# Coagulation

Coagulation is understood as a process originating from the collision of particles. When two particles collide, van der Waals forces cause them to stick together to form one larger agglomerate. As a result the number concentration of airborne particles decreases whereas the mean particle size increases. The collision frequency between particles is a function of the particle concentration and particle size, besides thermodynamic conditions of the gas.

An increased particle concentration increases the likelihood of particle collisions. Given that collisions only occur in case of particles moving relative to each other, small particles are much more prone to coagulation because of their constant random Brownian motion.

## Algorithms

 Particle size Particle concentration $N(t)=\frac{N_{0}}{1+N_{0}\cdot K\cdot t}$ $K=4\pi \cdot d_{p}\cdot D$ $d_{p}(t)=d_{p,0}\cdot \sqrt[3]{1+N_{0}\cdot K\cdot t}$     Change of particle size over time