Hello everyone,
Would you know any work where Smoluchowski equation for aggregation of particles is used with a finite number of particles ?
Meaning in general the number that is computed is the concentration of aggregates of size n. So we assume that the number N of aggregates of size n is very large for any n : N>>1, so that the variable of interest is the concentration in particles of size n. In general, in experiments, the size n_max of the largest aggregate is much smaller than the total number of particles n_ttl : n_max
A quick review of this article suggests it may help.
Article The Smoluchowski Ensemble—Statistical Mechanics of Aggregation
Since it is a statistical mechanistic approach, I will be little concerned about the sample size. A too little sample size or small number of particles are not advisable. I am not a statistician but from the mechanistic point of view the number of particles play a role on estimating the aggregation kinetics. Let the smaller particles aggregate and get them into less numbered but larger aggregate size category.
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