Shear aggregation

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] 

Brownian collisions also occur during shear aggregation. The collision rate due to shear is more important than the Brownian collision rate of particles for shear aggregation. This condition occurs for particles larger than a critical size, given by [87] 

This expression was obtained by setting the shear aggregation rate to the Brownian aggregation rate and solving for the size a to which this corresponds assuming the colloid stability ratio, W is unity. 

Problem 10J3. Critical Size for Shear Aggregation 

Determine the particle size above which shear aggregation is dominant for a room temperature aqueous suspension of particles when the shear rate is varied from 1 to 100 sec .  

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Shear aggregation brings an added complexity to the modeling of aggregation kinetics. This complication due to shear is not discussed further. 

Solution The radii of particles when the shear aggregation rate is equal to the Brownian aggregation rate are calculated by the preceding equation with y varied between 1 to 100 sec , T = 298 K, rj = 0.01 poise. The results follow ... 

With 0.05 jLim latex particles in a glycerol-salt solution, large-scale shear aggregates have been shown to have the same fractal dimension as that of Brownian aggregates (i.e.. Dp = 1.8 0.1) when the shear rate is less than 1500/sec [88]. Due to shear allegation, the aggregation rate for these experiments was much faster than that of comparative Brownian aggregation rates. 

It follows from Example 6a that the time constant for Brownian aggregation is inversely proportional to the cube of the particle diameter. That means that the aggregation slows down as the particles grow. When they reach a certain size, the shear aggregation will take over. 

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