Coagulation laminar shear flow

Swift DL, Friedlander SK. The coagulation of hydrosols by Brownian motion and laminar shear flow. J Colloid Sd 1964 19 621-647. 

APPENDIX 13.1 ADDITIONAL MECHANISMS OF COAGULATION 13.A. 1 Coagulation in Laminar Shear Flow... 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

Consider the flow of an aerosol through a 4-in. duct at a velocity of 50 ft/sec. Compare the coagulation rate by Brownian motion and laminar shear in the viscous sublayer, near the wall. Present your results by plotting the collision frequency function for particles with dp = 1 /im colliding with particle.s of other sizes. Assume a temperature of 20 C. Hint In the viscous. sublayer, the velocity distribution is given by the relation... 

The second mechanism of coagulation is coagulation of particles suspended in a laminar flow of Uquid whose velocity is a regular function of position. As the characteristic distance of particle interaction is small, the structure of the velocity field on such linear scales can be considered as linear. In other words, the flow may be regarded as a shear flow, hence the name of the coagulation mechanism. This problem was also studied by SmolukhowsM [59]. 

For shear coagulation in laminar flow, the collision rate for N, particles of size a, with Nj particles of size Cj is given by [3, p. 298]... 

When the stirring speed increases, there is a transition from laminar to turbulent flow. Treatment of this kind of orthokinetic coagulation is much more difficult than the case of laminar flow. An approximate way to treat this situation is to use the Smoluchowski equation for orthokinetic coagulation in laminar flow and to employ an average shear gradient in the turbulent flow. Various estimates of this average have been derived. One of these... 

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