Numerical Study of droplet deformation and jet formation inside a Liquid Medium

We conducted a numerical investigation on droplet deformation within a liquid medium and explored jet formation using the Volume of Fluid (VOF) method. A droplet moving at a higher velocity results in the creation of a mushroom-shaped jet. Our observations revealed that the velocity profile of the jet aligns well with the similarity solution for the axisymmetric free jet, expressed as 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 (Vj) = 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. Furthermore, we analytically predicted the critical Weber number required for the jet to completely traverse the droplet based on an energy analysis of Edgerton's experiment involving a bullet traversing an apple. The critical Weber number for jet formation was found to be approximately 23, which aligns well with our numerical findings. In this case, the jet velocity nearly matches the initial droplet velocity. We also observed that the maximum jet height (Hjmax ≈ 0.056We) and maximum jet radius (Rjmax≈ -0.036We) scale linearly with the Weber number. This linearity phenomenon suggests that the jet becomes narrower and longer as the droplet velocity increases.