arbitrary lagrangian-eulerian method

Droplet evaporation coupled with gravity and surface tension on a wall with the radial temperature gradients is numerically studied with the arbitrary Lagrangian‒Eulerian method. The influence of the wall temperature distribution on the droplet evaporation process, which is less considered in the existing literature, is mainly discussed. The droplet temperature coefficient of the surface tension and the viscosity on the droplet profile evolution, flow, heat and mass transfer characteristic are also discussed. The results indicate that the droplets become flat first and then retract under the gravity and Marangoni convection during droplet evaporation. There are two high-velocity regions inside the evaporating droplet. One region is at the droplet axis, in which fluid flows to the wall from the droplet top. The other region is near the droplet surface, where fluid flows to the droplet top. There are turning points on the two sides of which the influence of wall temperature distribution on the ratio between the droplet height and the radius of the three-phase contact line (h/Rc), the velocity in the droplet and the surface temperature converts. All of them are larger before the turning point when the wall temperature slope is positive. After the turning point, these are reversed. For both h/Rc and average surface temperature, there is one turning point, which are t*=1.63×10-4 and t*=1.05×10-4, respectively. For maximum velocity and average velocity in droplet, there are two turning points, which are both t*=1.63×10-4 and t*=1.7×10-5. The droplet morphology changes more obviously when it is with a greater temperature coefficient of surface tension. Moreover, the turning point is delayed from t*=6.41×10-5 while α is 8 K/m to t*=7.91×10-5 while α is -8 K/m, which indicates that the negative wall temperature slope is beneficial to inhibit the Marangoni effect on droplet evaporation.