Quantification and prediction of jet macro-mixing times in static microwell plates

Automated experimentation in microwell plate formats is widely used in high throughput drug discovery. Such approaches are now being considered for the study of bioprocess unit operations in order to speed the delivery of new medicines to market. The generation of useful design data from microwell formats requires an understanding of the engineering environment within individual microwells. Rapid and efficient macro-mixing is crucial in this respect to ensure the generation of quantitative and reproducible data. In this study, we have developed a high-speed video technique for the accurate quantification of jet macro-mixing times in static microwell plates which also enables visualisation of jet formation and liquid flow patterns within wells. Mixing times have been determined using both the fixed and disposable tips of a Perkin Elmer MultiProbe II^TM liquid handling robot for a range of jet Reynolds numbers (Re_j=1000-3960) and liquid addition volumes . Three microwell geometries have been investigated; one that is identical to a single well from a standard 96-round well plate and two novel designs based upon theories of jet mixing (V_i=200 and ). For conditions where macro-mixing was complete within the lifespan of the jet, t₉₅ mixing times for the standard round well were in the range 0.033-0.121 s while for the larger of the two designed wells they were in the range 0.228-0.705 s. The rapid mixing times in the standard round well are a consequence of increased energy dissipation as the liquid jet impinges on the base of the well. For the two designed wells maximising the jet length to nozzle diameter ratio (X/d_i) is shown to promote the most efficient macro-mixing due to entrainment and circulation of the bulk liquid in the well. For low volume additions and short jet lifespans it is also shown that mixing times can be of the order of minutes. Finally, the t₉₅ results for each of the well geometries have been correlated to the conditions used for jet formation using a correlation of the form first proposed by Baldyga and co-workers Baldyga, J., Bourne, J.R., Dubuis, B., Etchells, A.W., Gholap, R.V., Zimmermann, B., 1995. Jet reactor scale-up for mixing controlled reactions. Chemical Engineering Research & Design 73, 497-502]. This enables good prediction of the experimentally determined mixing times and estimation of the minimum liquid addition volume (V_Crit) that will ensure rapid and efficient macro-mixing. The correlation therefore enables automation users to optimise or control macro-mixing times in microwell experiments.