Modeling of Molecular Diffusion in Non-Homogeneous Media

Iaroslav V. Zagumennyi


Background. Due to combined effects of medium inhomogeneity and action of external forces, i.e. Earth’s gravitation, electro-magnetic forces, global rotation, etc., a number of specific fluid motions appear in the environmental and life systems even in absence of pure mechanical reasons. Among them are so called diffusion-induced flows which always exist around obstacles with arbitrary geometry due to breaking of natural molecular flux of a stratifying agent on an impermeable surface.

Objective. The aim of the paper is to analyze numerically a diffusion induced flow structure and dynamics around motionless obstacles immersed into a stably stratified medium, including a sloping plate, a wedge-shaped obstacle, a disc, and a circular cylinder. The numerical results obtained are compared with the available analytical and experimental data.

Methods. The problem is solved numerically using two different algorithms based on the finite difference and finite volume methods. The first approach is implemented in the specially developed Fortran program codes, and the second one is based on the open source package OpenFOAM with the use of C++ programming language for developing special own solvers, libraries, and utilities, which enable solving the problems under consideration.

Results. The numerical simulation reveals a complex multi-level vortex system of compensatory circulating flows around a motionless obstacle, which structure is strongly dependent on its position relative to the horizon. The most intensive and extended high-gradient horizontal interfaces attached to sharp edges or poles of obstacles are clearly observed in the numerical computations and laboratory experiments. Diffusion-induced flows form intensive pressure deficiency zones around an obstacle, which may lead to generation of propulsion mechanism resulting in self-movement of neutral buoyancy bodies in a continuously stratified fluid, e.g. horizontal movement of a wedge, rotation of a sloping plate, etc.

Conclusions. Diffusion-induced flows are a wide-spread phenomenon in biology, medicine, and environmental systems, since such flows inevitably occur in any inhomogeneous media, including different solutions, suspensions, mixtures, etc. A complex multilevel vortex structure of diffusion-induced flows on an obstacle becomes even more compli­­cated due to self-motion of the obstacle itself and displacement of various admixtures, suspended particles, additives, etc., which are always present in the real systems.


Molecular diffusion; Stratified fluid; Diffusion-induced flow; Propulsion mechanism; Finite volume method

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