Aggregation efficiency

Our microscopic formalism cannot give the distribution function over aggregate sizes, but having calculated a mean number of particles within aggregate, equation (7.2.8), we can assume approximate validity of the Poisson distribution (for the moderate aggregation efficiency)... 

Xia Z, Frojmovic MM. Aggregation efficiency of activated normal or fixed platdets in a simple shear field Effect of shear and fibrinogen occupancy. BiophysJ 1994, 66 2190-2201. 

Scaling theory can also be derived to explain the coagulation kinetics of Brownian particles in the presence of a low electrolyte concentration (RLCA conditions). With decreasing aggregation efficiency, w was found to become negative. This point can be explained by taking into account the probability of efficient collisions between g- and n-fold aggregates which is proportional to a Boltzmann factor ... 

Aggregation frequency = Collision frequency x Aggregation efficiency. 

The actual calculation of such an efficiency is accomplished by methods demonstrated by Muralidhar et al (1988), referenced in footnote 28. The objective of the discussion herein has been to provide broad guidelines for modeling of the aggregation efficiency, since mechanisms and (hence details) in individual applications can vary rather diversely. Before concluding this discussion, we refer to one further aspect of modeling that can produce valuable simplifications in the foregoing treatment. Such simplifications arise from a consideration of times scales as in the treatment of Muralidhar and Ramkrishna (1986). 

The simplicity of this model allows an analytical solution to the boundary value problem (3.3.60)-(3.3.62) so that an explicit expression is possible for the aggregation efficiency. For details of such analytical solutions, the reader is referred to Das et al (1988). 

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