Mixing Time in Intermediate‐Sized Orbitally Shaken Reactors with Small Orbital Diameters

Abstract

Orbitally shaken reactors (OSR) are widely used in bioprocess development; however, a scaling law between large reactors, usually shaken in incubators at an orbital diameter of d o = 1.5-5 cm, and microwell plates, shaken in benchtop thermomixers at d o = 3 mm, is still missing. Here, the mixing time was measured in two reactors with the same volume but either cylindrical or square geometry for d o = 3 mm. For such a small d o , the acceleration mode to reach the final speed in the cylinder was found to greatly affect the free surface oscillations and thus the mixing time. The stepwise mode resulted in mixing times approximately six times smaller than in the direct mode. The natural frequency of the reactor, which is independent of d o , was found to be an effective scaling parameter for systems with small d o .

Study on mixing characteristics in shaken microwell systems

“…It is evident that an increase in mixing time was resulted from a decrease in free surface height and vice versa. A similar phenomenon was also noticed in the work of Li et al [30] where a direct acceleration mode affected the free surface oscillations and thus the mixing time in an intermediate-sized cylindrical reactor when shaken in ThermoMixer. The reduced free surface oscillation in the square microwell is independent of acceleration modes, however, the longer mixing time at high speed range was also due to a significantly reduced free surface height.…”

“…300 -400 rpm), while no significant change in mixing time observed for shaken speeds greater than 400 rpm and the mixing process became very rapid afterwards. It should also be noticed that contrary to the work of Li et al [30], no difference in mixing time was identified in the cylindrical microwell when different acceleration modes was adopted.…”

“…The viscosity of the glycerol/water aqueous solution was determined based on the method proposed by Cheng [33]. The image processing method used in this work was the same as that used by Rodriguez et al [29] and Li et al [30] who measured mixing time in larger OSRs, thus allowing a more reliable and objective comparison of mixing time across different reactor scales.…”

“…They also demonstrated that the F r/F r cr is a useful parameter in scaling up/down between different reactor systems, where F r cr is the critical Froude number based on the rotational speed associated to the flow transition. Li et al [30] extended the mixing dynamics study to intermediate-sized OSRs for cylindrical and square geometries (d i = 35.4 and 40.0 mm, respectively) shaken in the Eppendorf ThermoMixer C with a significantly reduced orbital diameter of 3 mm, in an effort to assess the validity of scaling law identified in [29] in smaller OSRs. The acceleration mode to achieve the final shaken speed in the cylindrical reactor was found to greatly affect the mixing time due to difference in free surface oscillations and a new scaling parameter based on the natural frequency of the reactor was suggested as it was demonstrated to be more effective for shaken systems with very small d o .…”

“…It is evident in Table 1 that mixing time quantification has been conducted by a number of researchers, however, the vast majority of them focused on Erlenmeyer flasks and lab-scale cylindrical reactors. Despite the wide use of microwell plates in bioprocess development, the mixing process in microwell plates was only considered by two studies [31,23] [29] and Li et al [30] and aims at providing a thorough understanding of the mixing process induced by orbital shaking motion in microwell plates. From this perspective, mixing time was measured in two microwells (d i =17.1 and 15.6 mm, respectively) with square and cylindrical geometries, which are mimics of commercially-available microtitre plates, by means of DISMT technique.…”