Dynamics of a soluble surfactant and evolution of daughterly concentration tongue in a Hele-Shaw cell

The origin and evolution of a concentration tongue, which is generated in the volume of a fluid due to the non-uniform desorption of a soluble surfactant, is investigated theoretically by the method of direct numerical simulation. Initially, a film of the soluble surfactant is located on the surface of the fluid that fills up the thin vertical rectangular slot (Hele – Shaw cell), heated non-uniformly from above. The intensity of desorption into the volume is determined by the compression of the film, caused by the Marangoni force, acting along the up boundary in opposite direction to the tangential component of temperature gradient. The dynamics of concentration tongue depends on the intensity of a creeping convective flow, which is produced in the volume jointly by the Archimedean and thermocapillary forces. The spatial motion of the fluid and the process of an admixture exchange between the surface and the volume in the Hele – Shaw cell are carried out in the plane of wide vertical boundaries of the cavity. This permits to simulate numerically and clearly visualize behaviour of the contaminants in multifarious fluid systems.