Collision between particles influence

Before introducing the chemical reaction into the picture of the system, it is necessary to explore the motion of one or two particles in a little more detail. Consider a collision between particles a and jS, and the time a little before and afterwards, such that several other collisions between the particle a which has co-ordinates r, v, and all other particles (jS ce) may occur. All the other particles which do not collide with a may be ignored. Averaging over all the positions of the N — 2) particles removes their influence (which does not affect the motion of particle a) and leads to a doublet distribution, f2. Then averaging over all positions of the particles (3 (which are colliding with particle a) gives an equation for the singlet distribution [541,542]... 

His model paid special attention to the influence of particles on gas turbulence and the collision between particles, and was solved numerically to calculate radial profiles of voidage, gas velocity and particle velocity, showing good agreement with experiments. 

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. 

In many cases, even if collisions between particles do take place, the naturally available binding mechanisms, mostly molecular forces, which are considerably lower in a liquid environment than in a gas atmosphere, do not create bonds with sufficient strength to withstand the various separating effects and satisfactory flocculation does not occur. For quite some time it has been known that polymers, added to liquid-based particulate systems, have a dramatic influence on particle interaction. Molecules may attach themselves to solid surfaces and, depending on the characteristics of the exposed radicals, can cause particle attraction [B.29] or dispersion [B.63]. The second, dispersion, is applied to avoid agglomeration (Chapter 4) or enhance disintegration of aggregates. 

Chemical parameters determine the surface characteristics of the suspended colloids, the concentration of the coagulant and its effects upon the surface properties of the destabilized particles, and the influence of other constituents of the ionic medium upon the coagulant and the colloids. The extent of the chemical and physical interactions between the colloidal phase and the solution phase determines the relative stability of the suspended colloids. One speaks of stable suspensions when all collisions between the colloids induced by Brownian motion or by velocity gradients are completely elastic the colloidal particles continue their... 

Now, consider a gas with two different types of particles in a container. The radius of the sphere of influence for collision between the two different particles is... 

Brownian motion, which is a result of random collisions between the particles in the suspension, might influence suspension stability especially for smaller particles (smaller than... 

These trajectory methods have been used by numerous researchers to further investigate the influence of hydrodynamic forces, in combination with other colloidal forces, on collision rates and efficiencies. Han and Lawler [3] continued the work of Adler [4] by considering the role of hydrodynamics in hindering collisions between unequal-size spheres in Brownian motion and differential settling (with van der Waals attraction but without electrostatic repulsion). The results indicate the potential significance of these interactions on collision efficiencies that can be expected in experimental systems. For example, collision efficiency for Brownian motion will vary between 0.4 and 1.0, depending on particle absolute size and the size ratio of the two interacting particles. For differential... 

Consider an ensemble of noninteracting particles—the reactant—under the influence of (1) a force derived from an external one-dimmisional potential V(x) consisting of a well A and an adjacent barrier C (see Fig. 1) and (2) an irregular force resulting from random collisions between the reactant particles and solvent particles at a givoi temperature T. 

The influence of sedimentation flocculation on the final average floe diameter is small. The rate of collisions between 2 groups of particles because of a difference of sedimentation velocity can be calculated with (14) ... 

This result was interpreted by the manifestation of short range hydrodynamic interactions. The role of electrostatic interaction in flotation is confirmed by investigations of the influence of added sodium dodecylsulfate (SDS). Due to SDS adsorption the charge of bubbles increases und the collision efficiency decreases. When following the capture rate it is observed, that at SDS concentrations above 10 M particle deposition completely stops while the contact angle continues to be large. Thus, electrostatic repulsion prevents the contact between particles and bubbles. 

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