Model prediction and numerical calculation of critical breakage volumes of pendant droplets

There is an inherent link between droplet volume (V) and the diameter of the dropper influencing its creation. This research study calculates the fundamental profile of a pendant droplet created by a dropper. We confirm that the internal force N applied during the crucial rupture phase of the droplet, equal to the sum of the Laplace pressure Plap, the atmospheric pressure Patm, and the gravitational force ρlVg (ρl is the density of the liquid) is vital. Further, by applying the Bashforth–Adams curve (B-A curve), determining the curvature radius b for droplets of different volumes, identifying the shape factor β at the critical point, and simultaneously determining the essential pipe diameter, two separate types of droplet rupture were found to exist based on the crucial pipe diameter: (1) at the convex section and (2) at the neck's thinnest area. For both droplet cases of the droplets, consistently adjust β′s size and graph the B-A curve to evaluate droplet rupture shapes under different diameters, examine the force scenarios, and confirm that the variance between the anticipated and actual droplet volumes is within a feasible range. At this point, β is crucial for determining the shape of droplets. The study's findings are in line with the experimental data on the varying tensions and densities of droplets, as determined by the micro-scale fluid dynamics in managing droplets.