Walls particle collisions with

The attraction of the gas particles for each other tends to lessen the pressure of the gas, because the attraction slightly reduces the force of gas particle collisions with the container walls. The amount of attraction depends on the concentration of gas particles and the magnitude of the particles intermolecular force. The greater the intermolecular forces of the gas, the higher the attraction is, and the less the real pressure. Van der Waals compensated for the attractive force with ... 

This result verifies the correctness of the expression for r given in Ref. [7], where it was just a guess based upon the analogy with the one-dimensional E <8> e case. It has the same clear-cut physical meaning, r represents the probability of decay of the metastable state in the well. It is proportional to the number of particle collisions with the barrier wall per second, u>/2it, and to the exponential factor, that is the probability of tunneling through the barrier at each of these collisions. 

Without losing generality, in this section we only consider case (3), where the pipe bend is located in the vertical plane with a vertical gas-solid suspension flow at the inlet, as shown in Fig. 11.10. It is assumed that the carried mass and the Basset force are neglected. In addition, the particles slide along the outer surface of the bend by centrifugal force and by the inertia effect of particles. The rebounding effect due to particle collisions with the wall is neglected. 

Deposition by diffusion is the main mechanism for particles smaller than 0.5 pm, and is important in bronchioles, alveoli, and bronchial bifurcations. Aerosol particles are displaced by a random collision of gas molecules this results in particle collision with the airway walls [24]. Deposition by diffusion increases with the decrease in particle size, and breath-holding following inhalation was also found to increase this deposition [25]. 

This is of little significance for particles >1 pm. Particles below this size are displaced by a random bombardment of gas molecules, which results in particle collision with the airway walls. The probability of particle deposition by diffusion increases as the particle size decreases. Brownian diffusion is also more prevalent in regions where airflow is very low or absent, e.g. in the alveoli. 

The methods of destroying aerosols, whether liquid or sohd, are numerous. Some of the more common are illustrated in Figure 13.7. One of the most important from a practical standpoint is the use of a spray (usually water) to wash the aerosol from the gas phase. As already mentioned, for aerosols, almost every collision between aerosol particles, collisions with container walls, or collision with a water droplet will be sticky. For two aerosol particles the result is homocoagulation for the other cases the process is heterocoagulation. In each case the result will be an increase in the size of... 

All gas properties relate in some way to the kinetic character. Specifically, particle motion explains why gases fill their containers. Also, pressure results from the large numbers of particle collisions with the container walls. 3. Gas molecules move independently of each other in all directions. Therefore, they exert pressure on the container walls, including the top, uniformly in all directions. Liquid and solid pressures are the result of gravity, so they exert a downward pressure on the bottom of the container. Liquid particles can move amongst themselves, so they also exert horizontal pressures against the walls of their container. Solid particles lack this freedom of horizontal movement, so they exert no horizontal pressure on the walls of a container. 

Wall-collision broadening Particle collisions with the walls of the sample cell vo/2TtL Vo = mean velocity L = cell diameter lO -lO Hz... 

We are now going to use this distribution fiinction, together with some elementary notions from mechanics and probability theory, to calculate some properties of a dilute gas in equilibrium. We will calculate tire pressure that the gas exerts on the walls of the container as well as the rate of eflfiision of particles from a very small hole in the wall of the container. As a last example, we will calculate the mean free path of a molecule between collisions with other molecules in the gas. 

In the discussion so far, the fluid has been considered to be a continuum, and distances on the molecular scale have, in effect, been regarded as small compared with the dimensions of the containing vessel, and thus only a small proportion of the molecules collides directly with the walls. As the pressure of a gas is reduced, however, the mean free path may increase to such an extent that it becomes comparable with the dimensions of the vessel, and a significant proportion of the molecules may then collide direcdy with the walls rather than with other molecules. Similarly, if the linear dimensions of the system are reduced, as for instance when diffusion is occurring in the small pores of a catalyst particle (Section 10.7), the effects of collision with the walls of the pores may be important even at moderate pressures. Where the main resistance to diffusion arises from collisions of molecules with the walls, the process is referred to Knudsen diffusion, with a Knudsen diffusivily which is proportional to the product where I is a linear dimension of the containing vessel. 

Fig. 5—Change of the rates of particle-particle and particle-wall collisions with the inverse Knudsen number.

When bounding walls exist, the particles confined within them not only collide with each other, but also collide with the walls. With the decrease of wall spacing, the frequency of particle-particle collisions will decrease, while the particle-wall collision frequency will increase. This can be demonstrated by calculation of collisions of particles in two parallel plates with the DSMC method. In Fig. 5 the result of such a simulation is shown. In the simulation [18], 2,000 representative nitrogen gas molecules with 50 cells were employed. Other parameters used here were viscosity /r= 1.656 X 10 Pa-s, molecular mass m =4.65 X 10 kg, and the ambient temperature 7 ref=273 K. Instead of the hard-sphere (HS) model, the variable hard-sphere (VHS) model was adopted in the simulation, which gives a better prediction of the viscosity-temperature dependence than the HS model. For the VHS model, the mean free path becomes ... 

The first term, (1 - ty) /(I - z), corrects for the voidage difference between that in thejet and that in the emulsion phase. The second term, ( - z) /(I - z), takes into account the fact that only a fraction of the particles having the entrainment velocity Ve will be entrained, the remainder rebounding back to thejet wall due to collisions with the particles already in thejet. Substituting Eq. (63) into Eq. (62), we have... 

In addition, DNS of turbulent flow in a periodic box offer interesting opportunities for studying in a fully resolved mode the intimate details of the flow field, its interaction with particles and the mutual interaction between particles (including particle-particle collisions and coalescence). Such simulations may yield new insights see, e.g., Ten Cate et al. (2004) and Derksen (2006b). The same can be said about our understanding of particle-turbulence interactions in wall-bounded flows this has increased due to Portela and Oliemans (2003) exploiting both DNS and LES and due to Ten Cate et al. (2004). 

From a molecular point of view inside a catalyst particle, diffusion may be considered to occur by three different modes molecular, Knudsen, and surface. Molecular diffusion is the result of molecular encounters (collisions) in the void space (pores) of the particle. Knudsen diffusion is the result of molecular collisions with the walls of the pores. Molecular diffusion tends to dominate in relatively large pores at high P, and Knudsen diffusion tends to dominate in small pores at low P. Surface diffusion results from the migration of adsorbed species along the surface of the pore because of a gradient in surface concentration. 

Just like the walls in a squash court, against which squash balls continually bounce, the walls of the gas container experience a force each time a gas particle collides with them. From Newton s laws of motion, the force acting on the wall due to this incessant collision of gas particles is equal and opposite to the force applied to it. If it were not so, then the gas particles would not bounce following a collision, but instead would go through the wall. 

The gas particles are in constant motion, moving in straight lines in a random fashion and colliding with each other and the inside walls of the container. These collisions with the inside container walls comprise the pressure of the gas. 

Describe these three containers in relationship to each other in terms of particle speed and collisions with the walls of the container. All have same amounts of the same gas in them. 

The gas molecules fly about and among each other, at every possible velocity, and bombard both the vessel walls and collide (elastically) with each other. This motion of the gas molecules is described numerically with the assistance of the kinetic theory of gases. A molecule s average number of collisions over a given period of time, the so-called collision index z, and the mean path distance which each gas molecuie covers between two collisions with other molecules, the so-called mean free path length X, are described as shown below as a function of the mean molecule velocity c the molecule diameter 2r and the particle number density molecules n - as a very good approximation ... 

Louis Gay-Lussac continued the ballooning exploits initiated by Charles, ascending to over 20,000 feet in a hydrogen balloon in the early 1800s. Gay-Lussac s law defines the relationship between the pressure and temperature of an ideal gas. If the temperature of the air in the syringe increases while keeping the volume constant, the gas particles speed up and make more collisions with the inside walls of the syringe barrel. As we have seen, an increase frequency in the number of collisions of the gas particles with a container s wall translates into an increase in pressure. Gay-Lussac s law says that pressure is directly... 

Ideal gases consist of very large numbers of particles in constant random motion. These particles collide with the walls of their container, and these collisions with the walls cause the pressure exerted by the gas. 

The kinetic molecular theory (KMT see Sidebar 2.7) of Bernoulli, Maxwell, and others provides deep insight into the molecular origin of thermodynamic gas properties. From the KMT viewpoint, pressure P arises merely from the innumerable molecular collisions with the walls of a container, whereas temperature T is proportional to the average kinetic energy of random molecular motions in the container of volume V. KMT starts from an ultrasimplified picture of each molecule as a mathematical point particle (i.e., with no volume ) with mass m and average velocity v, but no potential energy of interaction with other particles. From this purely kinetic picture of chaotic molecular motions and wall collisions, one deduces that the PVT relationships must be those of an ideal gas, (2.2). Hence, the inaccuracies of the ideal gas approximation can be attributed to the unrealistically oversimplified noninteracting point mass picture of molecules that underlies the KMT description. 

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