Improved phase-field-based lattice Boltzmann method for thermocapillary flow

Implementation of contact line motion based on the phase-field lattice Boltzmann method

This paper proposes a strategy to implement the free-energy-based wetting boundary condition within the phase-field lattice Boltzmann method. The greatest advantage of the proposed method is that the implementation of contact line motion can be significantly simplified while still maintaining good accuracy. For this purpose, the liquid-solid free energy is treated as a part of the chemical potential instead of the boundary condition, thus avoiding complicated interpolations with irregular geometries. Several numerical testing cases, including droplet spreading processes on the idea flat, inclined, and curved boundaries, are conducted, and the results demonstrate that the proposed method has good ability and satisfactory accuracy to simulate contact line motions.

Phase-field-based lattice Boltzmann model for simulating thermocapillary flows

This paper proposes a simple and accurate lattice Boltzmann model for simulating thermocapillary flows, which can deal with the contrast between thermodynamic parameters. In this model, two lattice Boltzmann equations are utilized to solve the conservative Allen-Cahn equation and the incompressible Navier-Stokes equations, while another lattice Boltzmann equation is used for solving the temperature field, where the collision term is delicately designed such that the influence of the contrast between thermodynamic parameters is incorporated. In contrast to the previous lattice Boltzmann models for thermocapillary flows, the most distinct feature of the current model is that the forcing term used in the present thermal lattice Boltzmann equation is not needed to calculate space derivatives of the heat capacitance or the order parameter, making the scheme much more straightforward and able to retain the main merits of the lattice Boltzmann method. The developed model is first validated by considering the thermocapillary flows in a heated microchannel with two superimposed planar fluids. It is then used to simulate the thermocapillary migration of a two-dimensional deformable droplet, and its accuracy is consistent with the theoretical prediction when the Marangoni number approaches zero. Finally, we numerically study the motion of two recalcitrant bubbles in a two-dimensional channel where the relationship between surface tension and temperature is assumed to be a parabolic function. It is observed that due to the competition between the inertia and thermal effects, the bubbles can move against the liquid's bulk motion and towards areas with low surface tension.

Simplified wetting boundary scheme in phase-field lattice Boltzmann model for wetting phenomena on curved boundaries

In this work, a simplified wetting boundary scheme in the phase-field lattice Boltzmann model is developed for wetting phenomena on curved boundaries. The proposed scheme combines the advantages of the fluid-solid interaction scheme and geometric scheme-easy to implement (no need to interpolate the values of parameters exactly on solid boundaries and find proper characteristic vectors), the value of contact angle can be directly prescribed, and no unphysical spurious mass layer-and avoids mass leakage. Different from previous works, the values of the order parameter gradient on fluid boundary nodes are directly determined according to the geometric formulation rather than indirectly regulated through the order parameters on ghost solid nodes (i.e., ghost contact-line region). For this purpose, two numerical approaches to evaluate the order parameter gradient on fluid boundary nodes are utilized, one with the prevalent isotropic central scheme and the other with a local gradient scheme that utilizes the distribution functions. The simplified wetting boundary schemes with both numerical approaches are validated and compared through several numerical simulations. The results demonstrate that the proposed model has good ability and satisfactory accuracy to simulate wetting phenomena on curved boundaries under large density ratios.