Velocity of gas particles

The constant motion and high velocities of gas particles lead to some important practical consequences. One such consequence is that gases mix rapidly when they come in contact. Take the stopper off a bottle of perfume, for instance, and the odor will spread rapidly through the room as perfume molecules mix with the molecules in the air. This mixing of different gases by random molecular motion with frequent collisions is called diffusion. A similar process in which gas molecules escape without collisions through a tiny hole into a vacuum is called effusion (Figure 9.13). 

Root mean square velocity the square root of the average of the squares of the individual velocities of gas particles. (5.6)... 

Pore Radius r Particle Radius q = Face Velocity of Gas Particle Density E Particle Collection Efficiency. 

Actually, there are several ways to define this quantity. First of all, the kinetic theory of gases does not make any presumption about the velocity of any particular gas particle it could be anything. This does not imply that all possible velocities will exist in any gas sample at equal proportions For example, the velocities of gas particles could be anywhere between zero and the speed of light. The naive presumption would be that the average velocity is (0 -b c)/2 = c (where c represents the speed of light in a vacuum). This is clearly not the case, as illustrated by the answer in Example 19.1. 

We can use kinetic molecular theory to derive the expression for the root mean square velocity of gas particles. This velocity is inversely proportional to the molar mass of the gas, and... 

The study of Saturn s rings led Maxwell to the problem of the motions of large numbers of colliding bodies, such as would be found in the rings. This in turn led him to the study of gas kinetics. Here he introduced the use of statistical methods, not for data analysis but for a description of the physical process. He recognized that there must be a distribution of velocities of gas particles, and by 1860 he had developed a statistical formula for that... 

A well-known example of a Gaussian distribution is the celebrated Maxwell-Boltzmann distribution of velocities of gas particles. In one dimension, we write... 

The flows of gas and solid particles are assumed to be parallel. This means that the velocity of gas f and the velocity of solid particles c are both in the direction of the pipeline. On the other hand, because we do not assume a homogeneous flow at this stage of the theory, the absolute values of v and c may vary across the cross-section of the pipe. 

Vo = Average velocity of gas, feet/sec. u, = Terminal settling velocity of particle under action of gravity, feet/sec. gL = 32.2 feet/sec. ... 

The accelerating force exerted by the fluid on the particle will be a function of the properties of the gas, the shape and size of the particle, and the relative velocity. It will also depend on the dispersion of the particles over the cross-section and the shielding of individual particles. The process is complex and therefore it is not possible to develop a precise analytical treatment, but it is obviously important to know the velocity of the particles... 

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... 

Similar convection-diffusion equations to the Navier-Stokes equation can be formulated for enthalpy or species concentration. In all of these formulations there is always a superposition of diffusive and convective transport of a field quantity, supplemented by source terms describing creation or destruction of the transported quantity. There are two fundamental assumptions on which the Navier-Stokes and other convection-diffusion equations are based. The first and most fundamental is the continuum hypothesis it is assumed that the fluid can be described by a scalar or vector field, such as density or velocity. In fact, the field quantities have to be regarded as local averages over a large number of particles contained in a volume element embracing the point of interest. The second hypothesis relates to the local statistical distribution of the particles in phase space the standard convection-diffusion equations rely on the assumption of local thermal equilibrium. For gas flow, this means that a Maxwell-Boltzmann distribution is assumed for the velocity of the particles in the frame-of-reference co-moving with the fluid. Especially the second assumption may break dovm when gas flow at high temperature or low pressure in micro channels is considered, as will be discussed below. 

Another approach is to consider the particle for which the drag force of the gas at the edge of the core where the velocity is maximum just balances the centrifugal force. This reduces Eq. (12-42) to a steady state, with no net acceleration or velocity of this particle. The maximum velocity is given by Eq. (12-41) applied at the edge of the core Vl r2 = Encore- When this is introduced into Eq. (12-42), the result is... 

By definition, the terminal velocity of a particle (ut) is the superficial gas velocity which suspends an isolated particle without translational motion—i.e., the terminal free fall velocity for that particle. From force balance on the particle, the terminal velocity for an approximately spherical particle can be shown to be... 

As noted earlier, increasing gas velocity for any given fluidized bed beyond the terminal velocity of bed particles leads to upward entrainment of particles out of the bed. To maintain solid concentration in the fluidized bed, an equal flux of solid particles must be injected at the bottom of the bed as makeup. Operation in this regime, with balanced injection of particles into the bed and entrainment of particles out of the bed, may be termed fast fluidization, FFB. Figure 10 presents an approximate map of this fast fluidization regime, in terms of a dimensionless gas velocity and dimensionless particle diameter. 

The free-falling velocity of the particle u0, when the density of the particle is large compared with that of the gas, is given from equation 3.23 as ... 

In Chapter 3, equation 3.40 was proposed for the calculation of the free falling velocity of a particle in an infinite medium(61). This equation which was shown to apply over the whole range of values of Ga of interest takes the form ... 

Carlos and Latif both fluidised glass particles in dimethyl phthalate. Data on the movement of the tracer particle, in the form of spatial co-ordinates as a function of time, were used as direct input to a computer programmed to calculate vertical, radial, tangential and radial velocities of the particle as a function of location. When plotted as a histogram, the total velocity distribution was found to be of the same form as that predicted by the kinetic theory for the molecules in a gas. A typical result is shown in Figure 6.11(41 Effective diffusion or mixing coefficients for the particles were then calculated from the product of the mean velocity and mean free path of the particles, using the simple kinetic theory. 

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