Wang Lei, He Kun, Wang Huili
School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
School of Mathematical and Computer Sciences, Wuhan Textile University, Wuhan 430200, China.
Phys Rev E. 2023 Nov;108(5-2):055306. doi: 10.1103/PhysRevE.108.055306.
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.
本文提出了一种简单且准确的格子玻尔兹曼模型来模拟热毛细流动，该模型能够处理热力学参数之间的差异。在这个模型中，利用两个格子玻尔兹曼方程来求解守恒的艾伦 - 卡恩方程和不可压缩的纳维 - 斯托克斯方程，同时使用另一个格子玻尔兹曼方程来求解温度场，其中碰撞项经过精心设计，以纳入热力学参数差异的影响。与先前用于热毛细流动的格子玻尔兹曼模型相比，当前模型最显著的特点是，在当前热格子玻尔兹曼方程中使用的外力项不需要计算热容或序参量的空间导数，这使得该方案更加直接，并能够保留格子玻尔兹曼方法的主要优点。首先通过考虑在具有两种叠加平面流体的加热微通道中的热毛细流动来验证所开发的模型。然后用它来模拟二维可变形液滴的热毛细迁移，当马兰戈尼数接近零时，其精度与理论预测一致。最后，我们对二维通道中两个顽固气泡的运动进行了数值研究，其中假设表面张力与温度之间的关系为抛物线函数。可以观察到，由于惯性和热效应之间的竞争，气泡可以逆着液体的整体运动方向移动，并朝着表面张力低的区域移动。
