Three-dimensional color-gradient lattice Boltzmann model for simulating droplet ringlike migration under an omnidirectional thermal gradient

Thermocapillary migration is a typical flow problem in Marangoni flows, and it is driven by a temperature gradient, which is widely encountered in many engineering and scientific applications. The temperature distribution is heterogeneous on the substrates in many practical applications, which causes that the temperature gradient is directionally unstable and the droplet migration direction is uncertain or omnidirectional. To investigate the migration behavior of a droplet under an omnidirectional thermal gradient, a three-dimensional color-gradient lattice Boltzmann model is applied in the present study. The capability of this model to simulate the interactions of the fluid and solid for a small contact angle is first verified. Then the migration behavior of droplet initially in the center of the substrate (highest temperature region) is studied, and the droplet ringlike migration is observed and analyzed. Next a systematic study of the droplet volume and wetting properties is conducted. Finally, the migration behavior of droplet initially away from the center of the substrate is investigated and compared with that in the center, and the influence of the offset distance is explored.