Fractional collision efficiency

The excited intermediate C (n) may also be stabilized via reaction 10.179. A fractional collision efficiency ft is assumed, so by Eq. 10.155 the rate constant for this process is fikHs, or by Eq. 10.157 it is fiku-... 

The two major theories of flocculation, the bridging model (1) and the electrostatic patch model (2, 3 ), provide the conceptual framework for the understanding of polymer-aided flocculation, but they do not directly address the kinetics of the process. Smellie and La Mer (4) incorporated the bridging concept into a kinetic model of flocculation. They proposed that the collision efficiency in the flocculation process should be a function of the fractional surface coverage, 0. Using a modified Smoluchowski equation, they wrote for the initial flocculation rate... 

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-... 

The rate constant kp is given in terms of physical parameters (Boltzmann Constant KB, the absolute temperature T, and the absolute viscosity rj) that characterize these transport conditions. In the case of not completely destabilized colloids, when according to v. Smoluchowski so-called slow coagulation is observed, the rate constant contains in addition the collision efficiency factor, p, the fraction of collisions leading to permanent attachment under perikinetic conditions ... 

Howarth (H15) developed an expression for collision efficiencies by assuming an analogy to bimolecular gas reactions. He assumed that a critical relative velocity IV exists along the lines of centers of two colliding drops which must be exceeded for a collision to result in a coalescence. By assuming that the three-dimensional Maxwell s equation describes the drop turbulent velocity fluctuations, he obtained the coalescence efficiency as the fraction of drops which have kinetic energy exceeding IV. Thus,... 

In the case of slow coagulation the number of collisions between particles leading to their aggregation decreases due to the presence of a potential barrier, which prevents the particles from approaching each other. The fraction of successful (i.e. leading to aggregation) collisions is referred to as the collision efficiency, a. Inverse of collision efficiency is the stability ratio, W= la, which is equal to the ratio of true coagulation rate constant to that predicted by the Smoluchowski equation (VII.29). The stability ratio... 

A possibly substantial intensification of the microflotation process follows from the findings. If we provide a maximum intensive microflotation process, it simultaneously intensifies the purification of the system from molecular impurities. This leads to an increase of the residual mobility and, correspondingly, to an increase of the collision efficiency. Unfortunately this way of intensification is restricted by the existence of an optimal volume fraction of bubbles (Derjaguin Dukhin, 1986). 

If the polydispersity of bubbles generated in air-dissolved flotation or electroflotation is high, there is no need for additional introduction of centimicron bubbles. Optimal flow of two-stage flotation corresponds to the maximum attainable degree of monodispersity of bubbles. In this case the ratio between volume fractions of micro- and macrobubbles and collision efficiencies of the processes of particle capture by small bubbles and bubble coagulation must be such that the particle capture process outweighs the process of coalescence. 

Collision Efficiency In our discussion so far, we have assumed that every collision results in coagulation of the two colliding particles. Let us relax this assumption by denoting the coagulation efficiency (fraction of collisions that result in coagulation) by a. Then Fuchs (1964) showed that the coagulation coefficient becomes... 

Fig. 21. A comparison of the observed and predicted collision efficiencies of various partners in the relaxation of benzene. The vertical bars indicate the observed fraction of vibrational energy transfer into specific channels, the crosses the values calculated from the Parmenter-Tang rules. The column labeled 2 is sum of the fractions in channels A, B, C, and D.

The variables of equation (9) are the ratio (K) of the initial separation distance (d j) to the sum of the hard sphere collision radii (s), the ratio (L) of the proportionality constant for the combination reaction (k ) to the second order rate constant for pair diffusion (k(j2) ind the ratio (r) of the time elapsed since pair formation to the diffusive time constant (s /D). The fractional cage efficiency is the complement to the pair... 

The relationships corresponding to equations (l)-(5) above are as follows The obse ed rate constants (kjfobs) and activation parameters (AH xfobs AS -pfobs) for disappearance of R by reaction with T depend on the second order rate constant for diffusive collision to form the cage pair (k pj), equation 12) and the fractional cage efficiency (Fjc equation 11). The latter is determined by the first order rate constants for the chemical reaction (kjc) and diffusive (re)separation (kj j) of the T/R collisional cage pair. The associated activation parameters are given by equations (13) and (14). 

Fig. 7-18. Comparison of experimental data and modeling results (Elimelech et al., 2000) showing that the overall collision efficiency is linearly dependent on the degree of chemical heterogeneity. The surface of the quartz sand collector phase was modified with aminosilane, which created favorable deposition sites for quartz colloids. 1 is the fraction of favorable colloid deposition sites.

Interaction of acidic gases such as HCl with ice particles of PSCs is a key step in polar ozone hole chemistry [3]. The uptake efficiency of HCl, y, on ice is defined by the fractional collision frequency that leads to the reactant loss on ice surface. Until recently, a single laboratory measurement y 0.4 has been performed at HCl vapor... 

The rate of particle agglomeration depends on the frequency of collisions and on the efficiency of particle contacts (as measured experimentally, for example, by the fraction of collisions leading to permanent agglomeration). We address ourselves first to a discussion of the frequency of particle collision. 

Because the collisions between ions and molecules in the gas phase are governed by physical (ion-dipole, ion-induced dipole) rather than chemical forces, it is possible to calculate rather accurately the collision rate constant (6, 7). We then express the efficiency of the reaction as the fraction of collisions which lead to products. 

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