Kasumi Hiroki, Sides Paul J, Anderson John L
Mitsui Chemicals, 580-32 Nagaura, Sodegaura 299-0265, Japan.
J Colloid Interface Sci. 2004 Aug 1;276(1):239-47. doi: 10.1016/j.jcis.2004.03.051.
A temperature gradient normal to a planar wall produces two-dimensional motion and aggregation or separation of bubbles on the hot or cold wall, respectively. The origin of the motion is fluid convection driven by the thermal Marangoni stress on the surface of the bubbles. Previous theories for the dynamics of two or more bubbles have been based on an analysis of flow about a single bubble and the resulting convection that entrains its neighbors. Here we extend the theory by solving the quasi-steady equations for the temperature and velocity fields for two bubbles. The result is a quantitative model for the relative velocity between two bubbles as a function of both the distance between them and the gap between each bubble and the surface. Interactions between the bubbles strongly increase the approach velocity, which is counter-intuitive because the hydrodynamic resistance increases as the bubbles approach each other. An asymptotic analysis indicates the thermocapillary force bringing them together or pushing them apart is singular in the separation when the bubbles are close to each other. The two-bubble theory agrees reasonably well with the experimentally measured velocities of pairs of bubbles on hot or cold surfaces, though it slightly overestimates the velocities.
垂直于平面壁的温度梯度会分别在热壁或冷壁上产生二维运动以及气泡的聚集或分离。运动的起源是由气泡表面的热马兰戈尼应力驱动的流体对流。先前关于两个或更多气泡动力学的理论是基于对单个气泡周围流动以及由此产生的夹带其相邻气泡的对流的分析。在此，我们通过求解两个气泡的温度场和速度场的准稳态方程来扩展该理论。结果得到了一个定量模型，用于描述两个气泡之间的相对速度，该速度是它们之间距离以及每个气泡与表面之间间隙的函数。气泡之间的相互作用显著提高了靠近速度，这是违反直觉的，因为随着气泡彼此靠近，流体动力阻力会增加。渐近分析表明，当气泡彼此靠近时，使它们聚集或分开的热毛细力在间距上是奇异的。双气泡理论与在热表面或冷表面上成对气泡的实验测量速度相当吻合，尽管它略微高估了速度。
