Stochastic modeling of a fluid batch mixed system with variable dispersion coefficient

This contribution presents the numerical solution of the one-dimensional stochastic differential equation with a diffusion coefficient which is a function of the spatial coordinate, as a model of a fluid batch system stirred by a rotating mechanical impeller. It is demonstrated that neither the Ito nor the Stratonovich methods of solution, which are widely used to solve equations of this kind, lead to a uniform distribution of concentration of the blended species component at steady-state. A method of solution is suggested, with the aid of the so-called transport integral, which converges to the uniform steady-state distribution, consistent with the physical conception of the course of the mixing process.