The filtration media is comparatively vast and deep compared to these sub-micron particles. This makes it almost inevitable for a particle travelling with Brownian motion to collide with a fibre contained within the filtration media bed. This sounds quite grand. What it means is that the tiny particles actually cover so much ground in getting from A to B, that their chances of bumping into a similar sized particle, or into a larger particle is quite high. Either way, the tiny particle no longer moves randomly and now follows the direction of air flow.
Temperature gradients cause the effects of Brownian motion to increase.
Compressed air is rarely cold, this means that the tiny particles are bouncing around with an even greater energy. This increases the capture rate. A global terms which describes the combined effects of Brownian motion and Thermophoresis. Even though the bath water is perfectly still, the pink bath oil will slowly spread through the water until it is fully dispersed. This is called diffusion.