Prediction of nanoparticle size and the onset of dendrite formation using the method of characteristic times

The behaviour of an aerosol, in which particles are simultaneously growing by collisions and coalescing, is determined by the difference between the local collision and coalescence times. An equation is written for the dimensionless excess surface area of the agglomerates which shows the sharp change in the behaviour of the system when the characteristic times become equal. This sharp change and the growth of primary particles are illustrated by example calculations. The resulting primary particle size depends on the time-temperature history, volume loading and material properties of the system. Increasing initial temperature or volume loading increases primary particle size, while an increase in velocity decreases primary particle size.