Solid components separation from heterogeneous mixtures through turbulence control

• The geodesic equations are identified with streamlines of the fluid-solid mixture.
• At any point of fractal path local time dependences of parameters are in equilibrium.
• Different non-linearity degrees correspond to various flow regimes.
• Three scenarios of transition to turbulence via chaos are comparatively given.

Assuming that the particle movements of fluid–solid mixture occur along continuous but non-differentiable curves, in the framework of scale relativity, the separation processes of the solid components from heterogeneous mixtures are analysed. By means of a numerical simulation of “fuzzy” type in the dissipative approximation of motion of the scale relativity in its non-differentiable hydrodynamic version, it is shown that the separation processes imply both what we call the “relevant dimensions” of the solid components from heterogeneous mixtures and their positions in the fluid–solid mixture velocity field. The above-mentioned phenomena occur in the turbulence regimes of the fluid–solid mixtures. In the scale relativity dispersive approximation of motion, by means of space–time cnoidal oscillations modes of the fluid–mixture velocity field, it is shown that the separation process is controlled through the turbulence regimes of the fluid–solid mixtures. In such a situation three scenarios of transition to turbulence via chaos (quasi-periodicity, sub-harmonic bifurcations, and intermittences) are comparatively given from a theoretical and experimental point of view both for a plasma with complex structures (in the form of double layers), assimilated with fluid–solid mixtures.

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