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The problem of the influence of Brownian diffusion of nanoparticles on their sedimentation remains relevant [1]. Since the experiment of Robert Brown (the movement of pollen particles in a liquid drop), many scientists have studied the behavior of particles in different types of environments. The method of nanoparticle synthesis plays an important role in the distribution of nanoparticles’ sizes [2]. Theoretical investigation of the sedimentation of nanoparticles is described in [3, 4], Brownian motion of nanoparticles is described in [5–7]. In this work, we discuss the effect of the nanoparticles’ diffusion on their sedimentation along the lower boundary of the vessel bottom, called the boundary layer [8]. To find the solution of the diffusion equation, the Newton polygon method is used – a method allowing one to find the solution of the equation with perturbed coefficients.

Mathematical modeling of sedimentation of nanoparticles in the vessel of finite depth