Mechanism of collision and drainage of liquid droplet around sphere placed within a hollow cylinder

It is attempted earnestly to elucidate the mechanism of collision and drainage of liquid mass around the spherical substrate suspended within the hollow cylinder using Gerris open-source code by employing Volume of Fluid (VOF) methodology. Various influencing parameters, namely, sphere-to-droplet diameter ratio $\left(D_s/D_o\right)$, Weber number$\left(We\right)$, Ohnesorge number $\left(Oh\right)$, and Bond number$\left(Bo\right)$ are employed to observe the drainage mechanism through the constricted path. The pattern of the interfacial morphology of droplet collision and drainage mechanism is presented using numerical contours. It is important to mention herein that the droplet undergoes several important stages like collision, cap formation, engulfment, drainage, and pinch-off. The passage between the sphere and the cylinder is sufficiently wider at a lower value of $D_s/D_o$ due to which the liquid mass is drained out completely without any hindrance. The drainage process becomes considerably faster at a higher $We$ compared to a lower $We$. In addition, the flow of liquid mass through the passage gets delayed at a greater $Oh$ than a lower $Oh$ assuming a given value of $We$ and $D_s/D_o$. The liquid drop requires less time to pass through the constricted path at lower $Bo$ for a given value of $D_s/D_o$ and $We$. We have also attempted to quantify the drainage of liquid volume passes through the passage, which is denoted as $\left(Q^{*}=Q/Q_o\right)$. One can notice the increasing pattern of $Q/Q_o$ with continuous progress of time stamp for all cases of $D_s/D_o$ for a fixed value of $We$.