Orbitally shaken bioreactors—viscosity effects on flow characteristics

Abstract

Phase-resolved particle image velocimetry measurements were carried out to assess the flow dynamics occurring in orbitally shaken bioreactors of cylindrical geometry when working fluids of increasing viscosity are considered. Study of the phase-resolved flow characteristics allowed to built a Re-Fr map, where four quadrants associated to different flow regimes are identified: in-phase toroidal vortex (low Fr and high Re), out-of-phase precessional vortex (high Fr and high Re), in-phase single vortex (low Fr and low Re), out-of-phase counter-rotating toroidal vortex (high Fr and low Re). Turbulence levels are found to be significant only in the top right quadrant (high Fr and low Re) and scaling of the turbulent kinetic energy obtained with fluid of varying viscosity is obtained using the ratio of the operating Froude number to the critical Froude number associated to the mean flow transition, Fr=Fr c . Estimates of the mean flow strain deformation as well as of the flow dissipative scale are provided, while a comparison is made between the flow circulation times obtained for different regimes.

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

“…( / 1 ) * = 1.27 and 1.45, respectively). This means that damping in the model tests of [15,18] is basically associated with the boundary layer and bulk viscosity by (17). Adopting = 0.034 (the upper bound) in calculations with the constructed steady-state solution makes it possible to compare the theoretical wave elevations at the wall with the corresponding measurements in Figure 3.…”

“…Formulas (17) estimate the lower bound of the damping coefficient as ≥ 0.031 for the experimental tanks in [15,18] Mathematical Problems in Engineering filled with tap water. Using the experimentally established frequencies where a jump from the upper to lower branch occurs (point in Figure 2), the formula (34) makes it possible to estimate the upper bound for the damping coefficient as ≤ 0.034 (for the forcing amplitudes 0.01 and 0.02.…”

“…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.…”