Numerical Study On Droplet Dynamics With Marangoni Effect

Marangoni effect is referred to as a group of capillary phenomena induced by surface tension gradients.Such phenomena not only are widely seen in nature,but also play important roles in a lot of industrial applications,such as micro-fluidic chip,pharmacy,metallurgy and material purification.The aim of this study is to reveal the mechanisms of Marangoni effect in several flow cases,including delayed coalescence of miscible hydrophilic droplets,internal mass transfer of suspension droplets and morphology of self-rewetting droplets on a plate with temperature gradient.The major results and contributions are briefly given as follows:(1)We derived the governing equations for the numerical study of delayed coalescence of two miscible droplets in the framework of lubrication theory,taking account of the component transport equation and the solubility of the surface monolayer.This provides accurate concentration field for the calculation of tangential surface tension.Another contribution to the numerical modeling is to include the temperature equation and continuum surface tension model in the existing codes of our laboratory.(2)The early-stage delayed coalescence of miscible hydrophilic droplets was numerically studied.Due to the propagation of capillary waves on droplet surface and pinned contact line,capillary shock occurs in the droplet deformation.The inflow due to the Laplace pressure is much larger than the outflow due to the Marangoni effect,leading to the growth of the liquid bridge.On the other hand,the more significant the absorption rate,the slower the transportation of the surface concentration.This accounts for the limited effect of solubility on the threshold value of the delayed coalescence.(3)The mass transfer inside suspended droplets due to different temperatures was studied numerically.Through the observations of axis deformation and liquid bridge dynamics,three modes of coalescence named inertia,transition and viscous are found under different internal-outer viscous ratios.The velocity of the internal jet is studied as well,and the scaling laws in the inertial and viscous modes are derived and examined.By observing the long-term evolution of droplet centroid,the phenomenon of droplet moving towards the cooler side is found within a certain parameter range.From the point of view of the influence of jet velocity on the temperature field reversal,the theoretical explanation of the boundary of the phase diagram in direction reversal of centroid is given.(4)Through a 2D numerical simulation,the motion of self-rewetting droplets on a plate with a temperature gradient is studied.Two typical modes are discovered,named displacement and stretching.Through a static analysis,the theoretical explanation of the boundary of the phase diagram of the two modes is derived.Moreover,a static balance mode is also discovered in the hydrophilic cases,once given a tiny displacement,the droplet will oscillate near the symmetry plane.