Study Of Multiphase Contact Lines Model And Compound Droplets Dynamics

Multiphase flows with moving contact lines widely exist in daily lives and industrial applications.In this thesis,we develop moving contact line model involving ternary fluid flows.Investigate the dynamics of the compound droplet in shear flow,and the regime transition of compound droplets on a substrate through numerical simulation and theoretical analysis.The results and conclusions are briefly given as follows:(1)We developed a geometrical formulation of moving contact line model in the p-resence ternary fluid flows.Displacement of ternary fluid flows on the substrate leads to the occurrence of moving contact point,at which three moving contac-t lines meet.The geometrical moving contact line model replaces the jump in contact angles at the contact point by a relatively smooth transition of contact angle.Combining the ternary-fluid model and Navicr-Stokes solver,wc can sim-ulate ternary flows with moving contact lines.We simulated the spreading of a compound droplet on a substrate and validated the numerical results of the drop shape at equilibrium by comparing against the analytical solution.Finally,we applied the model to simulate complex mutiphase flow problem such as impact-ing of a circular cylinder into a pool of two layers of difcrent fluids,sliding of a three-dimensional compound droplet in shear flows and droplets engulfing.(2)Based on the numerical simulation of Janus compound droplets in shear flows,thc effect of interface dcformation on the angular velocity of compound droplets was investigated.Three modes,namely break-up,stretching and rotation were observed,and can be characterized by the distance between the centers of the component droplets,the distance between the three-phase points,and the defor-mation parameters.The deformation and angular speed of compound droplets were found to periodically change with the rotation angle,and significance of drop deformation increased with the shear force.The average rotation speed of the compound droplet was dominated by the shear force for small Ca(0iCai0.02).while dominated by the interface deformation for large Ca(0.liCai1).(3)The configurations and the regime transitions for compound droplets on a plate were studied through theoretical analysis and numerical simulations.The drop shape at equilibrium and the respective parametric phase diagram were obtained by solving the governing equation based on the balance between the surface ten-sion and the pressure.There are two critical conditions for the regime transition.One is the geometric condition at which the interface topology changes,and the other is the minimization of free energy.Numerical simulations of the typical regime transformation have been performed,and show the effect of inertia and capillary waves on the transition process.(4)A foam model was proposed based on the diffuse interface model,in which each bubble was represented by the respective phase,and the weighted wetting bound-ary condition was implemental to account for the contact of the foam with the solid wall.Because the liquid film scale is much smaller than the foam size,the mass of the thin liquid film and the liquid displacement in the film can be neglect-ed except for the surface tension.Similarly,the rupture time of the film is much shorter than the foam rearrangement time,the rupture process of the film is also ignored.Instead,the rupture was triggered artificially.The algorithm was veri-fied by numerical simulation of the foam dynamics.Such as the free development of foam in space and the foam rearrangement on a solid wall.