The dynamics of jet produced due to droplet

We numerically studied a moving droplet inside a quiescent liquid medium and studied the jet formation using Volume of fluid (VOF) method. When the droplet moves inside the liquid, it creates a lower-pressure zone at its rear side, which causes the surrounding liquid to rush toward the low-pressure zone creating a jet-like structure. Droplet moving with higher velocity creates mushroom-shaped jet. We found that the velocity profile of the jet matches well with the similarity solution for the axisymmetric free jet u/um = (1+η²)^-2, where η = σ` r/x is the similarity variable. Here, σ` is a constant, and um is the axial velocity along the centreline, i.e., u(x,y=0). Through capillary time scale and energy balance, we found that the jet velocity (V_j) = V (1-Oh)^-1/2, where Oh =μ / (ρ R σ)^1/2 , R and V the droplet radius and velocity, ρ, µ and σ indicating the liquid density, viscosity, and interfacial tension coefficient respectively. Within Oh ? 0.01, jet velocity is approximately equal to the droplet velocity. With an increase in Weber number (We = ρ V² R /σ) of the droplet, jet velocity gets increased, and the jet moves in the forward direction penetrating the droplet in a toroidal shape. We analytically predicted the critical Weber number needed for the jet to completely traverse the droplet from an energy analysis of Edgerton’s experiment of a bullet traversing an apple, and the critical Weber number required for the jet formation is ≈ 23, which matches well with our numerical findings. Here the jet velocity is almost equal to the initial droplet velocity, and the maximum jet height (H_j{max} ≈ 0.056 We) and maximum jet radius (R_j{max}≈ -0.036 We) scale linearly with the Weber number. From this linearity phenomenon, we can say that the jet becomes narrower and longer as the droplet velocity increases.