Aggregation and Dispersion in Shear

The introduction of long-range interaction forces between colloidal particles can produce well dispersed or aggregated systems under 

Now in convection we can obtain the velocity of the particle by multiplying the velocity gradient, i.e. shear rate, by the distance moved by the particle. We can think of this as some multiple of the particle radius,  

Suppose we normalise such that the force is dimensionless. This gives us the Peclet number  

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