Lattice Boltzmann phase-?eld modeling of thermocapillary ?ows in a con?ned microchannel

摘要

To understand how thermocapillary forces manipulate the droplet motion in a con?ned microchannel, a lattice Boltzmann phase-?eld model is developed to simulate immiscible thermocapillary ?ows with consideration of ?uid-surface interactions. Based on our recent work of Liu et al., 2013 [54], an interfacial force of potential form is proposed to model the interfacial tension force and the Marangoni stress. As only the ?rst-order derivatives are involved, the proposed interfacial force is easily combined with the wetting boundary condition to account for ?uid-surface interactions. The hydrodynamic equations are solved using a multiple-relaxation-time algorithm with the interfacial force treated as a forcing term, while an additional convection-diffusion equation is solved by a passive-scalar approach to obtain the temperature ?eld, which is coupled to the interfacial tension by an equation of state. The model is ?rst validated against analytical solutions for the thermocapillary-driven convection in two superimposed ?uids at negligibly small Reynolds and Marangoni numbers. It is then demonstrated to produce the correct equilibrium contact angle for a binary ?uid with different viscosities when a constant interfacial tension is taken into account. Finally, we numerically simulate the thermocapillary ?ows for a micro?uidic droplet adhering on a solid wall and subject to a simple shear ?ow when a laser is applied to locally heat the ?uids, and investigate the in?uence of contact angle and ?uid viscosity ratio on the droplet dynamical behavior. The droplet motion can be completely blocked provided that the contact angle exceeds a threshold value, below which the droplet motion successively undergoes four stages: constant velocity, deceleration, acceleration, and approximately constant velocity. When the droplet motion is completely blocked, three steady vortices are clearly visible, and the droplet is fully ?lled by two counter-rotating vortices with the smaller one close to the external vortex. The thermocapillary convection is strengthened with decreasing viscosity ratio of the droplet to the carrier ?uid. For low viscosity ratios, the droplet motion is completely blocked and exhibits the similar behavior, but the structure of the internal vortices is more complicated at the lowest viscosity ratio. For high viscosity ratios, the droplet motion is partially blocked and undergoes a series of complex transitions, which can be explained as a result of the dynamically varying Marangoni forces.