3.1.2 Mixing time in 24-DSW plate
Figure 2B shows the mixing time variation in the 24-DSW plate with varying shaker speed and four different fill volumes, ranging from 2 – 5 mL. From the graph, it is evident that mixing time was inversely proportional to shaker speed in the lower end range of shaker speeds investigated i.e. between 175 to 250 rpm. Within this range, mixing time was also reduced for smaller fill volumes. At the lowest shaker speed tested, mixing time for VL = 5 mL was approximately 4 times greater than that of 2 mL. For smaller fill volumes, mixing times are expected to be lower since there is a constant amount of energy being dissipated to a reduced volume, resulting in more turbulence and hence better circulation (Omar. Al Ramadhani, 2015). At shaker speeds greater than 250 rpm, the mixing process became very rapid with mixing times less than 10 s for all fill volumes evaluated.
For the same 24-DSW format, Li et al., 2020 reported an unexpected increase in mixing time in the higher speed range which was associated with a change in free surface dynamics in the well. The authors attribute this phenomenon to the very small shaking diameter (ds) used in their study (i.e. 3 mm). A similar increase in mixing time at higher shaker speeds was not observed in this work, perhaps due to the higher shaking diameter of 25 mm being used.
The mixing time results from this work were also compared against the scaling law proposed by Rodriguez et al., 2014 for orbitally shaken reactors (OSR’s) (Rodriguez, Anderlei, Micheletti, Yianneskis, & Ducci, 2014). A comparison between the two studies could be made since the same experimental technique and image processing methodology was used. In their study, Rodriguez et al ., 2014 demonstrated good correlation between two dimensionless parameters, mixing number (N.tm ) and Froude number ratio (Fr/Frc). From this, the power law relationship for scaling was derived as follows: N.tm = 100.7(Fr/Frc)-1.245 + 25. This relationship was found to best fit data from a wide range of operating conditions including reactors of different sizes (di = 8 – 13 cm) and orbital shaking diameters (ds = 15 – 50 mm). Li et al., 2020 assessed the applicability of the scaling law, however, the power law function over predicted the mixing numbers for the 24-DSW plate used in their study (Li, Ducci, & Micheletti, 2020). This was due to the very small orbital diameter used in which case the different fluid and mixing dynamics within the well meant that the Froude number ratio was not an effective scaling parameter. As the orbital diameter in this work was larger compared to Li et al., 2020, the applicability of the scaling law was re-assessed using the present data set. The mixing number curves for the 24-DSW plate from this study was plotted in Figure 3 and compared against the power law function. From the graph, all the mixing number curves showed good correlation with the power law function confirming its applicability as a scaling law for OSR’s of different sizes and geometries. Furthermore, it also demonstrates confidence in the accuracy of the mixing time values, given that mixing time was selected as the basis for scale-translation in this work.