Brownian coagulation in the transition regime

The effects of non-continuum hydrodynamics on the Brownian coagulation of aerosol particles

“…When Kn O(1), one must account for the finite persistence length of the particles' Brownian motion. Several approximate treatments of this effect have been given in the literature (Fuchs, 1964;Sitarski and Seinfeld, 1977;Narsimhan and Ruckenstein, 1984). However, one also requires a solution for the non-continuum gas flow driven by particle motion when the particle radius, interparticle separation, and mean-free path are all comparable, in order to accurately compute the interparticle hydrodynamic interactions.…”

“…We will consider the modification of the collision efficiency due to the non-continuum nature of the hydrodynamic interactions between the particles when the Knudsen number Kn = /a is small but non-zero. When the Knudsen number is order one or larger, the drag forces acting on the particles are reduced allowing the particles to undergo persistent Brownian motion, in which the typical distance a particle moves before changing direction is comparable with the particle separation (Sitarski and Seinfeld, 1977). However, in the limit Kn>1 considered here, the persistence distance for particle motion is much smaller than the interparticle separation and the simple pair diffusion equation that forms the basis of the standard Brownian coagulation theory (Russel et al, 1989) is still valid.…”

Effect of brownian diffusion on chemical kinetics

“…The above assumptions of the kinetic model are the same as for the coagulation of aerosol particles [3]. Thus the results obtained for the coagulation can be applied in our case.…”

“…K is defined as the ratio of the relaxation time t p for the Brownian particle A or B to the time during which the particle moves a reaction distance R with an average Maxwellian velocity C. It has been obtai-ied in terms of the diffusion coefficient D as follows [3]: The mathematical development regards a trapping molecule as a stationary sink around which a concentration gradient of approaching molecules is established. However, the trapping molecule is diffusing itself and changes position significantly in times comparable to those needed to establish the concentration gradient.…”

“…This is caused by the so-called shielding effect when the two colliding particles are close to each other and by the specific discrete molecular structure of the solvent around the reacting particles. Similar problems arose in building up the theory of coagulation of aerosol particles [3]. We then applied the ideas developed there to the kinetics of fast chemical reactions in solutions.…”