Particle-wall collisions

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 ... 

Because the total collision number, Cj, is the sum of the number of particle-particle collisions, Cp, and the number of particle-wall collisions, C, we can define the particle-wall collision ratio, M, as below. 

Because the distance S is distributed randomly, the particle-wall collision ratio can be given by the expectance of over... 

Considering the fact that the particle-wall collision rate... 

It is clear that if S> Xj, particle-particle collision happens most probably and X(9,P) = Xh. If Stravel distance of <5/cos 9. Then, the local free path of the test particle, X, is the average oiX 9,0) over the whole ranges of 6 and j3. That is. 

It is clear that the collision between two elastic but frictional spheres is inelastic due to the inevitable sliding at contact which yields the kinetic energy loss by frictional work. Furthermore, the preceding analyses of both Hertzian collision and frictional collision can also be applied to the particle-wall collision, where the radius of the wall is simply set to be infinitely large. 

Particles migrate to the wall region by means of particle-particle collisions and diffusion, and through particle-wall collision effects which tend to widen the particle velocity distribution in the radial direction. 

The mechanisms of a single particle-wall collision are given in Chapter 2. A particle-wall collision in pneumatic transport systems is a complex process. The bouncing characteristics depend on many parameters, including impact angle, translational and rotational velocities of the particle before collision, physical properties of the wall and particles, and wall roughness and particle shape. 

A machine for the comminution, or size reduction, of mineral or other particles. Such machines accelerate feed particles in a jet and cause size reduction by promoting interparticle and particle-wall collisions at high speed. Very small-sized particles can be produced with these mills. Also termed jet pulverizers. 

One important parameter contributing to different breakage mechanisms is solids concentration or density in the mill. This directly influences the number of particle-particle or particle-wall collisions and the force of those collisions. Particle density in the mill is controlled not only by feed rate to the mill, but also by mill residence time. Depending on the type of equipment and how it is operated, solids density in the mill can impact both the milling rate and its efficiency so understanding and control of this parameter are important for scale-up. 

Sommerfeld, M. (1990), Numerical simulation of the particle dispersion in turbulent flow the importance of particle lift forces and particle/wall collision models, in Numerical Methods for Multiphase Flows, Vol. 91, ASME, New York. 

The liquid to be dried is sprayed into the fluidized bed it coats the inert particle snrfaces. The coated layer dries as a result of combined convective heat transfer from hot air and contact heat transfer due to sensible heat of the particles. When the thin layer is dry, it becomes brittle, cracks, and is peeled off due to attrition by particle-particle and particle-wall collisions. As a result, a fine powder is formed and is carried over by the exhaust gas to be collected and separated in suitable gas-cleaning devices such as cyclones or bag filters. 

Does the dispersion process coincide with a contamination of the suspension Contamination may be caused by abrasion due to particle-wall collisions or interactions between cavities and the dispersion instrument. Size and concentration of the contaminant particles or the concentration of dissolved ionic species may impede the employment of certain dispersion techniques or at least require additional effort for decontamination (e.g. filtration). 

To describe the solids phase rheology, the widely used KTGF is adopted in this framework in addition to the mass and momentum conservation equations the granular temperature 0, accounting for frictional stresses due to particle—particle and particle—wall collisions, needs to be solved by ... 

The Nusselt number for particle/wall collision is obtained from Eq. (39) ... 

In order to provide an explanation for the observed increase in Up as the loading is raised, the kinetic theory analogy can be applied to describe the random motion of the particles. The particles engage in particle-particle and particle-wall collisions and have a random motion superimposed on their mean motion. The kinetic energy associated with these random velocity fluctuations is called the pseudo-tbermaJ (or granular) energy and is... 

At low gas pressures, the mean free path length of the molecules, A, which is related to their mean velocity vq and the mean free time Tcoh by the relation A = co Aoii, increases and can, in principle, become comparable to or even greater than the diameter of the gas cell. In that case, the time between collisions Tcou is determined not by particle-particle collisions but by collisions between particles and the walls of the gas cell. When the transverse dimension of the cell is a few centimeters, the particle-wall collisions cause a broadening of the order of 10 Hz. This value is rather small, but it exceeds the natural width of molecular transitions in the infrared region of the spectrum. 

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