Particle collision frequency, polymer

Particle collision frequency due to Brownian motion was estimated to be less than 1% of the collision frequency due to shear. The effects of Brownian motion could therefore be neglected in the flocculation rate calculations. However, for the smallest molecular size, radius of gyration 14 nm (see Table I), the effect of Brownian motion on the particle-polymer collision efficiency was of the same order of magnitude as the effect of shear. These two contributions were assumed to be additive in the adsorption rate calculations. Additivity is not fundamentally justified (23) but can be used as an interpolating... 

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 °... 

Rate of growth (high deformability) Decrease binder viscosity. Increase agitation intensity. Increase particle density. Increase rate of nuclei formation, collision frequency, and residence time, as above for low-deformability systems. Decrease binder concentration or change binder. Decrease any diluents and polymers that act as thickeners. Decrease operating temperature for systems with simultaneous drying. (Otherwise increase temperature. Increase mixer impeller or drum rotation speed or fluid-bed gas velocity. 

The role of gas phase initiation processes was further explored by Tibbitt et al. . These authors proposed that the polymerization of unsaturated hydrocarbons in a 13.56 MHz plasma is initiated by free radicals formed in the gas by electron-monomer collisions, the initiation reactions listed in Table 6. Moreover, it was assumed that the formation of free radicals on the polymer surface due to the impact of charged particles could be neglected. This assumption is supported by the fact that at 13.56 MHz and pressures near one torr the discharge frequency is significantly greater than either f, or f and that as a result the fluxes of charged particles to the electrode surfaces are quite small. 

Strongly non-linear rheology is characteristic of soft matter. In simple fluids, it is difficult to observe any deviations from Newtonian behavior, which is well described by the hydrodynamic equations of motion with linear transport coefficients that depend only on the thermodynamic state. Indeed, Molecular Dynamics simulations [9] have revealed that a hydrodynamic description is valid down to astonishingly small scales, of the order of a few collisions of an individual molecule. This means that one would have to probe the system with very short wave lengths and very high frequencies, which are typically not accessible to standard experiments (with the exception of neutron scattering [10]), and even less in everyday life. However, in soft-matter systems microstructural components (particles and polymers for example) induce responses that depend very much on frequency and length scale. These systems are often referred to as complex fluids. ... 

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