Flow, suspension, and mixing dynamics in DASGIP bioreactors: Part 1

Funding information Engineering and Physical Sciences Research Council, Grant/Award Number: EP/ L015218/1; Future Vaccine Research Manufacturing Hub (Vax-Hub), Grant/Award Number: EP/N509577/1 Abstract The bioreactor flow environment has a significant impact on process performance, especially in stem cell cultures. The work of Correia et al found intermittent agitation modes to improve induced pluripotent stem cell (iPSC)-cardiomyocyte differentiation yields; however, to date, the impact within the flow has not been fully characterized. This work aims to characterize the flow dynamics occurring within a commercially available DASGIP bioreactor, equipped with a two-blade paddle impeller, operating under different agitation modes and for two bottom geometries. The paddle impeller configuration generated an axial flow profile due to a large impeller D/T and blade confinement with the bioreactor wall. The application of intermittent agitation was shown to induce two transient spikes in flow velocity and shear stress, the amplification of which increased with dwell duration. Marginally increasing the dwell duration was shown previously to increase differentiation yields, therefore it can be stipulated that introduction of these spikes was favorable toward cardiogenic differentiation.

reactor wall with the upper vortex exhibiting a slight inclination when D/T and C/T = 0.33. [13][14][15] Axial pitched blade turbine impellers generate a single and inclined trailing vortex behind each turbine blade with axial velocities up to 0.45-0.55V tip. [16][17][18] Minimal radial displacement and downward/upward axial displacement is exhibited, depending upon whether agitation is in down-or up-pumping mode. 18 Of particular interest in this work is the impact of the impeller to tank diameter ratio, D/T, upon the flow, in addition to the difference between baffled and unbaffled bioreactor configurations. The study of Ramsay et al 19  achieved. Other studies also reported this effect. 24,25 In addition to the physical configuration of a bioreactor, the rotational speed and agitation strategy greatly affect cell behavior, the flow, mixing, and suspension dynamics. Ismadi et al 26   This flow characterization is essential to lay the foundations for a better understanding of stem cell differentiation processes and identify novel agitation strategies for optimal process control and performance.

| Particle image velocimetry and data processing
A green diode laser, with an output power rating of 300 mW and wavelength, λ = 532 nm, was used for the two-dimensional The cylindrical coordinate reference system (r, θ, z) shown in Figure 1c was employed, where the origin is positioned at the center of the reactor base and anticlockwise impeller rotation, when the system is seen from above, is considered positive. It should be noted that in some of the results reported in this work, reference is made to negative radial coordinates, r, which, although not consistent with the cylindrical coordinate system employed, are used to discriminate between the left and right side of the reactor about the impeller axis.
The origin of the phase angular coordinate, φ, is set on the leading blade of the impeller, φ = 0 .
The maximum local shear rate, γ max , in the vertical plane was obtained from the principal components of the strain rate tensor. 36,37 In continuous agitation modes, phase-resolved measurements were synchronized with the impeller position using the servo motor encoder. The impeller encoder signal is given to a timing box which synchronizes the camera trigger with the desired impeller position.

| RESULTS AND DISCUSSION
The following section is divided into four parts; Sections 3.1 and 3.  A quantitative comparison of the axial circulation loops, emanating from and returning to the impeller region, can be obtained from

| Trailing vortices characterization-continuous agitation
To visualize the trailing vortices generated in the impeller wake, 2D phase-resolved contour maps of the vorticity are vertically stacked for 24 phase angles, φ = 0-345 , at N = 90 rpm in Figure 8a where ω i and X i are the vorticity and axial or radial coordinates of any point within the stated iso-vorticity boundaries. Figure 9 shows the

| Flow dynamics during intermittent agitation
The second part of this study sought to investigate the impact on the local flow of intermittent agitation modes within the flat bottom configuration. A range of dwell durations were investigated to observe the transient occurring before, during and after the dwell phase such as to quantify changes in flow dynamics. Similar to Figure 9a, the axial coordinate of the vortex center is plotted in Figure 10 for both the continuous (red) and intermittent (purple) agitation modes (N = 90 rpm). For the continuous agitation mode, the data reported in Figure 10 correspond to one impeller revolution (θ = 0-360 ) and were obtained with the phase-resolved analysis described in the previous section. For the intermittent agitation condition, the impeller is stationary, and therefore the tangential coordinate on the abscissa was estimated by multiplying the hypothetical rotational speed of the impeller, if it had kept rotating, and the time elapsed from the stoppage of the impeller. It is interesting to note the good agreement between the two plots, which suggests that despite the impeller stoppage the fluid carries enough inertia to maintain the local flow and vortex dynamics also for intermittent agitation. The vortex strength decays only after the first revolution as vorticity goes below the selected threshold to determine its vortex center (Equation (1)).
To better observe the evolution of the flow during the transient in intermittent agitation modes, space averages were calculated according to Equation (2): where A is the measurement area and X * represents either the velocity magnitude or the shear rate. Figure 11 shows the space-averaged velocity magnitude,  increasing spike is observed to plateau when a fully static system is reached, between T dwell = 12,000-30,000 ms. It is apparent that the shorter dwell conditions maintain some degree of inertia in the flow.
There is less acceleration as the flow is already moving; therefore, the highest amplification of the spike is observed when lower velocities or a static flow is present in the reactor before the restart in impeller rotation. After approximately four revolutions, this spike is shown to drop back to the steady state, representing continuous impeller rotation (contour map #6). It is worth noting that Nt = 0-5 are not shown due to the spike from the previous dwell phase.
Of great interest in cell culture applications is the shear forces imparted within a bioreactor, especially during intermittent agitation.
To observe the overall impact of the transient between different dwell times, space-averaged results for shear rate, γ Ã max =πN , are presented in Figure 12. In this case, the space averages were carried over two different areas: the impeller region (z/H L ≤ 0.45) and the bulk region (z/H L > 0.45). As before, Figure 12 shows a nearly constant "steady-state" nondimensional shear rate, occurring during continuous impeller rotation (contour map #1, hγ max i/πN = 0-0.12) before a small spike is observed with the start of the dwell phase (contour map #2).
Rapid decay in the shear rate is observed (contour map #3) with the increased number of missed revolutions until the flow is considered fully static and the shear rate is negligible (contour map #4). It is interesting to observe the similar profiles between the impeller and bulk regions, with higher shear rates overall within the impeller region.
The initial spike with the stop in impeller motion (contour map #2) is slightly more prominent in the bulk region (+5% the steady-state shear value) and a second more intense spike is again observed during the transient with the restart in impeller motion (contour map #5). It is now interesting to observe for longer dwell durations (T dwell ≥ 12,000 ms) the space-averaged shear rate considered in the impeller region reduces in intensity and does not plateau, as previously seen in Figure 11. This is due to the fully static flow before the impeller restart resulting in a more intense circulation loop, which is distributed across the whole plane. Observing the bulk region in Figure 12, a small delay from the impeller restart to the peak space-averaged shear rate can be observed as the recirculation  26