Relaxation particles

The essential idea of the new model is that p2 is the probability that there will be enough free volume, v/, in the vicinity of a relaxing particle with its own volume, vo, to allow reorientation [69,70,78,155]. In other words, we imply that in order to participate in a relaxation a particle must have a defect in its vicinity. Then,... 

In the case of the second mechanism - the so-called Brown relaxation -particles can physically rotate to an extent dependant on the hydrodynamic parameters of both the particles and the medium, and at a characteristic... 

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

Model colloids have a number of properties that make them experimentally convenient and interesting systems to study. For instance, the timescale for stmctural relaxation of a colloidal fluid can be estimated as the time for a particle to diffuse a distance equal to its radius,... 

Although most cakes consist of polydisperse, nonspherical particle systems theoretically capable of producing more closely packed deposits, the practical cakes usually have large voids and are more loosely packed due to the lack of sufficient particle relaxation time available at the time of cake deposition hence the above-derived value of 17.6 pm becomes nearer the 10 pm limit when air pressure dewatering becomes necessary. 

This effect of concentration is particularly pronounced with irregularly shaped particles. A possible explanation of the variation in the specific resistance is in terms of the time available for the particles to orient themselves in the growing cake. At higher concentrations, but with the same approach velocities, less time, referred to as particle relaxation time, is available for a stable cake to form and a low resistance results. 

Because gravity is too weak to be used for removal of cakes in a gravity side filter (2), continuously operated gravity side filters are not practicable but an intermittent flow system is feasible in this arrangement the cake is first formed in a conventional way and the feed is then stopped to allow gravity removal of the cake. A system of pressure filtration of particles from 2.5 to 5 p.m in size, in neutralized acid mine drainage water, has been described (21). The filtration was in vertical permeable hoses, and a pressure shock associated with relaxing the hose pressure was used to aid the cake removal. 

The main problem of elementary chemical reaction dynamics is to find the rate constant of the transition in the reaction complex interacting with its environment. This problem, in principle, is close to the general problem of statistical mechanics of irreversible processes (see, e.g., Blum [1981], Kubo et al. [1985]) about the relaxation of initially nonequilibrium state of a particle in the presence of a reservoir (heat bath). If the particle is coupled to the reservoir weakly enough, then the properties of the latter are fully determined by the spectral characteristics of its susceptibility coefficients. 

Coupling to these low-frequency modes (at n < 1) results in localization of the particle in one of the wells (symmetry breaking) at T = 0. This case, requiring special care, is of little importance for chemical systems. In the superohmic case at T = 0 the system reveals weakly damped coherent oscillations characterised by the damping coefficient tls (2-42) but with Aq replaced by A ft-If 1 < n < 2, then there is a cross-over from oscillations to exponential decay, in accordance with our weak-coupling predictions. In the subohmic case the system is completely localized in one of the wells at T = 0 and it exhibits exponential relaxation with the rate In k oc - hcoJksTY ". 

Relaxation time The time necessary for a moving particle to adjust from one given steady state velocity to another, e.g., the time for a falling particle to reach its terminal velocity. It is independent of the nature of the force applied to the particle. 

Stopping distance The maximum distance a moving particle will travel in still air after all the external forces are removed. In the Stokes region it is the velocity of the particle times the relaxation time. 

Let us consider a simple model of a quenched-annealed system which consists of particles belonging to two species species 0 is quenched (matrix) and species 1 is annealed, i.e., the particles are allowed to equlibrate between themselves in the presence of 0 particles. We assume that the subsystem composed of 0 particles has been a usual fluid before quenching. One can characterize it either by the density or by the value of the chemical potential The interparticle interaction Woo(r) does not need to be specified for the moment. It is just assumed that the fluid with interaction woo(r) has reached an equlibrium at certain temperature Tq, and then the fluid has been quenched at this temperature without structural relaxation. Thus, the distribution of species 0 is any one from a set of equihbrium configurations corresponding to canonical or grand canonical ensemble. We denote the interactions between annealed particles by Un r), and the cross fluid-matrix interactions by Wio(r). 

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