Effect of Rotation on Boundary Conditions at the Interface of Two Immiscible Fluids

Abstract

Recent experimental studies revealed the development of slip at the interface of a steady axisymmetric swirling flow of two immiscible fluids. As swirl increases, the slip changes the flow topology scenario compared with that numerically predicted using the velocity continuity condition. This phenomenon of fundamental and practical interest has not been well understood yet. What condition should replace the velocity continuity has remained unknown. Our study addresses this problem by providing detailed experimental and numerical investigations of the flow in the interface vicinity. The bulk flow is driven by the rotating lid in a vertical cylindrical container—a model of vortex bioreactor. The centrifugal force pushes the upper fluid from the axis to the sidewall near the lid and the fluid goes back to the axis near the interface. This centrifugal circulation drives the anti-centrifugal circulation of the lower fluid at a slow rotation. As the rotation speeds up, a new flow cell emerges below the interface-axis intersection. It expands radially and downward occupying the lower-fluid domain. During these topological transformations, the flow remains steady and axisymmetric with no visible deformation of the interface. Using the advanced PIV experimental and numerical techniques, we explore the distribution of azimuthal and radial velocities in the interface vicinity and reveal that the azimuthal velocity is continuous while the radial velocity has a jump at the interface. The radial velocity tends to zero in the upper fluid. In contrast, the radial velocity does not tend to zero and satisfies the stress-free condition in the lower fluid at the interface. The numerical simulations under these conditions are in qualitative agreement with the experiment.