Brownian, Gradient Shear and Turbulent Coagulation

In the previous section, the possibility of the particles coagulation was considered for the case when the particles were pulled close enough together. For the coagulation to be possible under this condition, the suspension should be unstable. The coagulation rate in the system is determined by the particles collision frequency as a result of their relative motion in the ambient liquid. 

Listed mechanisms, as a rule, exist in a quiescent liquid or in liquid in a state of laminar flow. 

The third mechanism, named turbulent coagulation, is characteristic of coagulation of particles suspended in turbulent flow, for example in a pipe or in some special mixing devices - mixers, agitators, etc. In some aspects, the turbulent coagulation is similar to the Brownian one, since in the first case the particles approach is due to random turbulent pulsations, and in the second case it is due to random thermal motion of particles. 

For a quantitative description of slow coagulation, Smoluchowski has suggested to formally introduce into the expression for the particle collision frequency a factor a 1, describing the share of collisions resulting in formation of aggregates. Introduction of this factor is equivalent to increase of the characteristic coagulation time by a factor 1/a. The coagulation rate is characterized by stability factor W. It is the ratio of the partides collision rates without and with the force of electrostatic repulsion [58] 

Introduction of the stability factor gives the physical meaning to factor a. Since a = 1/W, the coagulation rate slows down by a factor of W. 

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