Numerical Simulation Of Immiscible Droplet Head-on Collision Dynamics

The collisions of droplets are ubiquitous in nature and industrial applications.Despite of the success of previous studies in this field,they only considered the droplets of the same liquid.It is still a challenge to quantitatively investigate the collisions of immiscible droplets of different liquids.In this thesis,we use a ternary-fluid diffuse-interface method combined with adaptive mesh refinement,in order to investigate the symmetric and asymmetric dynamics in the head-on collisions of two immiscible droplets of equal size.The main results of this thesis include:(1)A ternary-fluid diffuse-interface method combined with adaptive mesh refine-ment and parallel computation is developed.An open-source software package,PARAMESH,is used to achieve block-based adaptive mesh refinement technique and parallel computation with MPI protocol.Our method has been well validat-ed by simulating a case of a rising bubble,which shows good convergence of our method,and the cases of compound droplet spreading on a fiat substrate and ternary flow in a capillary tube,where the simulations well agree with the theo-retical analysis.We also show the parallel performance by simulating the impact of a droplet on an immiscible liquid pool with various refinement levels and CPU cores.(2)The symmetric dynamics in the head-on collisions of two immiscible droplets are numerically investigated,in which the droplets evolve symmetrically about the colliding plane.Droplet inertia and interfaces are expected to play a crucial role in the interaction between the two droplets.Therefore,simulations are per-formed with various Weber number,We,and surface tension ratio,??1,i.e.the ratio of surface tension coefficient of the liquid-liquid to the liquid-gas interfaces.To describe the collision dynamics,we propose an equivalent surface tension ?*based on the analysis of the energy conservation and morphology of the colliding droplets.Using the equivalent surface tension ?*,we theoretically predict the film thickness,maximal spreading time and deformation of the colliding droplets.The theoretical predictions are in good agreement with the numerical results.Fur-thermore,two different flow regimes are observed in the simulations,namely the droplet adhesion regime and droplet separation regime.The transitions between the regimes are well predicted by using the equivalent surface tension ?*and the energy conservation laws.(3)The asymmetric dynamics in the head-on collisions of two immiscible droplets are numerically investigated,in which the droplets evolve asymmetrically about the colliding plane.By varying the Weber number,We,and surface tension ratio,??2,i.e.the ratio of surface tension coefficients of liquid-gas interfaces between two droplets and ambient gas,six different flow regimes are identified,includ-ing penetration regime,encapsulation regime,adhesion regime,rebound regime,pinch-off regime and reflexive separation regime.After the colliding of droplets,the maximal spreading diameters show the nonmonotonic increment as the sur-face tension ratio ??2 increasing.We explain the reason for the nonmonotonic phenomenon by comparing the droplet shapes and relative positions.The ratio of maximal spreading diameters of two droplets is able to be predicted by using the equivalent surface tension ?*.Our predictions agree well with the numerical results.Moreover,we find the scaling law of the maximal spreading time and diameter,which exists in both situations whether the droplet is embraced by an-other one or not.We also find the linear relationship between the contact area at maximal spreading with the surface tension ratio ??2.