A viewpoint on the dynamics of bubble formation from a submerged nozzle

Asymmetric Bubble Formation at Rectangular Orifices

“…Figure illustrates the dependence of the experimentally measured ( V d * – 1 – ln V d * ) and that predicted by eq on We . Past work has recommended that the critical Weber number We c that distinguishes the quasi-static regime and dynamic regime is at the order of O (10 –3 ), which is similar to the We c that we calculated based on the experimentally observed critical flow rate of Q c ≈ 2 mL/min. We found that eq describes the trends well and captures the evolution of the experimental measured ( V d * – 1 – ln V d * ) as a function of We in the dynamic regime ( We > We c ).…”

“…To further quantify the bubble detachment diameter d d in the dynamic regime, where the dynamic force related to the gas flow rate plays an important role, we need to introduce these relevant forces into the model. The majority of previous studies have correlated the departing bubble size in the dynamic regime with dimensional parameters, which lack physical meaning and have difficulty scaling to different sizes and time scales. − Dimensionless force balance analysis shows that, the dominant forces determining the bubble detachment size in dynamic regimes include inertial force, virtual mass force, buoyant force, and surface tension force, while the viscous forces can be neglected in comparison. Based on the argument that the expansion stage follows the two-stage model, , the force balance equation can be finally deduced to the following equation, predicting the bubble size in the dynamic regimes as (detailed analyses and derivation can be found in the Supporting Information)­ where V d * = ( d d / d s ) 3 is the dimensionless bubble volume, and the quasi-static bubble diameter d s is predicted by eq .…”

“…In the dynamic regime, forces induced by gas flow such as inertial force, viscous force, and virtual mass force may need consideration in the force balance model when predicting bubble size. The majority of past studies have proposed empirical correlations relating the gas flow rate to the predicted bubble size. − Recently, Ma et al developed an expression for bubble size in the dynamic regime based on the Weber number, which captured the fundamental mechanisms of dynamic bubble formation and had good agreement with experiments. Furthermore, bubble formation has been extensively studied with regard to the influence of orifice wettability, , fluid properties, liquid column height above the orifice, and contaminants …”

Process Optimization for the Continuous Production of a Gastroretentive Dosage Form Based on Melt Foaming

“…We hypothesize that a bubble plug formed around the dispersing tool at a higher range of parameters, due to larger detached bubbles. Ji Ma et al published that the higher gas injection velocity increases the bubble detaching volume with a non-linear relationship [29]. The formation of bigger bubbles may cause a gas plug around the agitator causing decreased gas dispersion efficiency, which was reflected on the three-dimensional illustration of the three-factorial experimental design.…”