Theoretical Analysis for the Elastic Instability of Thermocapillary Liquid Layers for Upper Convected Maxwell (UCM) Fluid
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摘要: 通过对上随体Maxwell（UCM）流体热毛细液层线性稳定性的研究分析，发现流场会发生弹性失稳.扰动的增长速率随波数的增加而增加.与牛顿流体不同，UCM流体不存在临界Marangoni数，当波数达到某一临界值时会出现不稳定的弹性扰动波.该临界波数随弹性数和Marangoni数的增加而减小，当弹性数趋近于0时，流体即变为牛顿流体，而相应的临界波数趋于无穷.不同波数及传播方向上，弹性波的波速相同，而其增长速率在特定方向上达到最大.能量分析表明弹性波的扰动能量来自扰动应力做功.Abstract: The linear stability of thermocapillary liquid layers for Upper Convected Maxwell (UCM) fluid is investigated. Elastic instability is found. The rate of perturbation growth increases with the wave number. For UCM fluid, the critical Marangoni number does not exist, which is different from Newtonian fluid. Instead, a critical wave number is found above which unstable elastic waves appear. The critical wave number decreases with elastic number and Marangoni number. When elastic number approaches zero, the fluid becomes Newtonian fluid with the critical wave number tending to infinity. The wave speed of elastic wave stays constant for different wave numbers and propagating directions. However, the growth rate reaches its maximum in a specific direction. Energy analysis shows the work done by perturbation stress contributes most to the perturbation energy of elastic wave.
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Key words:
- UCM fluid /
- Thermocapillary liquid layers /
- Linear stability /
- Elastic instability
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