Classification and Prediction of Dripping Drop Size for a Wide Range of Nozzles by Wetting Diameter

In this study, dripping drops of water and glycerol/water mixtures from 83 nozzles (in the range of 0.065 mm ≤ D_o ≤ 40 mm and 0.043 mm ≤ D_i ≤ 35 mm, where D_o and D_i are the outer and inner diameters, respectively) were systematically investigated for four fluids, three wettable nozzle materials, and various liquid feeding rates under the simple dripping mode condition in an ambient gas, that is, air. It is important to point out that no single characteristic length scale mentioned in the literature can be used to satisfactorily predict all experimental data. A new characteristic parameter, that is, the wetting diameter ( D_w), has been introduced, and its usefulness in predicting the drop size by a simple relation in the whole nozzle range is shown for the first time. The critical wetting diameter ( D_c), which is related to the wettability (or advancing contact angle) of the dripping liquid and the nozzle material, is theoretically derived, and its dimensionless value ( D_c^*), normalized by the capillary length (λ), shows an excellent agreement with the experimental results. Five characteristic wetting regimes have been further classified. The D_c^* value is important for the dripping drop classification, that is, above which the regime is D_i^*-dependent and below which it is D_i^*-independent or mainly D_o^*-dependent. The characteristics and relationships of the wetting diameter with respect to the nozzle geometry and wettability for dripping drop formation are analyzed and compared in different regimes. A method to stably generate large dripping drops with diameters up to approximately 3 times the capillary length has also been demonstrated.