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Transient dynamics and structure of optimal excitations in thermocapillary spreading: Precursor film model

机译:热毛细管扩散中的瞬态动力学和最佳激发的结构:前体膜模型

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摘要

Linearized modal stability theory has shown that the thermocapillary spreading of a liquid film on a homogeneous, completely wetting surface can produce a rivulet instability at the advancing front due to formation of a capillary ridge. Mechanisms that drain fluid from the ridge can stabilize the flow against rivulet formation. Numerical predictions from this analysis for the film speed, shape, and most unstable wavelength agree remarkably well with experimental measurements even though the linearized disturbance operator is non-normal, which allows transient growth of perturbations. Our previous studies using a more generalized nonmodal stability analysis for contact lines models describing partially wetting liquids (i.e., either boundary slip or van der Waals interactions) have shown that the transient amplification is not sufficient to affect the predictions of eigenvalue analysis. In this work we complete examination of the various contact line models by studying the influence of an infinite and flat precursor film, which is the most commonly employed contact line model for completely wetting films. The maximum amplification of arbitrary disturbances and the optimal initial excitations that elicit the maximum growth over a specified time, which quantify the sensitivity of the film to perturbations of different structure, are presented. While the modal results for the three different contact line models are essentially indistinguishable, the transient dynamics and maximum possible amplification differ, which suggests different transient dynamics for completely and partially wetting films. These differences are explained by the structure of the computed optimal excitations, which provides further basis for understanding the agreement between experiment and predictions of conventional modal analysis.
机译:线性模态稳定性理论表明,在均匀,完全润湿的表面上,液膜的热毛细管扩散会由于形成的毛细脊而在前进的前沿产生小铆钉不稳定性。从山脊排出流体的机制可以稳定流动,防止小溪形成。即使线性化干扰算子是非正态的,通过这种分析得出的关于膜速度,形状和最不稳定波长的数值预测也与实验测量结果非常吻合,这使得扰动可以瞬时增长。我们以前的研究对描述部分润湿液体(即边界滑移或范德华相互作用)的接触线模型使用了更广义的非模态稳定性分析,结果表明瞬态放大不足以影响特征值分析的预测。在这项工作中,我们通过研究无限平坦的前体薄膜的影响来完成对各种接触线模型的检查,这是完全润湿膜的最常用接触线模型。给出了任意扰动的最大放大和在指定时间内引起最大增长的最佳初始激励,这些激励量化了薄膜对不同结构扰动的敏感性。尽管三种不同接触线模型的模态结果基本无法区分,但瞬态动力学和最大可能放大倍数却不同,这表明完全和部分润湿膜的瞬态动力学不同。这些差异由计算出的最佳激励的结构来解释,这为理解实验与常规模态分析的预测之间的一致性提供了进一步的基础。

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