Advancement of the kinetic approach to Brownian coagulation on the base of the Langevin theory

•The new approach to Brownian coagulation is further advanced.•Trajectory of particles are calculated using Langevin equation.•The new interpolation expression has a relatively high accuracy.

The kinetic approach to calculation of the coagulation kernel, derived in the two subsequent approximations of the random walk theory in the authors' previous papers avoiding semi-empirical assumptions of the traditional models, is further advanced by application of the Langevin equation for Brownian particle migration. The interpolation expressions for the collision rate derived in the simple random walk approximations were additionally justified and further improved.