Oscillatory instability and rupture in a thin melt film on its crystal subject to freezing and melting
Oscillatory instability and rupture in a thin melt film on its crystal subject to freezing and melting
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晶体上的薄熔膜在冻结和熔化过程中出现振荡不稳定性和破裂
DOI：
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发表时间：
2007
影响因子：
3.7
通讯作者：
L. Brush
中科院分区：
文献类型：
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作者：
M. Beerman;L. Brush
润滑理论用于推导一对耦合的强非线性偏微分方程，控制将纯熔体薄膜与其晶相和气体分开的界面的演化。自由熔体-气体（MG）界面根据局部应力状态而变形，而晶体-熔体（CM）界面只能通过冻结和熔化而变形。对受 MG 界面毛细管力、热毛细管力、熔化潜热、范德华吸引力、传热和凝固体积变化影响的静态均匀薄膜进行线性稳定性分析，揭示了静态和振荡不稳定性。温度梯度（通过增加气相温度）的作用是稳定薄膜。随着温度梯度减小，不稳定的开始是振荡的，并且处于唯一的、有限的波数。对于所有边缘稳定的非等温情况，不稳定性都是振荡的。密度高于熔体的晶体更稳定，而密度较低的晶体在施加温度梯度的情况下稳定性较差。完全非线性数值解表明，振荡不稳定性会因驻波或行波的增长而导致破裂。随着温度梯度的增加，破裂时间和破裂振荡次数增加。对于稳态线性不稳定的初始条件，由于薄膜变薄并接近破裂时热通量增加，CM 界面会从侵入的 MG 界面的尖端区域熔化而后退。较大振幅的扰动会增加给定波数下不稳定的最大允许温度，并减少固定温度和波数下的破裂时间。
Lubrication theory is used to derive a coupled pair of strongly nonlinear partial differential equations governing the evolution of interfaces separating a thin film of a pure melt from its crystalline phase and from a gas. The free melt–gas (MG) interface deforms in response to the local state of stress and the crystal–melt (CM) interface can deform by freezing and melting only. A linear stability analysis of a static, uniform film subject to the effects of MG interface capillary forces, thermocapillary forces, the latent heat of fusion, van der Waals attraction, heat transfer and solidification volume change effects, reveals stationary and oscillatory instabilities. The effect of a temperature gradient (by increasing the gas phase temperature) is to stabilize a film. As the temperature gradient is reduced, the onset of instability is oscillatory and is at a unique, finite wavenumber. Instability is oscillatory for all marginally stable, non-isothermal cases. Crystals with higher density than the melt are more stable, whereas crystals with lower density are less stable in the presence of an applied temperature gradient. Fully nonlinear numerical solutions show that oscillatory instabilities lead to rupture by growth of standing or travelling waves. Rupture times and the number of oscillations to rupture increase as the temperature gradient is increased. For stationary linearly unstable initial conditions, the CM interface retreats by melting away from the tip region of the encroaching MG interface due to a rise in the heat flux there as the film thins and nears rupture. Larger amplitude disturbances increase the maximum allowable temperature for instability, at a given wavenumber, and decrease the time to rupture at fixed temperature and wavenumber.