A slow thermocapillary migration of a droplet at vanishingly small Reynolds and Marangoni numbers was theoretically investigated. A force on the droplet released in another liquid subjected to arbitrary configuration ...A slow thermocapillary migration of a droplet at vanishingly small Reynolds and Marangoni numbers was theoretically investigated. A force on the droplet released in another liquid subjected to arbitrary configuration of the gravitational field and an imposed thermal gradient for the case of constant liquid properties was derived using the general solutions given by Lamb. A solution to the migration was thereby obtained, which corresponds to the well-known YGB result as t →∞. In the case of variable physical properties with temperature, a nonlinear migration of the droplet was described by the dynamical equation of motion, and the numerical results were compared with available experimental data. The comparison exhibits a reasonable agreement between the theoretical prediction and the experimental results, which shows the dependence of physical properties on temperature is a primary cause of the continuous velocity variation in the thermocapillary droplet migration.展开更多
Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unne...Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unnecessary.Since the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface.Standard second-order S-L method is used for evolving the level-set convection equation.The implementation is simple,including on the block-structured adaptive mesh.The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase flows.In terms of accuracy it is comparable to the other existing methods.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No: 10372060).
文摘A slow thermocapillary migration of a droplet at vanishingly small Reynolds and Marangoni numbers was theoretically investigated. A force on the droplet released in another liquid subjected to arbitrary configuration of the gravitational field and an imposed thermal gradient for the case of constant liquid properties was derived using the general solutions given by Lamb. A solution to the migration was thereby obtained, which corresponds to the well-known YGB result as t →∞. In the case of variable physical properties with temperature, a nonlinear migration of the droplet was described by the dynamical equation of motion, and the numerical results were compared with available experimental data. The comparison exhibits a reasonable agreement between the theoretical prediction and the experimental results, which shows the dependence of physical properties on temperature is a primary cause of the continuous velocity variation in the thermocapillary droplet migration.
基金This work is partially supported by National natural science fund of China(No.91430213 and No.11571293)Hunan Provincial Innovation Foundation for Postgraduate(No.CX2015B208)。
文摘Semi-Lagrangian(S-L)methods have no CFL stability constraint,and are more stable than the Eulerian methods.In the literature,the S-L method for the levelset re-initialization equation was complicated,which may be unnecessary.Since the re-initialization procedure is auxiliary,we propose to use the first-order S-L scheme coupled with a projection technique to improve the accuracy at the grid points just adjacent to the interface.Standard second-order S-L method is used for evolving the level-set convection equation.The implementation is simple,including on the block-structured adaptive mesh.The efficiency of the S-L method is demonstrated by extensive numerical examples including passive convection of interfaces with corners/kinks/large deformation under given velocity fields,a geometrical flow with topological changes,simulations of bubble/droplet dynamics in incompressible twophase flows.In terms of accuracy it is comparable to the other existing methods.
