In this study,a theoretical model was established for predicting the equilibrium shape of the droplet on flat and spherical surfaces.The theoretical equilibrium shape of heavy droplets could be obtained once contact a...In this study,a theoretical model was established for predicting the equilibrium shape of the droplet on flat and spherical surfaces.The theoretical equilibrium shape of heavy droplets could be obtained once contact angle and volume of droplets were given.It showed that the predictions of the theoretical flat model were in good agreement with the shape obtained by Surface Evolver when the contact angle is below 120 and the droplet size is on the order of capillary length.This available range will decrease and increase when the heavy droplet is on convex and concave spherical surface,respectively,in contrast to that on flat surface.The available range will decrease more for higher curvature of convex spherical surfaces.展开更多
Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given nu...Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10902015)the Research Funds for the Doctoral Program of Higher Education of China (Grant No. 20091101120001)
文摘In this study,a theoretical model was established for predicting the equilibrium shape of the droplet on flat and spherical surfaces.The theoretical equilibrium shape of heavy droplets could be obtained once contact angle and volume of droplets were given.It showed that the predictions of the theoretical flat model were in good agreement with the shape obtained by Surface Evolver when the contact angle is below 120 and the droplet size is on the order of capillary length.This available range will decrease and increase when the heavy droplet is on convex and concave spherical surface,respectively,in contrast to that on flat surface.The available range will decrease more for higher curvature of convex spherical surfaces.
文摘Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.
