After recalling the main ideas of kinetic theory of gases and of various scales of description of a material medium, the diffusion of the Brownian particles in a continuum subject to gravitation forces and a temperature field is discussed. The nonlinear energy conservation law for a thermodiffusion process with the Streater effect in which the potential energy of the Brownian particle is converted to a heat due to friction, is obtained, cf. [1]. The second law is satisfied if a nonlinear relation between the probability density function and temperature is postulated. The examples of the Brownian motion corresponding to particular gravitational fields and temperature differences are included. Also, a homogenisation method is used to describe a thermodiffusion process in porous media.