Mean mass transport in an orbitally shaken cylindrical container

Abstract

A cylindrical container partially filled with a liquid in orbital shaking motion, i.e. in circular translation with fixed orientation with respect to an inertial frame of reference, generates, along with a rotating sloshing wave, a mean flow rotating in the same direction as the wave. Here we investigate experimentally the structure and the scaling of the wave flow and the Lagrangian mean flow in the weakly nonlinear regime, for small forcing amplitude and for forcing frequency far from the resonance, using conventional and stroboscopic particle image velocimetry. The Lagrangian mean flow is composed of a strong global rotation near the center and a non trivial pattern of poloidal recirculation vortices of weaker amplitude, mostly active near the contact line. The global rotation near the center is robust with respect to changes in viscosity and forcing frequency, and its amplitude compares well with the predicted Stokes drift for an inviscid rotating sloshing wave. On the other hand, the spatial structure of the poloidal vortices show strong variation with viscosity and forcing frequency, suggesting that it results from the streaming flow driven by the complex oscillatory boundary layers near the contact line.arXiv:1702.04128v2 [physics.flu-dyn]

Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion

“…Substituting (19) and (20) into (7) and (8) and gathering the first Fourier harmonics lead to the secular system of nonlinear algebraic equations…”

“…5 in [1]). The theory fails at the primary resonance zone where it gives infinite wave amplitude but experiments [15][16][17][18][19] exhibit the hard-spring type wave-amplitude response. An integral effect of the wave breaking phenomenon may be accounted for by introducing the associated damping [21,22].…”

“…The phenomena (i) and (ii) were experimentally observed in [7,[14][15][16][17][18][19]. Practical interests in bioreactors [15][16][17][18][19] recently motivated some authors to conduct more systematic model tests [16,17,19].…”

“…However, [6] did not either establish a link with actual applications, where these threedimensional forcing types appear, or validate the obtained mathematical results by experimental data. Bearing in mind sloshing in bioreactor [15][16][17][18][19], the present paper modifies the Narimanov-Moiseev theory to study swirling-type resonant waves due to the rotary forcing.…”

Measurement of interfacial wave dynamics in orbitally shaken cylindrical containers using ultrasound pulse-echo techniques

“…These bioreactors are of particular interest for fluid dynamists since they offer a high potential for optimization in terms of mixing efficiency and power consumption. Various properties as the influence of different characterized wave and flow regimes to the mixing efficiency, the mass transport or shear stress distributions were numerically and experimentally studied by Weheliye et al (2012); Ducci and Weheliye (2014); Reclari et al (2014); Bouvard et al (2017); Weheliye et al (2018); Alpresa et al (2018a,b). Some of their findings can be directly transferred to interfacial wave systems, as we will discuss in Sect.…”