Mean flow generation in orbital sloshing
It is common knowledge that prescribing an orbital motion to a glass of
wine generates a rotating gravity wave that comes along with a swirling
mean flow. This mean flow rotates in the direction of the wave and
recirculates poloidaly (radially and vertically), thus permanently pushing
new fluid to the surface where it aerates and releases the wine's
Precisely the same kind of orbital shaking is used on a more
professional level in bioreactors for the cultivation of biological cells.
There, the presence of the mean flow prevents sedimentation and ensures
efficient gas exchange, avoiding the damagingly high shear rates that
immersed stirrers would cause.
In order to decipher the origin of this mean flow
induced by a swirling wave, wave have performed experiments using silicon oil
(a fluid more viscous than wine - don't drink it), orbitally shaken in a cylinder.
We use stroboscopic Particle Image Velocimetry synchronized with the forcing frequency to
measure the (Lagrangian) mean flow.
The mean flow is composed of a strong axial rotation and weaker
recirculation vortices, mostly active near the contact line. Analysis
suggests that the axial rotation is dominated by the Stokes drift (a kinematic mass transport
mechanism in non-homogeneous wave fields), whereas the
poloidal recirculations are essentially driven by the dynamics of the oscillating boundary
layers (streaming flow).
Now, what if you swirl a glass of beer? This is another story...
- Mean mass transport in an orbitally shaken cylindrical container
J. Bouvard, W. Herreman and F. Moisy, subm. to Phys. Rev. Fluids (2017)