Annular Geoinspired Soft Mixer

A geoinspired soft mixer with application to bladeless bioreactors is studied. It is fitted with an internal cylinder in order to shine light within the reactors, in order to grow microalgae (dinoflagellates), when the concentration of cells is large (and hence the optical penetration depth is small). This mixer is an evolution of the cylindrical soft mixer (Meunier (2020), J. Fluid Mech. 903, A15), inspired by the precession of the Earth. It consists of an annular cavity rotating around its axis and is tilted from the vertical. The base flow is forced by the free surface to a global inertial flow (Kelvin modes). When the height of fluid is equal to a multiple of a half-wavelength, there is a resonance of the base flow. At the resonance the amplitude of the base flow is saturated by Ekman pumping, with a scaling proportional to the inverse of the square root of the Ekman number. Furthermore, for sufficiently large tilt angles and small Ekman numbers, the base flow triggers a parametric triadic instability involving interaction with two additional Kelvin modes. This instability promotes an efficient mixing within the annulus, with a shear rate of the order of 50% the angular velocity. However, this shear intensity is weaker than with a standard Rushton turbine classicaly used in stirred tank (approximately 5 times smaller), making of the annulus an appropriate bladeless mixer for large-scale bioreactors.