Coagulation, velocity

W is the stability ratio, i. e. the factor by which the coagulation velocity is reduced due to interparticle repulsion. It is related to the height of the energy barrier. When coagulation is fast, W = 1. Various aspects of slow coagulation are still not fully understood (O Melia, 1987). Several theories of the kinetics of coagulation are discussed by Grand et al. (2001). 

Additionally, in this filtration process no flocculating polymers at all are needed to the exclusive benefit of the organic coagulant. Velocities are from 10 to 18 m h". ... 

In the first process, the Brownian motion velocity and presence of electrolytes influences the increase in viscosity of the immobilizing media, the coagulation velocity, the domain of attraction forces, and the concentration of colloidal solution. Consequently, from the Smoluchowski equation (Pomogailo and Kestelman 2005), the rate constant of particle coagulation, k, is inversely proportional to the viscosity of the media, r ... 

The dotted curve gives the coagulation of the small particles should they alone be present The curve in crosses (= 1) gives the increase of coagulation velocity when an equal number of large particles is present but the collision probability is retained at 4 Z>i Ti The drawn curves finally represent the cases for large particles of different sizes (10,20 and 100 times the diameter of the small particles) on introducing the collision factor... 

In other words, the lower the mass of the particle, the higher its velocity, because the average energy of any particle at a given temperature is constant, kT. A dispersed particle is always in random thermal motion (Brownian motion) due to coUisions with other particles and with the walls of the container (4). If the particles coUide with enough energy and are not well dispersed, they will coagulate or flocculate. 

This angle plate gravity separator removes suspensions of solids from a dilute liquid. The unit is more compact than a box-type settler due to the increased capacity achiev ed by the multiple parallel plates. The concept is fairly standard (U.S. Patent 1,458.805—year 1923) but there are variations in some details. For effective operation, the unit must receive the mixture with definite particles having a settling velocity. The units are not totally effective for flocculants or coagulated masses that may have a tendency to be buoyant. 

Precipitation is effected in hot solutions, provided the solubility and the stability of the precipitate permit. Either one or both of the solutions should be heated to just below the boiling point or other more favourable temperature. At the higher temperature (a) the solubility is increased with a consequent reduction in the degree of supersaturation, (b) coagulation is assisted and sol formation decreased, and (c) the velocity of crystallisation is increased, thus leading to better-formed crystals. 

Brunk, B. K., Koch, D. L., and Lion, L. W., Hydrodynamic pair diffusion in isotropic random velocity fields with application to turbulent coagulation. Phys. Fluids 9,2670-2691 (1997). 

Coagulation a Collision efficiency volumetric concentration of suspended particles G Velocity gradient t time i... 

With hydraulic residence times ranging from months to years, lakes are efficient settling basins for particles. Lacustrine sediments are sinks for nutrients and for pollutants such as heavy metals and synthetic organic compounds that associate with settling particles. Natural aggregation (coagulation) increases particle sizes and thus particle settling velocities (Eq. 7.1) and accelerates particle removal to the bottom sediments and decreases particle concentrations in the water column. 

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. 

A different approach which also starts from the characteristics of the emissions is able to deal with some of these difficulties. Aerosol properties can be described by means of distribution functions with respect to particle size and chemical composition. The distribution functions change with time and space as a result of various atmospheric processes, and the dynamics of the aerosol can be described mathematically by certain equations which take into account particle growth, coagulation and sedimentation (1, Chap. 10). These equations can be solved if the wind field, particle deposition velocity and rates of gas-to-particle conversion are known, to predict the properties of the aerosol downwind from emission sources. This approach is known as dispersion modeling. 

The presence of velocity gradients in the system may also increase the rate of coagulation above the value given by Equation (24) or (42). 

The ratio of the probability of a collision induced by a fluid velocity gradient (dv/dx) (i.e., orthokinetic coagulation) to the collision probability under the influence of Brownian motion (perikinetic coagulation—what we have considered so far) has been shown to be (Probstein 1994)... 

The temperature also affects the process of coagulation.8 With the chlorides of potassium, sodium, lithium and ammonium the velocity of flocculation varies inversely as the temperature 9 with the chlorides of barium, strontium, calcium, magnesium and cadmium the velocity varies directly as the temperature with aluminium chloride it is independent of the temperature. Heating thus stabilises the sol towards univalent cations but diminishes the stability towards bivalent ions.10 The... 

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