Collision between particles frequency

Frequency of Collisions between Particles. Particles in suspension collide with each other as a consequence of at least three mechanisms of particle transport ... 

The rate of coagulation of particles in a liquid depends on the frequency of collisions between particles due to their relative motion. When this motion is due to Brownian movement coagulation is termed perikinetic when the relative motion is caused by velocity gradients coagulation is termed orthokinetic. 

As mentioned before, the collisions between particles significantly affect the impinging stream process while the frequency of the collisions is related to the concentration of particles in the feeding stream. It would be of interest to make certain theoretical predictions for the relationship between the variables mentioned. The analysis presented by Elperin et al. [44] for this purpose is a valuable reference, which is briefly introduced below. 

Latex stability will be determined by the combined effect of two factors the probability of collision between particles and the fraction of the encounters between particles which lead to permanent contact. Tha first factor, the collision frequency, will increase with increasing particle size and particle number. It will also increase with increasing shear rate. The influence of various test conditions on the second factor ought to be discussed on the basis of the DLVO theory of colloid stability. 

A similar expression for the collisional rate of change for particle 2 can be obtained. In this case we utilize the collision s unmetry properties, so this relation is achieved by interchanging the labels 1 and 2 in (4.15) and replacing k by —k. As distinct from the previous analysis, to determine this probability frequency at the instant of a collision between particles labeled 1 and 2 we now take the center of the second particle to be located at position r and the center of particle 1 to be at r — di2k. This approach represents a collision dynamically identical but statistically different from the previous one [31] [49] [32]. The result is ... 

This assumption is reasonable for collisions between particles with the same properties (e.g. mass, diameter, etc.). However, for collisions between particles with different properties it is unlikely to hold when external forces affect unlike particles differently. For example, the fluid drag will be stronger for small particles than for large particles, causing each type to have a different mean velocity. It would then be more likely for collisions to occur on the upstream side (i.e. in the direction of the velocity difference) of the faster moving particles. In such cases, the model for go would need to include such information in order to accurately model the collision frequency. 

Factors such as surface area and temperature affect the rate of reactions because they affect the frequency and energy of collisions between particles. The concentrations of reactants can also affect the frequency of collisions. If other factors are... 

As it coats the inert surface, the wet film is dried due to rapid convective heat and mass transfer and, to certain extent, conductive heat transfer from the bed of inert particles. As a result of the intense, high-frequency collisions between particles, the dry shell... 

Certainly, coating can also be conducted by spraying from the top on a conventional fluidized bed or (and more easily) by spraying from the bottom in a spouted bed, if the operating conditions are appropriately selected for the material to be processed. However, assuming that agglomeration takes place in the spray zones of these two units, it may be concluded from the data listed in Tab. 4.8 that it would be faster in the ProCell, as the frequency of collisions between particles is much higher in the spray zone of this equipment (namely,... 

Consider the crystal size distribution in a model MSMPR crystallizer arising because of simultaneous nucleation, growth and agglomeration of crystalline particles. Let the number of particles with a characteristic size in the range L to L + dL be n L)dL. It is assumed that the frequency of successful binary collisions between particles (understood to include both single crystals and previously formed agglomerates) of size L to L + dL and L" to L"+dL" is equal to f3n L )n L")dL dL". The number density n L) and the collision frequency factor [3 are related to some convenient volumetric basis, e.g. unit volume of suspension. 

Microwave discharges at pressures below 1 Pa witli low collision frequencies can be generated in tlie presence of a magnetic field B where tlie electrons rotate witli tlie electron cyclotron frequency. In a magnetic field of 875 G tlie rotational motion of tlie electrons is in resonance witli tlie microwaves of 2.45 GHz. In such low-pressure electron cyclotron resonance plasma sources collisions between tlie atoms, molecules and ions are reduced and the fonnation of unwanted particles in tlie plasma volume ( dusty plasma ) is largely avoided. 

The following factors affect net diffusion of a substance (1) Its concentration gradient across the membrane. Solutes move from high to low concentration. (2) The electrical potential across the membrane. Solutes move toward the solution that has the opposite charge. The inside of the cell usually has a negative charge. (3) The permeability coefficient of the substance for the membrane. (4) The hydrostatic pressure gradient across the membrane. Increased pressure will increase the rate and force of the collision between the molecules and the membrane. (5) Temperature. Increased temperature will increase particle motion and thus increase the frequency of collisions between external particles and the membrane. In addition, a multitude of channels exist in membranes that route the entry of ions into cells. 

Modern analyses of perikinesis and orthokinesis take account of hydrodynamic forces as well as interparticle forces. In particular, the frequency of binary collisions between spherical particles has received considerable attention(27 30). 

Assuming an attractive potential only, given by equation 5.26, Smoluchowski showed that the frequency of collisions per unit volume between particles of radii ax and a2 in the presence of a laminar shear gradient y is given by ... 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

TJhe aggregation of particles in a colloidal dispersion proceeds in two distinct reaction steps. Particle transport leads to collisions between suspended colloids, and particle destabilization causes permanent contact between particles upon collision. Consequently, the rate of agglomeration is the product of the collision frequency as determined by conditions of the transport and the collision efficiency factor, the fraction of collisions leading to permanent contact, which is determined by conditions of the destabilization step (2). Particle transport occurs either by Brownian motion (perikinetic) or because of velocity gradients in the suspending medium (orthokinetic). Transport is characterized by physical parame-... 

In the above expression, C (pi z) is the finite frequency generalization of the Boltzmann-Lorentz collision operator. Cq1 (pi z) can be described by the finite frequency generalization of the Choh-Uhlenbeck collision operator. [57]. This operator describes the dynamical correlations created by the collisions between three particles. Using the above-mentioned description the expression of (pi z) can be shown to be written as [57]... 

Boyle s law (P oc /V) Gas pressure is a measure of the number and forcefulness of collisions between gas particles and the walls of their container. The smaller the volume at constant n and T, the more crowded together the particles are and the greater the frequency of collisions. Thus, pressure increases as volume decreases (Figure 9.11a). 

The particles in a sound field, however, behave in a peculiar manner which is not quite so simple. St. Clair points out that at a frequency of 5000 cycles, particles of 0.5 n or smaller (density = 1.5) have an amplitude and velocity the same as that of the surrounding gas, while particles of 10 p will scarcely vibrate at all. The intermediate sizes will pulsate out-of-phase with the pulsations of the gas stream. Thus particles 2 u will have an amplitude of 0.87 that of the gas and will be about 30 deg out-of-phase. It has been suggested by Brandt and Hiedemann that the flocculating effect is due to the increased number of collisions between the particles due to the kinetic energy imparted to them. However, as St. Clair points out, this cannot be the sole factor since flocculation is observed at a few hundred cycles for which the suspended particles remain stationary. 

With increasing Ekin the particle size diminishes at first, but afterwards increases from a certain Ek n value onwards. If one considers the implemented specific energy to be a product of the intensity and frequency of the collision between beads and grinding medium, it follows that, at E/pV = const and an increasing intensity of the collision, the frequency has to diminish and this results in a coarser product. This also explains why, in the previously discussed investigation [77], particles no finer than d50 = 1 pm were found, see Fig. 52 and 53. 

As the frequency and the number of effective collisions between reacting particles increases, the rate of the reaction... 

This condition is defined as rapid coagulation in which the rate of disappearance of primary particles, Jq, is equal to the frequency of collision between the particles ... 

The same apparatus was used to measure the kinetics of emulsion crystallization under shear. McClements and co-workers (20) showed that supercooled liquid n-hexadecane droplets crystallize more rapidly when a population of solid n-hexa-decane droplets are present. They hypothesized that a collision between a solid and liquid droplet could be sufficient to act as a nucleation event in the liquid. The frequency of collisions increases with the intensity of applied shear field, and hence shearing should increase the crystallization rate. A 50 50 mixture of solid and liquid n-hexadecane emulsion droplets was stored at 6 -0.01 °C in a water bath (i.e., between the melting points and freezing points of emulsified n-hexadecane). A constant shear rate (0-200 s ) was applied to the emulsion in the shear cell, and ultrasonic velocities were determined as a function of time. The change in speed of sound was used to calculate the percentage solids in the system (Fig. 7). Surprisingly, there was no clear effect of increased shear rate. This could either be because increase in collision rate was relatively modest for the small particles used (in the order of 30% at the fastest rate) or because the time the interacting droplets remain in proximity is not affected by the applied shear. 

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