| Summary: | 博士 === 國立中央大學 === 機械工程研究所 === 99 === Recently, the migration of a liquid droplet on a horizontal solid surface has attracted widespread attention from many researchers and engineers because of its promising prospective in a variety of applications in biology, chemistry, and industry. In this dissertation, a proper computational model is developed for investigating the transient migration of a liquid droplet on a horizontal solid surface subjected to uniform temperature gradients. Numerical calculations are carried out by solving the Navier - Stokes equations coupled with the energy equation through the finite element method (FEM). The conservative level set method, the arbitrary Lagrangian Eulerian (ALE) method, and the continuum surface force (CSF) method are employed to treat the movement and deformation of the droplet/air interface and the surface tension force during the motion process. Some physical properties of fluids dependent on temperature are also considered.
The study indicates that when a liquid droplet is of small size, two asymmetric thermocapillary vortices are generated inside the droplet. The thermocapillary vortex on the hot side is always larger in size than that appearing on the cold one. The net momentum of the thermocapillary convection inside droplet pushes the droplet moves from the larger vortex (hot side) to the smaller one (cold side). The variation of the size of the thermocapillary vortex during the movement causes the speed of the droplet to initially increase and then decrease slowly until approaching a constant value. A higher imposed temperature gradient leads the droplet velocity to reach the maximal value earlier and have a higher final speed. If the static contact angle of the droplet is less (or higher) than 90 degrees, the droplet speed is lower (or higher) since the net thermocapillary momentum in the horizontal direction is diminished (or enhanced) by the presence of capillary force. The lower slip length leads to the smaller droplet speed. In addition, the quasisteady migration speed of a small droplet is linearly proportional to its size due to the stronger net thermocapillary momentum. The effect of gravity is insignificant and the thermocapillary convection is dominated. The computational model is verified by comparing to the previous experimental results.
When the droplet turns into larger, the influence of gravity becomes important. The combined thermocapillary and buoyancy force driven convection produce complex dynamic behavior of fluid motion inside the droplet. In the middle size regime, the quasisteady migration speed of the droplet reaches a maximum, but this is gradually reduced as the droplet size increases due to the suppression of the net thermocapillary momentum by the buoyancy force. In the large droplet size regime, two pairs of convection vortices exist inside the droplet as a result of the appearance of the buoyancy-driven convection accompanying the thermocapillary convection. The quasisteady migration speed quickly diminishes, mainly due to the reduction of the net thermocapillary momentum from the stronger buoyancy convection. The droplet speed tendency is found to be a good agreement with the experimental results.
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