Robust low-dimensional modelling of falling liquid films subject to variable wall heating
Robust low-dimensional modelling of falling liquid films subject to variable wall heating
复制标题
受可变壁加热影响的下降液膜的鲁棒低维建模
DOI：
10.1017/jfm.2019.580
复制
发表时间：
2019
影响因子：
3.7
通讯作者：
S. Kalliadasis
中科院分区：
文献类型：
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作者：
A. Thompson;S. Gomes;Fabian Denner;M. Dallaston;S. Kalliadasis
对于局部加热或时变加热下的液膜下降动力学，精确的低维模型对于涉及图案或控制的应用是必不可少的。然而，现有的模拟方法要么不能考虑基本的热力学性质，要么不能准确地捕捉平流和扩散对温度分布的影响。我们认为，表现最好的长波模型是那些将表面温度隐式地作为演化方程的解的模型，其中壁面温度单独（而不是其导数）作为源项出现。我们表明，对于平面和非均匀薄膜，可以通过扩展其自由表面值的温度场来合理地推导出该模型。我们在线性和非线性条件下对该模型进行了测试，并表明其预测结果与完全的Navier-Stokes计算结果在数量上非常一致，其中包括表面温度、内部温度场和温度诱发的马兰戈尼应力引起的表面位移。
Accurate low-dimensional models for the dynamics of falling liquid films subject to localized or time-varying heating are essential for applications that involve patterning or control. However, existing modelling methodologies either fail to respect fundamental thermodynamic properties or else do not accurately capture the effects of advection and diffusion on the temperature profile. We argue that the best-performing long-wave models are those that give the surface temperature implicitly as the solution of an evolution equation in which the wall temperature alone (and none of its derivatives) appears as a source term. We show that, for both flat and non-uniform films, such a model can be rationally derived by expanding the temperature field about its free-surface values. We test this model in linear and nonlinear regimes, and show that its predictions are in remarkable quantitative agreement with full Navier–Stokes calculations regarding the surface temperature, the internal temperature field and the surface displacement that would result from temperature-induced Marangoni stresses.