Mixing at the microscale: Power input in shaken microtiter plates

Power input and local energy dissipation are crucial parameters for the engineering characterization of mixing and fluid dynamics at the microscale. Since hydrodynamic stress is solely dependent on the maximum power input, we adapted the clay/polymer method to obtain flock destruction kinetics in six-, 24-, and 96-well microtiter plates on orbital shakers. We also determined the specific power input using calorimetry and found that the power input is at the same order of magnitude for the six- and 96-well plates and the laboratory-scale stirred tank reactor, with 40 to 90 W/m³ (Re' = 180 to 440), 40 to 140 W/m3 (Re' = 320 to 640), and 30 to 50 W/m³ (Re = 4000 to 8500), respectively. All of these values are significantly below 450 to 2100 W/m³ determined for the pilot-scale reactor. The hydrodynamic stress differs significantly between the different formats of MTPs, as the 96-well plates showed very low shear stress on the shaker with a shaking amplitude of 3 mm. Thus, the transfer of mixing conditions from the microtiter plate to small-scale and pilot-scale reactors must be undertaken with care. Our findings, especially the power input determined by the calorimetric method, show that the hydrodynamic conditions in laboratory- and pilot-scale reactors cannot be reached.