitation elements greatly exceeds the dry deposition velocity of trace constituents. In discussion of removal caused by clouds and precipitation it is reasonable to differentiate processes taking place in the clouds (rain-out) and beneath the cloud base (wash-out). 

Aerosol particles below the cloud base are captured by precipitation elements due to gravitational coagulation. This type of coagulation is caused by the difference between falling speeds of the aerosol particles and the raindrops or snow crystals. In other words, this means that precipitation elements overtake the particles. The air molecules go around the falling drops (or crystals) while large particles are impacted against the drops due to their inertia. For this reason precipitation elements are considered to be small impactors (see Subsection 4.1.2). 

The change of the mass concentration of aerosol particles (M) caused by washout can also be calculated easily. Let us designate by v(R) the falling speed of the drops with number concentration N(R). Suppose that this speed is much higher than the deposition velocity of the particles. Under these conditions the particle mass loss in the air per unit time is... 

All of the particles with a free-falling speed greater than that of Dp(t) as given by Stokes law or some related law, where Dp(t) is the size of particle that has a velocity of fall h/t... 

Electrophoretic particle speed Mean fluid velocity in tube Particle fall speed, hindered settling speed... 

Particle fall speed in infinitely dilute suspension... 

In the case of a dilute suspension [/, = Uj vvhere Uq is the infinitely dilute suspension, particle fall speed, which for the case of rigid spheres is given... 

Thus the discontinuity speed is the fall speed of the particles, which is physically evident, since all the particles at the topmost layer will be sedimenting with the speed L/y. 

In other words, the speed with which the front moves up from the bottom is approximately the density ratio of the sedimenting to sedimented particles (p(,/p, ) multiplied by the dilute particle fall speed. 

The above equations can be used to deduce the properties of the suspension from observations of the front speeds, typically the one separating the clarified layer from the suspension. For example, knowing the fall speed (Eq. 5.4.6), we can determine the effective particle size if the particle density has been found independently. The extension of the results to infinitely dilute systems containing particles of two or more sizes (polydisperse systems) is straightforward and will not be discussed further here. It may only be mentioned that with different fall speeds there will be as many distinct downward-moving fronts as there are particle sizes. From measurements of these front speeds the particle sizes can be determined as for the monodisperse system. 

---