Dynamics in the boundary layer of a flat particle

The paper presents a theoretical study of the source of the spinning movement of the solid particles flowing in a moving fluid and the influence of the resulting Magnus force on the particles' trajectories along the stream lines, based on interactions occurring in the boundary layers. The subject is important for technological applications, like aerodynamic separation process of a mixture of solid particles. First, it is shown that the boundary layer equations generate local soliton-type, kink-type and soliton-kink-type nonlinear solutions for the velocity field. Using Prandtl's equations for boundary layer, nonlinear solutions of the velocity field are obtained. It was found that through the interaction on the boundary layers, the transition from the movement on continuous and differentiable curves (stream lines) to the movement on continuous and non-differentiable curves (fractal curves) occurs. This last characteristic can be used in the separation process of the solid components from a heterogeneous mixture.

Graphical abstractThe diagrams of the force field induced by Magnus effect and of the local velocity show that the two parameters have a maximum along y direction, with a rapid decrease to zero for larger y values. The angular velocity has a similar variation, but the decrease is to a limit value. The variations confirm the existence of the limit layer.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Considerations on generation/dynamics analysis in the boundary layer are made. ► Prandtl's equations for boundary layer are written. ► Nonlinear solutions of the velocity field are obtained. ► The force field induced by Magnus effect is given.