Aggregation kernels for fine particles

Eor higher values of Kn, we move into the free-molecular (or Epstein) regime where the following aggregation kernel is used  

In order to work with a single expression that covers both regimes as well as the transition between them, very often the Euchs (1964) equation is used  

It is useful to compare the standard Stokes-Einstein equation in Eq. (5.116) with the corrected expression of Eq. (5.169). 

These kernels are valid for inertialess particles (i.e. Stp = 0) and can be extended to finite Stokes numbers only by employing ad hoc corrections. For example, Ammar Reeks (2009) derived for the kernel proposed by Salfman Turner (1956) a correction that is based on the local Stokes number. The relative importance of perikinetic aggregation versus orthokinetic aggregation is quantified by a Peclet number  

In fact, when Pe 0.001 only perikinetic aggregation need be considered, whereas when Pe 10 the perikinetic contribution is negligible. 

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